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Chapter 08 - Location Planning and Analysis
8-1
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
CHAPTER 08
LOCATION PLANNING AND ANALYSIS
Teaching Notes
Facility location refers to the location of a service or manufacturing facility with respect to customers,
suppliers, and other existing facilities such that it allows the company to gain a competitive and/or
strategic edge. In making a location decision, both tangible costs (e.g., cost of operating the facility; cost
of land (if it applies); cost of labor, taxes, and utilities; cost of inbound and outbound transportation) and
intangible costs (e.g., availability of qualified labor and labor climate) must be considered. Because the
location decision usually involves making a large capital investment, it not only affects the firm’s ability
to compete but also has long-term strategic implications. Therefore, in making the location decision, we
should consider issues related to marketing, production, transportation and other relevant costs as well as
the strategy of the organization. The importance of various factors in relation to the location decision will
vary between service and manufacturing organizations and from industry to industry as well.
Reading: Innovative MCI Unit Finds Culture Shock in Colorado Springs
1. The most severe fallouts from the move to Colorado were:
a. Numerous key executives and engineers, and hundreds of the division’s minority
population refused to relocate, or fled Colorado Springs soon after relocating.
b. The move isolated engineers from top management and from marketing colleagues at
headquarters, undermining collaboration.
c. The professionals whom Mr. Liebhaber hoped to recruit proved difficult and expensive to
woo to Colorado Springs.
d. Thousands of workers (more than expected) took advantage of the relocation package,
undercutting plans to recruit lower-cost employees in Colorado.
e. The move cost more than $200 million, far more than anticipated, and most of the
expected savings never materialized.
2. Mr. Liebhaber should have sought out more information by conducting surveys of workers,
managers, and engineers asking them for the following information: how likely they were to
move, ratings of factors that would affect their decision to move, ratings of factors that they
valued about their current work environment, and ratings about factors that they considered
important for quality of life issues. Mr. Liebhaber seems to have considered his own quality of
life and work issues only.
Reading: Site Selection Grows Up: Improved Tech Tools Make the Process
Faster, Better
1. Tech tools have improved the process of site selection by providing in-depth market research
analyzing traffic volumes, concentration of other retail businesses, and demographic data. In
addition, some of these tools provide aerial photographs of proposed sites and surrounding areas.
Some tools allow users to plug in the site characteristics criteria and a proposed location and then
push a button to receive output such as maps, reports, and models. Other tools provide market
optimization software that informs the user on how best to carve out territories, helping to
eliminate encroachment and cannibalization.
2. Franchisors also can use geoVue and other similar tools to analyze changes in performance,
demographics, or other factors that would warrant closing or relocating a facility.
Chapter 08 - Location Planning and Analysis
8-2
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Answers to Discussion and Review Questions
1. Location decisions can have an impact on access to markets, costs (including materials, labor,
rent, construction, and transportation), quality of work life (e.g., community-related factors), and
growth potential.
2. The fact that similar businesses are located widely underscores the futility of searching for that
“one best” location. However, it does not necessarily follow that little attention is needed in
finding a suitable location. Many organizations that have not been successful are no longer in
business (e.g., service stations in poor locations, motels bypassed by an expressway, and so on).
Moreover, others currently in operation might be much more profitable in another location. For
some businesses (e.g., restaurants) regional factors are not particularly significant, and even
community-related factors are of little importance. However, site-related factors are extremely
important. Similarly, there are numerous examples of firms that are less affected by community
or site factors than they are by regional factors (i.e., nearness to market, labor, or raw materials).
3. Important community factors include size of the community, public transportation, schools,
recreational facilities, libraries, restaurants, shopping centers, cultural and entertainment
selections, and so on.
4. Manufacturing and non-manufacturing organizations tend to approach location decisions in a
similar way, but the factors that are important to each tend to differ. Although both tend to take
costs and profits into consideration, manufacturing firms are often concerned with location of raw
materials, transportation costs, availability of energy and water, and similar factors. Non-
manufacturing firms often are more concerned with convenience, access to markets, traffic flow,
and the like.
5. Foreign locations may offer lower taxes, access to markets, availability of raw materials, lower
transportation costs (due to nearness to market), and lower labor costs than a comparable
domestic location. Potential drawbacks often relate to the political and economic stability of the
host country and attitudes of the populace towards a particular nation, industry, or firm.
6. Location rating, or factor rating, is a qualitative technique used to develop an overall composite
index for an alternative, which can be used to compare location alternatives. It involves
identifying relevant factors, assigning relative weights to the factors, and rating each alternative
with respect to the factors.
7. The first step is to decide on the criteria to use to evaluate location alternatives (e.g., cost, profits,
community service, etc.). The second step is to identify any important factors that will dominate
the decision. The third step is to develop location alternatives (country, general region, small
number of community alternatives, and site alternatives among the community alternatives). The
fourth step is to evaluate the alternatives and make a selection.
8. Locational breakeven analysis generally assumes the following:
a. Fixed costs are constant for the range of probable output.
b. Variable costs are linear for the range of probable output.
c. The level of output that will be required can be estimated within a narrow range.
d. A single product is involved.
9. Recent trends include the location of foreign manufacturing plants in the United States, having
smaller factories located close to markets, choosing nearby suppliers, low-cost labor is becoming
less of a factor in many industries, and advances in information technology make it less important
to have design, engineering, etc. close to the factory.
Taking Stock
1. Due to economies of scale, the centrally located large facility will be more efficient. The
scheduling and coordination between the large facility and suppliers or customers will be
Chapter 08 - Location Planning and Analysis
8-3
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
simplified. However, due to distance, transportation/distribution costs to or from the large facility
will be much higher than those costs would be when using several smaller dispersed facilities
instead. Having several smaller dispersed facilities will not only reduce the transportation cost but
also increase the flexibility of the firm in terms of being able to reduce distribution lead time, thus
resulting in faster deliveries or receipts of goods or merchandise.
2. Unlike the process design decision, the facility location decision is a macro decision and thus
requires the involvement of top-level management. The larger the facility, the higher the level of
involvement of the company personnel will be. In terms of various functions or departments
within the company, manufacturing (or operations), logistics and distribution, marketing, and
strategic planning must be involved. Depending on the type of facility considered, other groups
may also need to be included in making this important decision.
3. Due to the advancement of data mining and data warehousing, and the related improvements in
computers’ ability to store and exchange data, we can generate much more useful information to
make the facility location decision.
Critical Thinking Exercises
1. The company does have some social responsibility. Because the company employs such a large
percentage of the city’s workforce, its leaving is certain to have a major impact on town
businesses. It is likely that unless new sources of employment emerge, some residents may be
forced to move away, and many businesses may fail, or barely get by.
Thus, the company must weigh the projected benefits of the move against the actual and social
costs of the move. It also must factor in the primary reasons for the move. These might include
high taxes, adverse weather conditions, a shift in its markets, poor public relations, labor strife, an
aging facility that has to be replaced, an insufficient supply of essential labor skills, and a need to
be closer to a major customer.
2. Trade-offs involved would include:
a. The nature of current, and more importantly, the forecasted future demand.
b. Current demographics and the future expected changes in demographics for this area.
c. The nature and type of competition for this area. We will need to predict what our
competitors will be doing in the short-term as well as in the long-term.
d. We need to divide the area into several sub-areas and consider the advantages and
disadvantages of opening a store in each of the sub-areas.
e. What is the projected impact of the new location(s) on the sales of the existing locations?
If the demand is too low and we decide to open more than one site, we will have to experience
the cost of closing at least one of the existing locations and perhaps absorb the loss of sales in
our existing store. On the other hand, if the demand is higher than we expected, and we opened
up a store only on one site, we will have to consider the opportunity cost of lost sales and profit.
Chapter 08 - Location Planning and Analysis
8-4
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
3.
Options Pros Cons
Avoid such locations. Avoid the problem completely. Miss out on potential business.
Locate there and deal with it. Potential business. Need to make sure workers
know and abide by the policy.
Risk cheating and possible
consequences.
When in Rome … (assuming
“bribes” are more like “tips”
to service people).
Potential business. Probably a fine line between
tipping and bribing, very risky.
4. Student answers will vary. Some possible answers follow:
a. If a company located a manufacturing facility that creates heavy pollution adjacent to an
elementary school or a retirement home, this action would violate the Common Good
Principle.
b. If the CEO of a corporation accepted a bribe to locate a new facility in a city, this action
would violate the Virtue Principle.
c. If an executive asked a subordinate to alter some numbers in a factor-scoring model so that
the executive’s location choice came out on top, this action would violate the Rights Principle
and the Virtue Principle.
Solutions
1. Given: We have the following information shown below for two plant location alternatives:
Omaha Kansas City
R $185 $185
v $36 $47
Annual FC $1,200,000 $1,400,000
Expected annual
demand (units) (Q)
8,000 12,000
Determine the expected profits per year for each alternative:
Profit = Q(R – v) – FC
Omaha: 8,000($185 – $36) – $1,200,000 = -$8,000
Kansas City: 12,000($185 – $47) – $1,400,000 = $256,000
Conclusion: Kansas City would produce the greater profit.
Chapter 08 - Location Planning and Analysis
8-5
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
2. Given: We have the following information shown below for three potential locations for a new
outlet:
A B C
R $2.65 $2.65 $2.65
v $1.76 $1.76 $1.76
Monthly FC $5,000 $5,500 $5,800
a. Determine the monthly volume necessary at each location to realize a monthly profit of
$10,000 (round to 1 decimal).
𝑄 =
𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑒𝑑 𝑝𝑟𝑜𝑓𝑖𝑡+𝐹𝐶
𝑅−𝑣
Location A Volume:
𝑄 =
𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑒𝑑 𝑝𝑟𝑜𝑓𝑖𝑡+𝐹𝐶
𝑅−𝑣
=
10,000 + 5,000
2.65−1.76
= 16,853.9 𝑢𝑛𝑖𝑡𝑠
Location B Volume:
𝑄 =
𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑒𝑑 𝑝𝑟𝑜𝑓𝑖𝑡+𝐹𝐶
𝑅−𝑣
=
10,000 + 5,500
2.65−1.76
= 17,415.7 𝑢𝑛𝑖𝑡𝑠
Location C Volume:
𝑄 =
𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑒𝑑 𝑝𝑟𝑜𝑓𝑖𝑡+𝐹𝐶
𝑅−𝑣
=
10,000 + 5,800
2.65−1.76
= 17,752.8 𝑢𝑛𝑖𝑡𝑠
b. Determine the expected profits at each facility given the expected monthly volumes:
A = 21,000 per month, B = 22,000 per month, & C = 23,000 per month.
Profit = Q(R – v) – FC
Location A: 21,000($2.65 – $1.76) – $5,000 = $13,690 per month
Location B: 22,000($2.65 – $1.76) – $5,500 = $14,080 per month
Location C: 23,000($2.65 – $1.76) – $5,800 = $14,670 per month
Conclusion: Location C would yield the greatest profits.
Chapter 08 - Location Planning and Analysis
8-6
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
3. Given: There are two alternatives for which costs and revenue are listed below:
A B
R $17,000 $17,000
v $14,000 $13,000
Annual FC $800,000 $920,000
a. Find the volume at which the two locations have the same total cost (TC).
TC = FC + VC
TC = FC + (Q x v)
TC (Location A) = $800,000 + $14,000Q
TC (Location B) = $920,000 + $13,000Q
Set the two cost equations equal and solve for Q:
$800,000 + $14,000Q = $920,000 + $13,000Q
$14,000Q – $13,000Q = $920,000 – $800,000
$1,000Q = $120,000
Q = $120,000 / $1,000
Q = 120 units
b. Range over which A and B would be superior:
Location A has the lowest fixed costs; therefore, it is preferred at lower volumes.
Conclusion:
Location A Preferred: 0 < 120 units
Location B Preferred: > 120 units
4. Given: There are three alternatives for which costs are given below:
A (new) B (sub) C (expand)
v $500 $2,500 $1,000
Annual FC $250,000 --- $50,000
a. Step 1: Determine the total cost equation for each alternative.
TC = FC + VC
TC = FC + (Q x v)
A: TC = $250,000 + $500Q
B: TC = $2,500Q
C: TC = $50,000 + $1,000Q
Chapter 08 - Location Planning and Analysis
8-7
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Step 2: Graph the alternatives.
Step 3: Determine over what range each alternative is preferred.
Looking at the graph, we can tell that Alternative B is preferred over the lowest range,
Alternative C is preferred over the middle range, and Alternative A is preferred over the
highest range.
First, we find the indifference (break-even) point between Alternatives B & C by setting their
total cost equations equal to each other and solving for Q.
B: TC = $2,500Q
C: TC = $50,000 + $1,000Q
$2,500Q = $50,000 + $1,000Q
$2,500Q – $1,000Q = $50,000
$1,500Q = $50,000
Q = $50,000 / $1,500
Q = 33.33 units
Second, we find the indifference (break-even) point between Alternatives C & A by setting
their total cost equations equal to each other and solving for Q.
C: TC = $50,000 + $1,000Q
A: TC = $250,000 + $500Q
$50,000 + $1,000Q = $250,000 + $500Q
$1,000Q – $500Q = $250,000 – $50,000
$500Q = $200,000
Q = $200,000 / $500
Q = 400 units
A (new location)
C (expansion)
B (sub-
contract)
33.3 100 200 300 400
500
400
300
200
100
0
TC
($000)
B C A
[250]
[50]
No. of Boats/yr.
Chapter 08 - Location Planning and Analysis
8-8
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Conclusion:
Alternative B preferred: < 33.33 units
Alternative C preferred: > 33.33 units to < 400 units
Alternative A preferred: > 400 units
b. Expected volume of 150 boats:
Based on the graph, Alternative C would yield the lowest total cost (TC) at a volume of 150
boats.
c. Other factors that might be considered when deciding between the expansion and
subcontracting alternatives include subcontracting costs will be known with greater certainty,
subcontracting provides a secondary (backup) source of supply, and expansion offers more
control over operations.
5. Rework Problem 4b using this additional information: Alternative A (New Location) will have an
additional $4,000 in fixed costs per year. Alternative B (Subcontracting) will have $25,000 in
fixed costs per year. Alternative C (Expansion) will have an additional $70,000 in fixed costs per
year.
Step 1: Change the costs in the table.
A (new) B (sub) C (expand)
v $500 $2,500 $1,000
Annual FC $254,000 $25,000 $120,000
Step 2: Determine the total cost equation for each alternative.
TC = FC + VC
TC = FC + (Q x v)
A: TC = $254,000 + $500Q
B: TC = $25,000 + $2,500Q
C: TC = $120,000 + $1,000Q
Step 3: Find TC for 150 units.
A: TC = $254,000 + $500(150) = $329,000
B: TC = $25,000 + $2,500(150) = $400,000
C: TC = $120,000 + $1,000(150) = $270,000
Conclusion: Alternative C (Expand) would yield the lowest total cost for an expected volume of
150 boats.
Chapter 08 - Location Planning and Analysis
8-9
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
6. Given: Expected annual volume (Q) = 10,000 units. There are three lease alternatives for which
costs are given below:
Memphis Biloxi Birmingham
Lease building &
equipment $40,000 $60,000 $100,000
Transportation $50,000 $60,000 $25,000
v $8 $4 $5
Step 1: Determine fixed cost (FC) for each alternative & add FC to table.
FC = Lease cost + transportation cost.
Memphis Biloxi Birmingham
Lease building &
equipment $40,000 $60,000 $100,000
Transportation $50,000 $60,000 $25,000
Annual FC $90,000 $120,000 $125,000
v $8 $4 $5
Step 2: Determine the total cost equation for each alternative.
TC = FC + VC
TC = FC + (Q x v)
Memphis: $90,000 + $8Q
Biloxi: $120,000 + $4Q
Birmingham: $125,000 + $5Q
Step 3: Find TC for 10,000 units.
Memphis: $90,000 + $8(10,000) = $170,000
Biloxi: $120,000 + $4(10,000) = $160,000
Birmingham: $125,000 + $5(10,000) = $175,000
Conclusion: The Biloxi alternative yields the lowest total cost for an expected annual volume of
10,000 units.
Chapter 08 - Location Planning and Analysis
8-10
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
7. Given: There are two alternative shop locations for which costs are shown below:
City Outside
R $90 $90
v $30 $40
Monthly FC $7,000 $4,700
a. (1) Monthly profit for Q = 200 cars:
Step 1: Determine total profit equation for each alternative.
Total profit = Q(R – v) – FC
City: Q($90 – $30) – $7,000
Outside: Q($90 – $40) – $4,700
Step 2: Determine total profit for each alternative at the expected monthly volume.
City: 200($90 – $30) – $7,000 = $5,000
Outside: 200($90 – $40) – $4,700 = $5,300
Conclusion: Outside location yields the greatest profit if monthly demand is 200 cars.
(2) Monthly profit for Q = 300 cars:
City: 300($90 – $30) – $7,000 = $11,000
Outside: 300($90 – $40) – $4,700 = $10,300
Conclusion: City location yields the greatest profit if monthly demand is 300 cars.
b. Determine the indifference (break-even point) between the two locations.
Set their total profit equations equal to each other and solve for Q:
Q($90 – $30) – $7,000 = Q($90 – $40) – $4,700
$60Q – $7,000 = $50Q – $4,700
$60Q – $50Q = -$4,700 – (-$7,000)
$10Q = $2,300
Q = $2,300 / $10
Q = 230 cars
Chapter 08 - Location Planning and Analysis
8-11
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
8. Given: We are provided the location factors below for four different types of organizations.
Factor Local bank Steel mill Food warehouse Public school
Convenience for
customers
Attractiveness of
building
Nearness to raw
materials
Large amounts
of power
Pollution
controls
Labor cost and
availability
Transportation
costs
Construction
costs
Student answers will vary regarding how they rate the importance of each factor in terms of
making location decisions using L = low importance, M = moderate importance, and H = high
importance. One possible set of answers is given below.
Factor Local bank Steel mill Food warehouse Public school
Convenience for
customers H L M–H M–H
Attractiveness of
building H L M M–H
Nearness to raw
materials L H L M
Large amounts
of power L H L L
Pollution
controls L H L L
Labor cost and
availability L M L L
Transportation
costs L M–H M–H M
Construction
costs M H M M–H
Chapter 08 - Location Planning and Analysis
8-12
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
9. Given: We are given factors, weights, and factor rating scores for three locations. Scores range
from 1 – 100 (best).
Location Score
Factor Wt. A B C
Convenience .15 80 70 60
Parking .20 72 76 92
Display area .18 88 90 90
Shopper traffic .27 94 86 80
Operating costs .10 98 90 82
Neighborhood .10 96 85 75
1.00
Multiply the factor weight by the score for each factor and sum the results for each location
alternative.
Weight x Score
Factor Wt. A B C
Convenience .15 .15(80) = 12.00 .15(70) = 10.50 .15(60) = 9.00
Parking .20 .20(72) = 14.40 .20(76) = 15.20 .20(92) = 18.40
Display area .18 .18(88) = 15.84 .18(90) = 16.20 .18(90) = 16.20
Shopper traffic .27 .27(94) = 25.38 .27(86) = 23.22 .27(80) = 21.60
Operating costs .10 .10(98) = 9.80 .10(90) = 9.00 .10(82) = 8.20
Neighborhood .10 .10(96) = 9.60 .10(85) = 8.50 .10(75) = 7.50
1.00 87.02 82.62 80.90
Conclusion: Based on composite score, Location A seems to be the best.
Chapter 08 - Location Planning and Analysis
8-13
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
10. Given: We are given factors, weights, and factor rating scores for three locations. Scores range
from 1 – 100 (best).
Location Score
Factor Wt. East #1 East #2 West
Initial Cost 8 100 150 140
Traffic 10 40 40 30
Maintenance 6 20 25 18
Dock space 6 25 10 12
Neighborhood 4 12 8 15
Multiply the factor weight by the score for each factor and sum the results for each location
alternative.
Weight x Score
Factor Wt. East #1 East #2 West
Initial Cost 8 8(100) = 800 8(150) = 1200 8(140) = 1120
Traffic 10 10(40) = 400 10(40) = 400 10(30) = 300
Maintenance 6 6(20) = 120 6(25) = 150 6(18) = 108
Dock space 6 6(25) = 150 6(10) = 60 6(12) = 72
Neighborhood 4 4(12) = 48 4(8) = 32 4(15) = 60
1518 1842 1660
Conclusion: Based on composite score, Location East #2 seems to be the best.
Chapter 08 - Location Planning and Analysis
8-14
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
11. Given: We are given factors and factor rating scores for three locations. Scores range from 1 – 10
(best).
Location Score
Factor A B C
Business services 9 5 5
Community services 7 6 7
Real estate cost 3 8 7
Construction costs 5 6 5
Cost of living 4 7 8
Taxes 5 5 4
Transportation 6 7 8
a. Assume that the manager weights each factor equally.
Because there are seven factors, each factor will have a weight of 1/7. Therefore, we can
sum the scores and divide by 7 to determine the weighted score for each alternative.
Factor A B C
Business services 9 5 5
Community services 7 6 7
Real estate cost 3 8 7
Construction costs 5 6 5
Cost of living 4 7 8
Taxes 5 5 4
Transportation 6 7 8
Total 39 44 44
Total / 7 5.57 6.29 6.29
Conclusion: Location B or C is best, followed by Location A.
Chapter 08 - Location Planning and Analysis
8-15
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Education.
b. Two of the factors (business services and construction costs) are given weights that are
double the weights of the other factors.
We will give these two factors weights of 2/9 and the other five factors weights of 1/9.
Then, we will multiply each factor’s rating by that factor’s weight.
Factor Location Score Weight Weight x Score
Business Services 9 5 5 2/9 18/9 10/9 10/9
Community Services 7 6 7 1/9 7/9 6/9 7/9
Real Estate Cost 3 8 7 1/9 3/9 8/9 7/9
Construction Costs 5 6 5 2/9 10/9 12/9 10/9
Cost of Living 4 7 8 1/9 4/9 7/9 8/9
Taxes 5 5 4 1/9 5/9 5/9 4/9
Transportation 6 7 8 1/9 6/9 7/9 8/9
1.0 53/9 55/9 54/9
Conclusion: Location B is best, followed by Location C, and then Location A.
12. Given: A toy manufacturer produces toys in five locations and will ship raw materials from a
new, centralized warehouse. The monthly quantities to be shipped to each location are identical.
The coordinates for all five locations are shown below.
Location X Y
A 3 7
B 8 2
C 4 6
D 4 1
E 6 4
We know that the quantities to be shipped to each location are identical so we can eliminate
quantities from consideration. The correct formulas for the center of gravity are shown below:
𝑥̅ =
∑ 𝑥𝑖
𝑛
𝑦
̅ =
∑ 𝑦𝑖
𝑛
Chapter 08 - Location Planning and Analysis
8-16
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Sum the values in each coordinate’s column.
Location X Y
A 3 7
B 8 2
C 4 6
D 4 1
E 6 4
Sum 25 20
n = 5 locations.
𝑥̅ =
∑ 𝑥𝑖
𝑛
=
25
5
= 5.0 (round to 1 decimal)
𝑦
̅ =
∑ 𝑦𝑖
𝑛
=
20
5
= 4.0 (round to 1 decimal)
Conclusion: The new warehouse should be located at 5.0, 4.0.
13. Given: A clothing manufacturer produces clothes at four locations. The manufacturer must
determine the location of a central shipping point. The coordinates and weekly shipping quantities
to the four locations are shown below.
Location X Y
Weekly
Quantity (Q)
A 5 7 15
B 6 9 20
C 3 9 25
D 9 4 30
The correct formulas for the center of gravity are shown below:
𝑥̅ =
∑ 𝑥𝑖𝑄𝑖
∑ 𝑄𝑖
𝑦
̅ =
∑ 𝑦𝑖𝑄𝑖
∑ 𝑄𝑖
Sum the values in the quantity column.
Location X Y
Weekly
Quantity (Q)
A 5 7 15
B 6 9 20
C 3 9 25
D 9 4 30
Sum 90
Chapter 08 - Location Planning and Analysis
8-17
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Education.
𝑥̅ =
∑ 𝑥𝑖𝑄𝑖
∑ 𝑄𝑖
=
5(15)+6(20)+3(25)+9(30)
90
= 6.0 (round to 1 decimal)
𝑦
̅ =
∑ 𝑦𝑖𝑄𝑖
∑ 𝑄𝑖
=
7(15)+9(20)+9(25)+4(30)
90
= 7.0 (round to 1 decimal)
Conclusion: The central shipping point should be located at 6.0, 7.0.
14. Given: A company handling hazardous waste wants to minimize shipping cost for shipments to a
disposal center from five stations that it operates. The coordinates for each of the five stations and
the volumes shipped to the new disposal center are shown below.
Location X Y
Volume in Tons
per Day (Q)
1 10 5 26
2 4 1 9
3 4 7 25
4 2 6 30
5 8 7 40
The correct formulas for the center of gravity are shown below:
𝑥̅ =
∑ 𝑥𝑖𝑄𝑖
∑ 𝑄𝑖
𝑦
̅ =
∑ 𝑦𝑖𝑄𝑖
∑ 𝑄𝑖
Sum the values in the quantity column.
Location X Y
Volume
Tons per
Day (Q)
1 10 5 26
2 4 1 9
3 4 7 25
4 2 6 30
5 8 7 40
Sum 130
𝑥̅ =
∑ 𝑥𝑖𝑄𝑖
∑ 𝑄𝑖
=
10(26)+4(9)+4(25)+2(30)+8(40)
130
= 6.0 (round to 1 decimal)
𝑦
̅ =
∑ 𝑦𝑖𝑄𝑖
∑ 𝑄𝑖
=
5(26)+1(9)+7(25)+6(30)+7(40)
130
= 6.0 (round to 1 decimal)
Conclusion: The disposal center should be located at 6.0, 6.0.
Chapter 08 - Location Planning and Analysis
8-18
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Education.
15. Given: A company is considering two locations for a distribution center: L1 & L2. The five
shipment destinations and the monthly shipments (Q) to all five destinations are shown below.
Destination Q
D1 900
D2 300
D3 700
D4 600
D5 1200
Step 1: Use the map to determine the coordinates of each destination (use a ruler if necessary).
Add those coordinates to the table. Then, sum the values in the quantity column.
Destination X Y Q
D1 1 2 900
D2 2 4 300
D3 3 1 700
D4 4 2 600
D5 5 3 1200
Sum 3700
Step 2: Determine the center of gravity for the optimal location for the distribution center.
The correct formulas for the center of gravity are shown below:
𝑥̅ =
∑ 𝑥𝑖𝑄𝑖
∑ 𝑄𝑖
=
1(900)+2(300)+3(700)+4(600)+5(1200)
3700
= 3.2 (round to 1 decimal)
𝑦
̅ =
∑ 𝑦𝑖𝑄𝑖
∑ 𝑄𝑖
=
2(900)+4(300)+1(700)+2(600)+3(1200)
3700
= 2.3 (round to 1 decimal)
Step 3: Use the map to determine the coordinates for L1 & L2. Use a ruler if necessary.
L1 coordinates ≈ 2.6, 2.4
L2 coordinates ≈ 3.5, 2.5
Step 4: Determine the distance between each proposed location and the center of gravity.
Distance between two points = |Difference in X coordinates| + |Difference in Y coordinates|
Distance between L1 & Center of Gravity |2.6 – 3.2| + |2.4 – 2.3| = 0.6 + 0.1 = 0.7
Distance between L2 & Center of Gravity |3.5 – 3.2| + |2.5 – 2.3| = 0.3 + 0.2 = 0.5
Conclusion: L2 is closer to the center of gravity and is the better site.
Chapter 08 - Location Planning and Analysis
8-19
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Case: Hello Walmart?
[This is a good case for in-class discussion. Three groups can be formed: one to take the position of
residents, one to take the position of small businesses, and one to take the position of Walmart.]
1. Owners of small businesses:
Pro: Restaurants and other businesses that do not compete directly with Walmart generally would
welcome the additional traffic that Walmart would attract.
Con: Businesses that compete directly would not fare well unless they provided a product or
service value that would offset Walmart’s lower price.
2. Residents:
Pro: Another shopping option, lower prices, and other, non-competing businesses that would be
attracted by the increased traffic that Walmart would generate.
Con: Increased traffic and noise, construction inconveniences, loss of small-town atmosphere,
and loss of local businesses and jobs.
Walmart responses: The company would be a “good neighbor,” supporting the community
and providing jobs for low-skilled and handicapped workers. Construction would create
construction jobs and generate taxes and revenues for the community. Shoppers would benefit
from Walmart’s low prices. In addition, there would be an increase in the tax base.
Enrichment Module
A. Distance Measurement
B. Center of Gravity Method with Predetermined Sites
C. Factor Scoring Model
D. Emergency Facility Location
A. Distance Measurement
The companies measure distance when making two important decisions:
1. Facility Layout Decision:
Distances are estimated/measured in determining the best layout of equipment or departments
within a manufacturing facility such as a plant, a distribution facility such as a warehouse, or
a service facility such as a department store. Distance is an important input in determining the
best possible layout that minimizes the total distance traveled between departments or
workstations.
2. Facility Location Decision:
Distance measurement also is a very important input measure in determining the best location
for a new service or a manufacturing facility, relocation of an existing facility, or elimination
of an existing facility.
In most instances, distance measurements are used to estimate the distances between existing
warehouses or plants and the newly proposed potential location sites. The estimated distance
measures then are used to estimate the transportation costs. Transportation cost is considered
a critical factor in the facility location decision.
Chapter 08 - Location Planning and Analysis
8-20
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Distance Measurement Methods:
There are four methods of measuring distance:
1. Empirical Method
2. Rectilinear Method
3. Euclidean Method
4. Weighted Average Method
1. Empirical Method:
The empirical method is the most accurate distance measure. Using the empirical method,
distance can be measured in one of two ways. The first type of empirical measurement is the
actual recorded travel distance, where a driver records the distance based on a vehicle
odometer reading. The second type of empirical measurement of distance is estimation from a
map. When there are no actual travel data available, then the map estimation can be very
useful. However, the actual travel data obviously provides a more accurate measure of
distance than the map estimation.
The main advantage of using either empirical method is that they generally provide the most
accurate distance measures. On the other hand, the disadvantage is that it can be very time
consuming to gather the data and use it as a part of a computerized layout or a location
technique, especially if there are many existing and/or proposed locations.
2. Rectilinear Method
This mathematical method is very easy to compute and lends itself to easy implementation of
computerized layout or location techniques. Rectilinear method requires the use of a two
dimensional space with a horizontal axis, X, and a vertical axis, Y. Rectilinear distance often
is called “Manhattan” distance because it requires going around the block when no straight-
line route is available.
If A and B are the locations in question, the Rectilinear distance between A and B is given by
the following formula:
Dr = B
A
B
A Y
Y
X
X −
+
−
Where:
Dr = Rectilinear distance measure between location A and location B;
XA = X coordinate of location A;
XB = X coordinate of location B;
YA = Y coordinate of location A;
YB = Y coordinate of location B.
Chapter 08 - Location Planning and Analysis
8-21
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Example Problem—Calculation of the Rectilinear Distance:
When answering this question, refer to textbook, Chapter 8, Problem 13.
a. Determine the Rectilinear distance between location A and B.
b. Determine the Rectilinear distance between location A and D.
c. Determine the Rectilinear distance between location B and D.
Solution to Example Problem—Measurement of Rectilinear Distance:
a. The Rectilinear distance between location A and B is:
Dr = B
A
B
A Y
Y
X
X −
+
−
Dr = 3
9
7
6
5 =
−
+
−
b. The Rectilinear distance between location A and D is:
Dr = D
A
D
A Y
Y
X
X −
+
−
Dr = 7
4
7
9
5 =
−
+
−
c. The Rectilinear distance between location B and D is:
Dr = D
B
D
B Y
Y
X
X −
+
−
Dr = 8
4
9
9
6 =
−
+
−
The main advantage of this method is the ease of calculations, while the disadvantage is that
it generally overestimates the distance. Because of its propensity to overestimate distance,
Rectilinear distance is sometimes referred to as the pessimistic distance measurement
method. Rectilinear measure of distance is more commonly used in solving facility layout
problems.
3. Euclidean Method
This mathematical method is based on the Pythagorean Theorem. Euclidean distance
measures distance “as the crow flies” and is most applicable when a straight-line route is
possible.
The following formula for the hypotenuse of a right triangle provides us with the Euclidean
distance:
C2
= A2
+ B2
or C = 2
2
B
A +
C is the side of a right triangle opposite the right angle, and A and B are the right degree sides
of a right degree triangle.
The Euclidean distance method also requires the use of a two dimensional space with a
horizontal axis, X, and a vertical axis, Y.
If F and G are the locations in question, then the Euclidean distance between F and G is given
by the following formula:
Chapter 08 - Location Planning and Analysis
8-22
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
( ) ( )2
2
G
F
G
F
e Y
Y
X
X
D −
+
−
=
Where:
De = Euclidean distance measure between location F and location G;
XF = X coordinate of location F;
XG = X coordinate of location G;
YF = Y coordinate of location F;
YG = Y coordinate of location G.
Example Problem—Calculation of the Euclidean Distance:
Refer to textbook, Chapter 8, Problem 13.
a. Determine the Euclidean distance between location A and B.
b. Determine the Euclidean distance between location A and D.
c. Determine the Euclidean distance between location B and D.
Solution to Example Problem—Calculation of the Euclidean Distance:
a.
b.
c.
The Euclidean distance is the direct or the shortest distance between two given sites.
Therefore, for any given pair of sites, the Euclidean distance provides the most direct or the
straight-line connection. In most cases, however, there is no straight route between a pair of
locations. Therefore, the Euclidean measure provides an optimistic measure of distance and
in most cases underestimates the true distance.
( ) ( )
( ) ( )
236
.
2
5
9
7
6
5
2
2
2
2
=
=
−
+
−
=
−
+
−
=
e
e
B
A
B
A
e
D
D
Y
Y
X
X
D
( ) ( )
( ) ( )
5
25
9
16
4
7
9
5
2
2
2
2
=
=
+
=
−
+
−
=
−
+
−
=
e
e
e
D
A
D
A
e
D
D
D
Y
Y
X
X
D
( ) ( )
( ) ( )
831
.
5
34
25
9
4
9
9
6
2
2
2
2
=
=
+
=
−
+
−
=
−
+
−
=
e
e
e
D
B
D
B
e
D
D
D
Y
Y
X
X
D
Chapter 08 - Location Planning and Analysis
8-23
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
4. Weighted Average Method
As we discussed in the previous sections, the Rectilinear method is a conservative,
pessimistic measure of distance, and the Euclidean method is an optimistic measure of
distance. Both Euclidean and Rectilinear measures of distance are frequently the only
standard distance options used as a part of many layout and location software programs.
However, some managers prefer the weighted average method that provides a compromise
distance between the optimistic Euclidean and the pessimistic Rectilinear methods.
If A and B are the locations in question, then the weighted average distance between A and B
is given by the following formula:
)
(
)
(
)
(
)
( r
r
e
e
wa D
w
D
w
D 
+

=
Where:
Dr = Rectilinear distance measure between location A and location B;
De = Euclidean distance measure between location A and location B;
wr = weight associated with the Rectilinear distance;
we = weight associated with the Euclidean distance.
0
1

i
i i
w
w =

Example Problem—Calculation of the Weighted Average Distance:
Refer to textbook, Chapter 8, Problem 13 and the two examples given earlier in this section.
Assume that the pessimistic (Rectilinear) weight is 0.4 and the optimistic (Euclidean) weight
is 0.6.
a. Determine the weighted average distance between location A and B.
b. Determine the weighted average distance between location A and D.
c. Determine the weighted average distance between location B and D.
Solution to Example Problem—Weighted Average
a. The weighted average distance between location A and B is:
DWA = (0.4)(3) + (0.6)(2.236) = 2.5416
b. The weighted average distance between location A and D is:
DWA = (0.4)(7) + (0.6)(5) = 5.8
c. The weighted average distance between location B and D is:
DWA = (0.4)(8) + (0.6)(5.831) = 6.7
Chapter 08 - Location Planning and Analysis
8-24
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Exercise Problems
1. Refer to textbook Problem 15 in Chapter 8, and measure the Rectilinear distance between
destination 1 and destination 5.
2. Refer to textbook Problem 15 in Chapter 8, and measure the Euclidean distance between
destination 1 and destination 5.
3. Refer to textbook Problem 15 in Chapter 8, and measure the Weighted Average distance
between destination 1 and destination 5 (wr = 0.3 and we = 0.7).
4. Refer to textbook Problem 15 in Chapter 8 and measure the Rectilinear distance between
destination 1 and destination 3.
5. Refer to textbook Problem 15 in Chapter 8, and measure the Euclidean distance between
destination 1 and destination 3.
6. Refer to textbook Problem 15 in Chapter 8, and measure the Weighted Average distance
between destination 1 and destination 3 (wr = 0.5 and we = 0.5).
Solutions to Exercise Problems
6181
.
2
)
2361
.
2
)(
5
.
0
(
)
3
)(
5
.
0
(
.
6
2361
.
2
5
.
5
3
1
2
3
1
.
4
3862
.
4
)
1231
.
4
)(
7
.
0
(
)
5
)(
3
.
0
(
.
3
1231
.
4
17
.
2
5
3
2
5
1
.
1
=
+
=
=
=
=
−
+
−
=
=
+
=
=
=
=
−
+
−
=
WA
e
r
WA
e
r
D
D
D
D
D
D
B. Center of Gravity Method with Predetermined Sites:
(Weighted Distance Technique)
The center of gravity method in its original form identifies a central location relative to its
distance to other existing locations and the amount of goods shipped to and from other existing
locations. However, the center of gravity method in its original form is unable to evaluate specific
location alternatives. If we have narrowed the choice of the new location to a few known specific
sites, then the weighted distance technique can evaluate these known locations.
For each candidate site, a weighted distance value is computed using the following formula:
i
n
i
id
w
WD 
=
where:
Chapter 08 - Location Planning and Analysis
8-25
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
WD = weighted distance value for a given site
wi = weight associated with existing location i
di = the distance between existing site i and the proposed location
For a typical facility location problem, wi (weight) represents the amount of goods or units
shipped between the proposed location and the existing location i.
For a facility layout problem, wi (weight) represents the number of trips between the existing
location i and the proposed location.
Distance is calculated using either Rectilinear, Euclidean or Weighted Average methods. The site
with the lowest weighted-distance would be selected, because the lowest weighted-distance
usually results in the lowest transportation costs.
Problem 1
Based on the destination locations and quantities given in textbook problem 15, the company is
considering two locations for a new plant. The coordinates of the first plant location are: (x = 2, y
= 3) and the coordinates of the second location are: (x = 4, y = 3).
a. Determine the Euclidean distance from the first proposed plant location to all of the
destination locations.
b. Determine the Rectilinear distance from the first proposed plant location to all of the
destination locations.
c. Determine the Euclidean distance from the second proposed plant location to all of the
destination locations.
d. Determine the Rectilinear distance from the second proposed plant location to all of the
destination locations.
e. Determine the Weighted Distance value for the first and second proposed plant locations
based on Euclidean distance and decide where the new plant should be located.
f. Determine the Weighted Distance value for the first and second proposed plant locations
based on Rectilinear distance and decide where the new plant should be located.
Solution to Problem 1
Destination X coordinate Y coordinate Q
D1 1 2 900
D2 2 4 300
D3 3 1 700
D4 4 2 600
D5 5 3 1200
Chapter 08 - Location Planning and Analysis
8-26
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
a. Plant Site 1—Euclidean Distance
From Plant Site 1 (P1) to Destination j (Dj)
3
9
)
3
3
(
)
5
2
(
)
(
Distance
Euclidean
236
.
2
5
)
2
3
(
)
4
2
(
)
(
Distance
Euclidean
236
.
2
5
)
1
3
(
)
3
2
(
)
(
Distance
Euclidean
1
1
)
4
3
(
)
2
2
(
)
(
Distance
Euclidean
414
.
1
2
)
2
3
(
)
1
2
(
)
(
Distance
Euclidean
2
2
5
1
2
2
4
1
2
2
3
1
2
2
2
1
2
2
1
1
=
=
−
+
−
=
−
=
=
−
+
−
=
−
=
=
−
+
−
=
−
=
=
−
+
−
=
−
=
=
−
+
−
=
−
D
P
D
P
D
P
D
P
D
P
b. Plant Site 1—Rectilinear Distance
From Plant Site 1 (P1) to Destination j (Dj)
3
3
3
5
2
)
(
Distance
r
Rectilinea
3
2
3
4
2
)
(
Distance
r
Rectilinea
3
1
3
3
2
)
(
Distance
r
Rectilinea
1
4
3
2
2
)
(
Distance
r
Rectilinea
2
2
3
1
2
)
(
Distance
r
Rectilinea
5
1
4
1
3
1
2
1
1
1
=
−
+
−
=
−
=
−
+
−
=
−
=
−
+
−
=
−
=
−
+
−
=
−
=
−
+
−
=
−
D
P
D
P
D
P
D
P
D
P
c. Plant Site 2—Euclidean Distance
From Plant Site 2 (P2) to Destination j (Dj)
1
1
)
3
3
(
)
5
4
(
)
(
Distance
Euclidean
1
1
)
2
3
(
)
4
4
(
)
(
Distance
Euclidean
236
.
2
5
)
1
3
(
)
3
4
(
)
(
Distance
Euclidean
236
.
2
5
)
4
3
(
)
2
4
(
)
(
Distance
Euclidean
162
.
3
10
)
2
3
(
)
1
4
(
)
(
Distance
Euclidean
2
2
5
2
2
2
4
2
2
2
3
2
2
2
2
2
2
2
1
2
=
=
−
+
−
=
−
=
=
−
+
−
=
−
=
=
−
+
−
=
−
=
=
−
+
−
=
−
=
=
−
+
−
=
−
D
P
D
P
D
P
D
P
D
P
Chapter 08 - Location Planning and Analysis
8-27
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Education.
d. Plant Site 2—Rectilinear Distance
From Plant Site 2 (P2) to Destination j (Dj)
1
3
3
5
4
)
(
Distance
r
Rectilinea
1
2
3
4
4
)
(
Distance
r
Rectilinea
3
1
3
3
4
)
(
Distance
r
Rectilinea
3
4
3
2
4
)
(
Distance
r
Rectilinea
4
2
3
1
4
)
(
Distance
r
Rectilinea
5
2
4
2
3
2
2
2
1
2
=
−
+
−
=
−
=
−
+
−
=
−
=
−
+
−
=
−
=
−
+
−
=
−
=
−
+
−
=
−
D
P
D
P
D
P
D
P
D
P
e. Weighted Distance Values Based on Euclidean Distances
P1 = Plant 1
P2 = Plant 2
k = # of existing locations

=
k
i
i
id
w
1
WDP1 = 900(1.414) + 300(1) + 700(2.236) + 600(2.236) + 1,200(3) = 8,079.4
WDP2 = 900(3.162) + 300(2.236) + 700(2.236) + 600(1) + 1,200(1) = 6,881.8
Because 6,881.8 < 8,079.4, choose proposed Plant Location 2.
f. Weighted distance values based on Rectilinear distances
WDP1 = 900(2) + 300(1) + 700(3) + 600(3) + 1,200(3) = 9,600
WDP2 = 900(4) + 300(3) + 700(3) + 600(1) + 1,200(1) = 8,400
Because 8,400 < 9,600, choose proposed Plant Location 2.
C. Factor Scoring Model
This simplistic selection procedure has many areas of application. The two most common areas of
application are: 1) Facility Location; 2) Product Selection.
Factor Scoring is a very flexible method that considers both tangible and intangible factors. It has
the capability to consider multiple decision criteria simultaneously.
Steps of the Factor Scoring Model:
1. Develop a list of (factors) criteria to be considered. The decision maker should consider these
factors important in evaluating each decision alternative.
2. Assign a weight to each factor that describes the factor’s relative importance.
Chapter 08 - Location Planning and Analysis
8-28
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Education.
Let wi = the weight for factor i, where i = 1, 2, ….., F
F = the number of factors considered.
The higher the weight, the more important the criterion.
We will use a five-point scale to establish the relative importance of the factors considered.
The following table provides an interpretation of the weight scale:
Factor Weight Interpretation Table
Importance Weight
Very important 5
Somewhat important 4
Average importance 3
Somewhat unimportant 2
Very unimportant 1
For example, if a factor has a weight of 4, it is somewhat more important than the average
factor.
If a factor has a weight of 1, relative to the other factors being considered, the factor in
question is very unimportant.
3. Determine a list of decision alternatives. Let dj = decision alternative j and assign a rating for
each factor/decision alternative combination.
Let rij = the rating for factor i and decision alternative j.
Where j = 1, 2,……, D and
D = number of decision alternatives considered.
Chapter 08 - Location Planning and Analysis
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Education.
For the purposes of rating each decision alternative/factor combination, we use the following
9-point scale.
Level of Satisfaction Rating
Extremely High 9
Very high 8
High 7
Slightly High 6
Average 5
Slightly Low 4
Low 3
Very Low 2
Extremely Low 1
For example, a score of 7 for a given decision alternative would indicate that the decision
maker (manager) rates this decision alternative (location) high with respect to a given factor.
4. Compute the factor score for each decision alternative. Let Sj = factor score

=
F
i
ij
i
j r
w
S
5. Sequence the decision alternatives from the highest score to the lowest score. The decision
alternative with the highest factor score is the recommended decision alternative. The
decision alternative with the second highest factor score is the second choice decision
alternative and so on.
Three popular areas of application for the Factor Scoring model are product selection, facility
location, and job selection. Product selection and facility location are company-related
problems while the job selection is an individual problem. An example for each of the three
applications is provided in the following pages.
PRODUCT SELECTION EXAMPLE
An appliance manufacturing company is considering expanding its product line. It has sufficient
capital to introduce only one of the three following products:
1. Microwave Ovens
2. Refrigerators
3. Stoves
Management thinks that the following decision criteria should be used in selecting the product:
1. Manufacturing capability/cost
Chapter 08 - Location Planning and Analysis
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Education.
2. Market demand
3. Unit profit margin
4. Long term profitability/growth
5. Transportation costs
6. Useful life
The company has determined the following weights for the decision criteria (factors):
FACTOR WEIGHT
Manufacturing capability/cost 4
Market demand 5
Unit profit margin 3
Long term profitability/growth 5
Transportation costs 2
Useful life 1
The decision factor ratings for each criteria are given in the following table:
DECISION FACTOR RATINGS
FACTOR MICROWAVE REFRIGERATOR STOVE
1 4 3 8
2 8 4 2
3 6 9 5
4 3 6 7
5 9 2 4
6 1 5 6
Based on the information provided, determine the factor scores for all three products. What is the
best choice for the appliance manufacturing company? What is the second best choice?
Other documents randomly have
different content
offered by the highest bidder. If negotiation failed, escape to France
would not be difficult.
For six months Charles had succeeded in playing off Parliament
against Army, and Army against Parliament. But the result had been
to make him thoroughly distrusted by both, and his flight from
Hampton Court united them against him. The King had hoped much
from the divisions of the army, but simultaneously with his arrival at
Carisbrooke Cromwell and Fairfax reduced their troops to obedience
again. On November 8th, Cromwell carried a vote for the temporary
suspension of the sittings of the Council, and sent Agitators and
officers back to their regiments. A week later Fairfax held a general
review of the army, dividing it into three brigades, which met at three
different places. At each review he solemnly engaged himself to the
soldiers to stand by them in securing the redress of their military
grievances and the reform of Parliament, exacting from them in
return a signed pledge to obey the orders of the General and council
of war. At the first rendezvous, which took place near Ware on
November 15th, there was some opposition. The Levellers tried to
convert it into a general demonstration in favour of the “Agreement
of the People.” Two regiments came there unsummoned, wearing the
“Agreement of the People” in their hats, with the motto, “England’s
Freedom, Soldiers’ Rights.” They had driven away their own officers,
called on other regiments to do the like, and planned the seizure of
Cromwell as a traitor to the cause of the people. But when he rode up
to the mutineers none dared to lay hands on him. “Lieutenant-
General Cromwell’s carriage, with his naked waved sword, daunted
the soldiers with the paper in their hats, and made them pluck it out
and be subjected to command.” One soldier was tried, and shot on
the field; others, including several officers, were reserved for the
judgment of a future court-martial. On November 19th, Cromwell
was able to report to Parliament that the army was very quiet and
obedient, and received the thanks of the Commons for his services.
Meanwhile the King sent a message to Parliament from the Isle of
Wight, offering various concessions and asking to be admitted to a
personal treaty at London. He applied also to the army leaders,
urging them to support his request, to which they coldly replied that
they were the Parliament’s army, and must refer those matters to it.
Parliament, equally distrustful of Charles, answered his overtures by
drawing up an ultimatum, consisting of four bills, to which his assent
was required before any treaty should begin. Their chief demand was
the direct control of the militia for the next twenty years, and a share
in its control when that period ended. Other constitutional questions
might be left to discussion, but they must make sure that the King
could never use force to impose his will upon the nation. Driven to
extremity by this demand, Charles turned once more to the Scottish
Commissioners, who had now arrived at Carisbrooke. He found them
ready enough to sacrifice the liberties of Englishmen, and they
promised him restoration to all the rights of his crown in return for
the three years’ establishment of Presbyterianism in England, the
rigid suppression of Independents and other heretics, and certain
privileges for Scotland and the Scottish nobility. If Parliament
refused to disband its forces and to treat with the King in London, an
army was to cross the border and replace Charles on his throne
(December 27, 1647). “The Engagement,” as this treaty was termed,
was wrapped in lead and buried in the castle garden till it could be
safely smuggled out of the island. The next day the King definitely
rejected the ultimatum of the English Parliament, and prepared to
effect his escape to the continent.
It was too late. As soon as the King’s answer was delivered, his
guards were doubled and he was made a close prisoner. The two
Houses were well aware that his refusal of their terms was due to
some agreement with the Scots, although they were ignorant of its
precise nature.
“The House of Commons,” wrote Cromwell to Hammond, “is very sensible of the
King’s dealings and of our brethren’s in this late transaction. You should do well, if
you have anything that may discover juggling, to search it out, and let us know it. It
may be of admirable use at this time, because we shall I hope go upon business in
relation to them tending to prevent danger.”
On January 3, 1648, the House of Commons voted that they would
make no further addresses to the King, and receive no more
messages from him. Cromwell and Ireton, who had opposed the
resolution to that effect which Marten had brought forward in the
previous September, now spoke earnestly in its favour. “It was now
expected,” said Cromwell, “that the Parliament should govern and
defend the kingdom by their own power, and not teach the people
any longer to expect safety and government from an obstinate man
whose heart God had hardened.” In such a policy, he added, the
army would stand by the Parliament against all opposition: but if the
Parliament neglected to provide for its own safety and that of the
nation, the army would be forced to seek its own preservation by
other means.
Events had thus driven Cromwell to be the foremost advocate of that
policy of completely setting aside the King which he had long so
stubbornly opposed. Yet, though convinced that the King could not
be trusted, he was not prepared to abandon monarchy. At a
conference on the settlement of the government which took place
early in 1648, the “Commonwealth’s-men,” as the republicans were
termed, pressed for the immediate establishment of a free
commonwealth and the trial of the King. Ludlow noted with great
dissatisfaction that Cromwell and his friends “kept themselves in the
clouds, and would not declare their judgments either for a
monarchical, aristocratic, or democratic government; maintaining
that any of them might be good in themselves, or for us, according as
Providence should direct us.” When he pressed Cromwell privately
for the grounds of his objection to a republic, Cromwell replied that
he was convinced of the desirableness of what was proposed, but not
of the feasibility of it. There is evidence that during the spring of
1648 the Independent leaders discussed a scheme for deposing
Charles I., and placing the Prince of Wales or the Duke of York upon
the throne. But the unwillingness of the Prince and the escape of the
Duke to France frustrated this plan.
While seeking to find some compromise which would prevent a new
war, Cromwell endeavoured to unite all sections of the parliamentary
party to meet it, if it came. The reunion of the army had already been
effected. It was completed in a series of council meetings held at
London during December, 1647, in which the officers under arrest
for insubordination were pardoned, and a personal reconciliation
took place between Cromwell and Rainsborough. In February and
March, 1648, Cromwell made conciliatory overtures to the
Presbyterians of the City, but as nothing short of the restoration of
the King to his authority would content them, the negotiations failed.
As little could Cromwell succeed in overcoming the distrust and
hostility which the advanced party amongst the Independents now
felt towards him. On January 19, 1648, John Lilburn, at the bar of
the House of Lords, publicly accused him of high treason. Nor was it
only his dealings with the King that made him the object of
suspicion. During the last year his political attitude had continually
altered. In April, he had urged the army to disband peaceably; in
June, he had headed its revolt; in November, he had forced it into
obedience to the Parliament again. And besides his apparent
inconsistency, he was notoriously indifferent to principles which
Levellers and Commonwealth’s-men held all-important. To them a
republic meant freedom and a monarchy bondage. For him the
choice between the two was a question of expediency, and dependent
upon circumstances. In open council he had declared that he “was
not wedded or glued to forms of government,” and in private he was
said to have avowed that it was lawful to pass through all forms of
government to accomplish his ends. It was not surprising, therefore,
that men to whom his opportunism was unintelligible thought self-
interest or ambition the natural explanation of his conduct, and that
charges of hypocrisy and apostacy were freely made against him.
Through this cloud of detraction Cromwell pursued his way
unmoved. Sometimes he answered his accusers with blunt defiance.
“If any man say that we seek ourselves in doing this, much good may
it do him with his thoughts. It shall not put me out of my way.” At
other times he referred to these slanders with a patient confidence
that justice would be done to him in the end. “Though it may be,” he
wrote in September, 1647, “for the present a cloud may lie over our
actions to those not acquainted with the grounds of them; yet we
doubt not but God will clear our integrity from any other ends we
aim at but His glory and the public good.” Neither loss of popularity,
misrepresentations, nor undeserved mistrust could diminish
Cromwell’s zeal for the cause. “I find this only good,” he wrote on his
recovery from a dangerous illness in the spring of 1648: “to love the
Lord and His poor despised people, to do for them, and to be ready
to suffer with them, and he that is found worthy of this hath obtained
great favour from the Lord.”
Not Cromwell’s utterances only but his acts testify to the integrity of
his motives. In March, 1648, Parliament settled an estate upon him
as a reward for his services, to which he responded by offering to
contribute a thousand a year, out of the seventeen hundred it
brought in, to be employed in the recovery of Ireland. And so little
did he dream of ever becoming himself the ruler of England, that at
the very moment when fortune had opened the widest field to
ambition, he began negotiations for the marriage of his eldest son to
the daughter of a private gentleman of no great influence or position.
T
CHAPTER X
THE SECOND CIVIL WAR
1648
he Second Civil War broke out in Wales. It began with a revolt of
officers and soldiers who had fought zealously for the Parliament
throughout the first war. In February, 1648, Colonel Poyer, the
governor of Pembroke Castle, refused to hand his charge over to the
officer whom Fairfax had appointed to succeed him. In March, he
openly declared for the King, and the troops of Colonel Laugharne,
followed soon afterwards by their leader, joined Poyer’s forces. In
April, it became known in London that the Scots were raising an
army to invade England, and at the end of the month parties of
English Royalists, by Scottish help, seized Berwick and Carlisle. To
meet these two dangers Fairfax sent Cromwell to suppress the Welsh
insurgents and prepared to march north himself against the Scots.
At the beginning of May, Cromwell left London, taking with him two
regiments of horse and three of foot. Poyer was full of confidence. He
had won several small victories, and told his men that he would meet
Cromwell in fair field, and that he would be himself the first man to
charge “Ironsides,” adding that if Cromwell “had a back of steel and a
breast of iron, he durst and would encounter with him.” But before
Cromwell reached Wales, Colonel Horton defeated the boastful Poyer
at St. Fagans, on May 8th, and when Cromwell arrived the war
became a war of sieges. Chepstow was stormed by Colonel Ewer on
May 25th, and Tenby surrendered to Colonel Horton at the end of
May, but Pembroke Castle held out for over six weeks. Its walls were
strong and its garrison desperate. Cromwell had no heavy artillery
with him, and though he “scraped up,” as he said, a few little guns,
and made a breach, his assaults were repulsed with loss. The hostility
of the country people and want of provisions added to the difficulties
of the besiegers. “It’s a mercy,” wrote Cromwell to Fairfax, “that we
have been able to keep our men together in such necessity, the
sustenance of the foot for the most part being bread and water.” The
besieged, however, were in worse straits, and at last, on the 11th of
July, starvation forced Poyer and Laugharne “to surrender
themselves to the mercy of the Parliament” and give up town and
castle.
Three days before Pembroke fell, Hamilton and the Scottish army
crossed the border, and Fairfax was not there to face them. London
was seething with discontent: there were riots in the city and in the
eastern counties, and mass petitions from Essex, Kent, and Surrey
urged Parliament to come to terms with the King and to disband the
army. At the end of May a royalist rising broke out in Kent, and the
fleet in the Downs declared for the King.
PEMBROKE CASTLE.
(From a photograph.)
Fairfax collected eight or nine thousand men and set out for Kent.
On June 1st, he forced his way into Maidstone, where the main body
of the Kentish Royalists had posted themselves, and, after hard
fighting in the barricaded streets, mastered the town, and broke up
the insurgent army. A part of them, under old Lord Norwich,
marched towards London, but found the city gates closed against
them, and dispersed. Norwich himself, with five or six hundred
horse, crossed the Thames, and called the Royalists of Essex to arms.
Ere long four thousand men gathered round him, and Fairfax,
leaving detachments to complete the subjugation of Kent, hurried to
Essex to suppress this new rising. Norwich threw himself into
Colchester, and a bloody battle took place in the suburbs, in which
the raw levies of the Royalists repulsed Fairfax’s veterans with great
loss. The parliamentary general, seeing that he could not carry the
town by a coup de main, was obliged to sit down to a regular siege,
which ultimately developed into a blockade. Forts were built round
Colchester, and connected by lines of intrenchments, to cut off all
supplies and prevent any escape. The militia of Suffolk and Essex
swelled Fairfax’s small force of regulars and completed the
investment. The besieged fought well and made vigorous sallies, but
unless help came from without the end was inevitable. When the
siege began, such relief seemed very probable. All over England little
local risings were incessantly breaking out which threatened to
become general unless they were at once suppressed. In June, there
were risings in North Wales, Northamptonshire, and
Nottinghamshire. At the beginning of July, Lord Holland and the
young Duke of Buckingham gathered about six hundred Cavaliers at
Kingston in the hope of relieving Colchester. But they were hunted
from place to place by Fairfax’s cavalry, and could never stay long
enough anywhere to collect their partisans. The few who kept
together were captured at St. Neots, in Huntingdonshire, on July
10th. At the end of July, Prince Charles and the revolted ships
blockaded the Thames, hoping to persuade London to declare for the
King by threatening its trade. But a fleet alone could not relieve
Colchester, for Fairfax had occupied Mersea Island and cut off the
town from the sea. Moreover, London remained quiet, for, though
strongly Presbyterian in feeling, it had no desire to see the King
restored unconditionally. The only hope of the besieged lay in the
advance of Hamilton and the Scottish army.
In the north of England the Parliament had no force afoot strong
enough to stop the Scots from marching southwards. Major-General
Lambert, the commander-in-chief in the northern counties, with
three or four regiments of regular horse and the local levies of
Yorkshire and Lancashire, more than held his own against the
English Royalists under Langdale and Musgrave, defeating them in
the field and reducing the garrison of Carlisle to extremities. But
when Hamilton advanced to relieve his allies, Lambert could only fall
back, stubbornly skirmishing, into north Yorkshire, leaving the Scots
to overrun Cumberland and the north. He, too, was hampered by
risings in his rear, for early in June Pontefract Castle had been
surprised by the Royalists, and later in the month Scarborough had
declared for the King. On the 8th of July, when Hamilton entered
England, he brought with him no more than ten thousand or eleven
thousand men, but additional forces followed later, and including the
English Royalists under Langdale and Musgrave he had, by the next
month, about twenty-four thousand men under his command. He
marched slowly in order to give time for his reinforcements to come
up, and spent some time in besieging Appleby and other northern
castles. It was only about the middle of August that he resumed his
advance and determined to push south through Lancashire.
Meanwhile, Cromwell was hurrying north to Lambert’s aid. Even
before Pembroke fell he had sent a portion of his horse northwards.
As soon as it surrendered, he set out at once with the rest of his horse
and the infantry. His men had not been paid for months, but his iron
discipline kept them from plundering. The most part of his foot were
shoeless and in rags, but boots were provided to meet them at
Leicester. Marching by way of Gloucester and through the midlands,
Cromwell reached Leicester on August 1st, Nottingham on August
5th, and joined Lambert near Knaresborough in the West Riding on
Saturday, August 12th. Some regiments had to be left to besiege
Pontefract and Scarborough, so that their united forces came to no
more than about eight thousand five hundred men, of whom about
three thousand were horse. But three quarters of this army were old
soldiers, and, as one of Cromwell’s officers wrote, it was “a fine,
smart army, fit for action.”
Cromwell had hitherto been under the impression that the Scots
intended to advance through Yorkshire, and, relieving Pontefract on
their way, to march straight for London. He now learnt that
Hamilton had chosen the Lancashire route, and was already on his
way through that county. Accordingly, on Sunday, August 13th, he
set out to cross the hills which separate Lancashire from Yorkshire,
and to attack the invaders. On Monday night, he quartered at
Skipton; on Tuesday night, at Gisburn. On Wednesday, he marched
down the valley of the Ribble into Lancashire. Two courses were now
open to him. He might cross by Hodder Bridge to the southern bank
of the Ribble, and seek to bar Hamilton’s advance southwards by
placing himself somewhere in his path; or he might keep along the
northern bank of the river and engage Hamilton somewhere near
Preston itself. Cromwell chose the second course, and he did so with
a full consciousness of the importance of the choice. “It was
thought,” he wrote, “that to engage the enemy to fight was our
business,” and to march straight upon Preston was more likely to
bring about a battle because it seemed probable that Hamilton would
stand his ground there. There was also a second reason. If he put
himself to the south of Hamilton, a defeat would throw Hamilton
back upon his supports in Westmoreland and on the road to
Scotland. If he defeated Hamilton at Preston, he might be able to
drive him southwards, separating him from his supports, and cutting
off his line of retreat. Under such circumstances, a defeat would lead
to the annihilation of the Scottish army instead of merely forcing it to
retire to Scotland. It was for these reasons, and not by any happy
accident, that Cromwell adopted the second plan. As he explained a
couple of years later, “Upon deliberate advice we chose rather to put
ourselves between their army and Scotland.” All Wednesday,
therefore, he continued his march down the northern bank of the
Ribble, and camped his army for the night at Stonyhurst, about nine
miles from Preston.
Meanwhile, Hamilton’s army was marching through Lancashire as
carelessly and loosely as if Cromwell were fifty miles away. Hamilton
himself, with ten thousand foot and perhaps fifteen hundred horse,
was at Preston. The Earl of Callendar and General Middleton, with
the bulk of the Scottish horse, were at Wigan, fifteen miles ahead of
the infantry, while thirty miles in the rear, at Kirby Lonsdale, in
Westmoreland, lay Major-General Monro, with about three thousand
veteran horse and foot drawn from the Scottish army in Ulster, and
two or three thousand English Royalists under Sir Philip Musgrave.
Between Cromwell and Preston, covering Hamilton’s flank, was Sir
Marmaduke Langdale’s division of English Royalists, numbering
three thousand foot and six hundred horse. Hamilton had been
warned of the enemy’s approach by Langdale, but discredited his
information, and believed he was threatened merely by some
Lancashire militia forces.
Early on Thursday, the 17th of August, Cromwell fell upon Langdale’s
division with tremendous vigour, and beating his foot from hedge to
hedge drove them towards Preston. Langdale sent pressing appeals
to Hamilton, but the Duke gave him no adequate support. Instead of
helping him, he drew the Scottish foot out of Preston and to the
south of the Ribble, in order to facilitate their junction with the
cavalry at Wigan. To defend Preston, he kept merely a couple of
brigades of foot, and the fifteen hundred or sixteen hundred horse of
his rearguard. Against forces so divided, Cromwell’s attack was
irresistible. At nightfall on Thursday, Preston was in his possession,
and not only the town but the bridge over the Ribble, and the second
bridge over the Darwen, a mile or so to the south of it. His whole
army was solidly planted between Hamilton and Scotland.
Langdale’s division had ceased to exist, and of Hamilton’s two
brigades of foot hardly a man had escaped. A thousand had fallen in
the fight, Cromwell had four thousand prisoners, and his cavalry had
chased Hamilton’s flying horse ten miles on the road to Lancaster.
In the Scottish camp there was great distraction and depression.
Hamilton’s forces were still superior in number to Cromwell’s, for he
had six or seven thousand foot on the south side of the river, who
had scarcely fired a shot, besides Middleton and the vanguard of
cavalry at Wigan. But the Duke, who had shown plenty of personal
courage, was weak and irresolute in council. Major-General Baillie,
who commanded his foot, urged him to make a stand where he was
until Middleton and the horse rejoined them. The Earl of Callendar,
Hamilton’s second in command, proposed that the foot should
march away as soon as it was dark, to join Middleton, and
Callendar’s proposal was accepted. It involved the abandonment of
Hamilton’s train, for they had no horses left to draw the waggons;
and all the ammunition except what the men carried in their flasks
fell into Cromwell’s hands. All night the Scottish infantry marched.
“Our march,” says one of them, “was very sad, the way being
exceeding deep, the soldiers both wet, hungry, and weary, and all
looked on their business as half ruined.” They had lost many
stragglers when they arrived at Wigan. On Friday morning,
Cromwell, leaving the Lancashire militia to guard Preston and his
prisoners, set out in pursuit of Hamilton with three thousand foot
and twenty-five hundred horse. The fighting on Friday was mainly
between the horse of the two armies. While the Scottish infantry
were marching to Wigan to join Middleton, Middleton was marching
to Preston to join them, and as he went by a different road they failed
to meet. On reaching the camp of the infantry, he found nothing but
deserted fires and a few stragglers, and turned back to follow
Hamilton’s track to Wigan. Cromwell’s horsemen were at his heels
all the way, “killing and taking divers,” though Colonel Thornhaugh,
who commanded Cromwell’s van, was killed by a Scottish lancer.
Hamilton’s army, when the horse joined, drew up on the moor, north
of Wigan, as if to give battle, but, judging the ground
disadvantageous, Hamilton retreated into the town before Cromwell
came up. “We lay that night in the field,” says Cromwell, “close by the
enemy, being very dirty and weary, and having marched twelve miles
of such ground as I never rode in my life, the day being very wet.”
There was no rest, however, for the Scots in Wigan. Their
commanders resolved to make another night march to Warrington,
intending to break down the bridge, and put the Mersey between
themselves and their pursuer. On Saturday, Cromwell’s cavalry
found the Scottish foot posted in a good position at Winwick, about
three miles from Warrington.
“We held them in dispute,” wrote Cromwell, “till our army came up, they
maintaining the pass with great resolution for many hours, ours and theirs coming
to push of pike and very close charges, which forced us to give ground; but our men
by the blessing of God quickly recovered it, and charging very home upon them,
beat them from their standing. We killed about a thousand of them, and took, as
we believe, about two thousand prisoners.”
This was the last stand the Scots made. When Cromwell reached
Warrington the same Saturday evening, General Baillie and the rest
of the Scottish infantry surrendered as prisoners of war. Hamilton
and Callendar, with two or three thousand horse escaped into
Cheshire, intending to join Lord Byron who was in arms for the King,
but their fate was not long delayed. Cromwell sent Lambert with four
regiments of horse in pursuit, and called on the neighbouring
counties to send all the horses they could muster after the fugitives.
“They are so tired, and in such confusion, that if my horse could but trot after them
I could take them all. But we are so weary we can scarce be able to do more than
walk after them. My horse are miserably beaten out—and I have ten thousand of
them prisoners.”
Skirmishing incessantly with the country people and the local militia,
Hamilton made his way as far as Staffordshire, party after party of
his followers dropping off by the way, either to surrender or to
escape in disguise. With the few who remained, he capitulated to
Lambert at Uttoxeter, on Friday, August 25th. On the Monday
following, Colchester surrendered to Fairfax, and the Second Civil
War was practically over.
After the capitulation at Warrington, Cromwell turned northwards
again as soon as his soldiers could march. Monro and his six
thousand men were still undisposed of, and he feared an attack from
them upon the forces left at Preston. Colonel Ashton, who
commanded at Preston, had under his charge prisoners more in
number than his troops, and like Henry V. at Agincourt Cromwell
had ordered Ashton to put the prisoners to the sword if he were
attacked. But nothing was farther from Monro’s mind than an
advance. On the news of the defeat at Preston, he retreated at once,
marched through Durham, and re-entered Scotland. Garrisons were
left in Berwick and Carlisle, which Cromwell summoned as soon as
he came up, and when they refused to surrender he made a formal
application to the Scottish Committee of Estates for their restoration.
To give force to his demand he marched his army across the Tweed,
protesting at the same time that he had no quarrel with the Scottish
nation. If he entered Scotland it was simply to overthrow the faction
which had instigated the late invasion.
“We are so far from seeking the harm of the well affected people of Scotland, that
we profess as before the Lord, that we shall use our endeavours to the utmost that
the trouble may fall upon the contrivers and authors of this breach, and not upon
the poor innocent people, who have been led and compelled into this action, as
many poor souls now prisoners to us confess.”
A revolution in Scotland facilitated Cromwell’s policy. The rigid
Presbyterians of the west country, who abhorred any union with
Episcopalians and Malignants, and cared more for the Kirk than the
Crown, had risen in arms and seized Edinburgh. Argyle and his
Highlanders backed them, and on September 26th the Hamiltonian
faction, who formed the Committee of Estates, agreed to send
Monro’s force back to Ireland, to disband their men, and to give up
power to their rivals. Argyle’s party was only too glad to come to
terms with Cromwell, and to procure the support of his army against
their opponents, till they could organise a substantial force of their
own. Orders were sent for the immediate surrender of Carlisle and
Berwick, and Cromwell came to Edinburgh to treat with Argyle.
“Give assurance,” demanded Cromwell, “that you will not admit or
suffer any that have been active in or consenting to the engagement
against England, to be employed in any public place or trust
whatsoever. This is the least security I can demand.” There was
nothing the rival faction would more willingly do, and by an Act of
the Scottish Parliament “the Engagers,” as Hamilton’s partisans were
called, were permanently excluded from political power.
Cromwell left three regiments in Scotland for a few weeks to secure
the new government, and returned with the bulk of his army to
England. Scarborough and Pontefract still remained to be captured,
but the Second Civil War was over. Some of Cromwell’s friends
amongst the Independent leaders blamed his agreement with Argyle,
and saw no security for England in the predominance of a bigoted
Presbyterian faction at Edinburgh. They thought that Cromwell
should either have exacted more substantial guarantees for future
peace, or divided power between the two parties, so that they would
balance each other, and be incapable of injuring England. Cromwell
answered that the one hope of future peace between the two nations
lay in creating a good understanding between English Independents
and Scotch Presbyterians, and that he had taken the only course
which could produce it.
“I desire from my heart—I have prayed for—I have waited for the day to see—union
and right understanding between the godly people—Scots, English, Jews, Gentiles,
Presbyterians, Anabaptists, and all. Our brothers of Scotland—sincerely
Presbyterians—were our greatest enemies. God hath justified us in their sight—
caused us to requite good for evil—caused them to acknowledge it publicly by acts
of State and privately, and the thing is true in the sight of the Sun.... Was it not fit
to be civil, to profess love, to deal with clearness with them for the removing of
prejudices; to ask them what they had against us, and to give them an honest
answer? This we have done and no more: and herein is a more glorious work in our
eyes than if we had gotten the sacking and plunder of Edinburgh, the strong castle,
into our hands, and made a conquest from the Tweed to the Orcades; and we can
say, through God, we have left such a witness amongst them, as, if it work not yet,
by reason the poor souls are so wedded to their Church government, yet there is
that conviction upon them that will undoubtedly have its fruit in due time.”
He came back to England with the confident hope that peace with
Scotland was henceforth secure.
Operations Management 12th Edition Stevenson Solutions Manual
W
CHAPTER XI
CROMWELL AND THE KING’S EXECUTION
1648–1649
hile Fairfax and Cromwell were fighting the armies raised in
the King’s name, the Parliament was once more negotiating
with Charles I. In spite of the vote for no addresses, passed on
January 17, 1648, April was not over before both Houses were
discussing the reopening of negotiations. Petition after petition came
from the City demanding a personal treaty with the King, and the
House of Lords echoed the demand. The Lords were so zealous for a
peace that when Hamilton and the Scots invaded England they
refused to join the Lower House in declaring them enemies. The
Commons, more cautious, insisted that the King should accept
certain preliminaries before any treaty began, and refused to allow
him to come to London to treat. At last the two Houses arrived at a
compromise, and on August 1st it was agreed that there should be a
personal treaty with Charles in the Isle of Wight. The Commissioners
of Parliament met the King at Newport on September 18th, a couple
of days before Cromwell entered Scotland. Charles consented to
annul his former declarations against the Parliament, and to admit
that they had undertaken the war “in their just and lawful defence.”
He promised the establishment of the Presbyterian system for three
years, and a limited Episcopacy afterwards. He even offered the
control of the militia for twenty years and the settlement of Ireland
in such fashion as Parliament should think best. The question
whether these concessions were a sufficient basis for lasting peace is
one on which modern historians have differed as much as
contemporary politicians did. It is certain that the King was not
sincere in making them. “To deal freely with you,” wrote Charles to
one of his friends, “the great concession I made this day—the Church,
militia, and Ireland—was made merely in order to my escape.... My
only hope is, that now they believe I dare deny them nothing, and so
be less careful of their guards.” The Presbyterian leaders argued and
haggled in the hope of obtaining the permanent establishment of
Presbyterianism, but the question whether any treaty would bind the
King they neglected to take into account.
Meanwhile a dangerous excitement was spreading in the army. From
an agreement between the Presbyterians and the Royalists, an
Independent army had much to fear. The first result of the treaty
would be a general disbanding. To be dismissed with a few shillings
in his pocket, but without security for his arrears, or indemnity for
his acts during the war, was the most a soldier could expect. If any
sectary who had fought for the Parliament hoped that it would give
him freedom to worship as his conscience dictated, the act against
heresy and blasphemy, passed in May, 1648, had shown the futility
of his hopes. Whether Episcopacy or Presbyterianism gained the
upper hand, toleration would be at an end as soon as he laid down
his arms. Add to this, that the soldiers were firmly convinced that the
proposed treaty afforded no security for the political liberties of the
nation. Once restored to his authority, Charles would, either by force
or by intrigue, shake off the restrictions the treaty imposed, and rear
again that fabric of absolutism, which it had cost six years’ fighting to
overthrow. The renewal of the war had heightened their distrust of
Charles, and embittered their hostility to him. The responsibility for
the first Civil War had been laid upon the King’s evil counsellors; the
responsibility for the second was laid upon the King himself. It was
at his instigation, said the officers, that conquered enemies had taken
up arms again, old comrades apostatised from their principles, and a
foreign army invaded England. In a great prayer-meeting held at
Windsor before they separated for the campaign, they pledged
themselves to bring this responsibility home to the King. “We came,”
wrote one of them, “to a very clear resolution, that it was our duty, if
ever the Lord brought us back again in peace, to call Charles Stuart,
that man of blood, to an account for the blood he had shed, and
mischief he had done to the utmost, against the Lord’s cause and
people in these poor nations.” They were equally determined to
punish the King’s instruments. At the close of the first war, the army
had shown itself more merciful than the Parliament, but the second
war made it fierce, implacable, and resolute to exact blood for blood.
Fairfax’s execution of Lucas and Lisle, two royalist leaders taken at
Colchester, “in part of avenge for the innocent blood they have
caused to be spilt,” was a sign of this change of temper.
Cromwell shared this vindictive feeling towards the authors of the
second war. When he took Pembroke, he excepted certain persons
from the terms of the capitulation and reserved them for future
punishment.
“The persons excepted,” he wrote to Parliament, “are such as have formerly served
you in a very good cause; but being now apostatised, I did rather make election of
them than of those who had always been for the King; judging their iniquity
double, because they have sinned against so much light, and against so many
evidences of Divine Providence going along with and prospering a just cause, in the
management of which they themselves had a share.”
He was equally exasperated against those who had promoted the
Scottish invasion.
“This,” he said, “is a more prodigious treason than any that hath been perfected
before; because the former quarrel was that Englishmen might rule over one
another, this to vassalise us to a foreign nation. And their fault that appeared in
this summer’s business is certainly double to theirs who were in the first, because it
is the repetition of the same offence against all the witnesses that God hath borne.”
The moral he drew from his victory at Preston was that Parliament
should use it to protect peaceable Christians of all opinions, and
punish disturbers of the peace of every rank.
“Take courage,” he told them, “to do the work of the Lord in fulfilling the end of
your magistracy, in seeking the peace and welfare of this land—that all that will live
peaceably may have countenance from you, and they that are incapable, and will
not leave troubling the land, may speedily be destroyed out of the land. If you take
courage in this God will bless you, and good men will stand by you, and God will
have glory, and the land will have happiness by you in despite of all your enemies.”
When Cromwell returned from Scotland, he found the Parliament
preparing to replace the King on his throne, and to content itself with
banishing some dozen of the royalist leaders. Regiment after
regiment of Fairfax’s army was presenting its general with petitions
against the treaty and demands for the punishment of the authors of
the war. Cromwell’s troops imitated their example, and in forwarding
their petitions to Fairfax, their leader expressed his complete
agreement with his soldiers.
“I find,” he wrote, “a very great sense in the officers ... for the sufferings and ruin of
this poor kingdom, and in them all a very great zeal to have impartial justice done
upon all offenders; and I do in all from my heart concur with them, and I verily
think they are things which God puts into our hearts.”
On November 20, 1648, the army in the south sent Parliament a
“Remonstrance,” demanding the rupture of the negotiations, and the
punishment of the King as “the grand author of all our troubles.”
Cromwell approved of this declaration, and told Fairfax he saw
“nothing in it but what is honest, and becoming honest men to say
and offer.” It would have been better, he thought, to wait till the
treaty was concluded, before making their protest, but now that it
had been made he was prepared to support it. The Newport treaty
seemed to him to be a complete surrender to Charles. “They would
have put into his hands,” he said later, “all that we had engaged for,
and all our security would have been a little bit of paper.” No one
knew better than Cromwell that a mere protest would not stop the
Parliament, and he was ready to use force if necessary. The
arguments by which he justified its employment are fully stated in
his letter to his friend, Robert Hammond, whose scruples he sought
to overcome.
Was it not true that the safety of the people was the supreme law?
Was it not certain that this treaty would undo all that had been
gained by the war, and make things worse than before the war
began? If resistance to authority was lawful at all, was it not as lawful
to oppose the Parliament as it was to oppose the King?
“Consider,” he urged, “whether this army be not a lawful power called by God to
oppose and fight against the King upon some stated grounds; and being in power
to such ends, may not oppose one name of authority for those ends as well as
another name,—since it was not the outward authority summoning them that by its
power made the quarrel lawful, but the quarrel that was lawful in itself.”
These, however, were but “fleshly reasonings,” and there were higher
arguments. “Let us look into providences; surely they mean
somewhat. They hang so together; have been so constant, so clear,
unclouded.”
The victories God had given could not be meant to end in such a
sacrifice of His cause and His people as “this ruining hypocritical
agreement.” “Thinkest thou in thy heart that the glorious
dispensations of God point to this?” The determination of the army
to prevent the treaty was also God’s doing. “What think you of
Providence disposing the hearts of so many of God’s people this way?
We trust the same Lord who hath framed our minds in our actings is
with us in this also.” There were difficulties to be encountered and
enemies not few—“appearance of united names, titles, and
authorities”; yet they were not terrified, “desiring only to fear our
great God that we do nothing against His will.”
Briefly stated, Cromwell’s argument was that the victories of the
army, and the convictions of the godly, were external and internal
evidence of God’s will, to be obeyed as a duty. It was dangerous
reasoning, and not less dangerous that secular and political motives
coincided with the dictates of religious enthusiasm. Similar
arguments might be held to justify not merely the temporary
intervention of the army, but its permanent assumption of the
government of England. Practical good sense and conservative
instincts prevented Cromwell from adopting the extreme
consequences of his theory; with most of his comrades the logic of
fanaticism was qualified by no such considerations.
As Parliament continued the treaty without attending to their
Remonstrance, the army determined to employ force. On December
1st, officers sent by Fairfax seized Charles at Newport and removed
him to Hurst Castle in Hampshire. The next day, Fairfax and his
troops occupied London. Undeterred, the House of Commons
resolved by 129 votes to eighty-three that the King’s answers were a
ground to proceed upon for the settlement of the kingdom. The same
evening, the commanders of the army and the leaders of the
parliamentary minority held a conference to decide what was to be
done. On their march, the officers had declared their intention of
dissolving the Long Parliament, and constituting the faithful
minority a provisional government until a new Parliament could
meet. But now, in deference to the wishes of their friends in
Parliament, they resolved, instead, to expel the Presbyterian majority
from the House, and to leave the Independent minority in possession
of the name and authority of a Parliament. On December 6th,
accordingly, Colonel Pride and a body of musketeers beset the doors
of the House of Commons, seized some members as they sought to
enter, and turned others back by force. The same process continued
on the 7th, till forty-five members were under arrest, and some
ninety-six others excluded.
Cromwell arrived at London on the night after “Pride’s Purge” began,
and took his seat next day amongst the fifty or sixty members who
continued to sit in the House. Like the rest of the officers, he had
contemplated a forcible dissolution and the calling of a new
Parliament. But seeing that a different plan had been adopted by his
friends on the spot, he did not hesitate to accept it. He said, “that he
had not been acquainted with this design, but since it was done he
was glad of it, and would endeavour to maintain it.”
On the question of the King, a difference of opinion between
Cromwell and the bulk of the officers soon showed itself. He
approved of their seizure of Charles, and had no doubt of the justice
of bringing him to trial. But he doubted the policy of the King’s trial
and condemnation, if any other satisfactory expedient could be
devised to secure the rights of the nation. It might be that the King’s
deposition would be sufficient, or that he would at last make the
concessions which he had hitherto refused. Of the discussions which
went on in the council of officers during the next three weeks very
little is known. There are vague rumours of a great division of
opinion amongst them, of one party sternly insisting on the King’s
punishment, of another willing to be content with his deposition or
imprisonment. We get glimpses of Cromwell negotiating with
lawyers and judges about the settlement of the nation, inspiring a
final attempt to come to terms with Charles, and arguing that it
would be safe to spare the King’s life, if he would accept the
conditions now offered him. All these attempted compromises failed.
The King preferred to part with his life rather than with his regal
power, and unless he yielded no constitutional settlement was
possible. So the military revolution, for a moment arrested in its
progress, moved inevitably forward, and Cromwell went with it.
On December 23rd, Charles was brought to Windsor. “The Lord be
with you and bless you in this great charge,” wrote Cromwell to the
governor, sending him therewith minute instructions for the safe-
keeping of his captive. On the same day, the House of Commons
appointed a committee “to consider how to proceed in the way of
justice against the King.” “If any man,” Cromwell is reported to have
said, “had deliberately designed such a thing, he would be the
greatest traitor in the world, but ‘the Providence of God’ had cast it
upon them.”
Five days later an ordinance was introduced erecting a tribunal to try
the King, to consist of three judges and a jury of 150 commissioners.
On January 2, 1649, the ordinance was transmitted to the Lords,
with a resolution declaring that “by the fundamental laws of this
kingdom it is treason in the King of England for the time being to
levy war against the Parliament and the kingdom of England.” The
unanimous rejection of this ordinance, and the discovery that the
judges would refuse the part assigned to them, did not make the
Commons draw back. A new ordinance was brought in, creating a
court of 135 commissioners, who were to act both as judge and jury,
and omitting the three judges. Fresh resolutions declared the people
the original of all just power, the House of Commons the supreme
power in the nation, and the laws passed by the Commons binding
without consent of King or Lords. This ordinance, or, as it was now
termed, act, was passed on January 6, 1649. It set forth that Charles
Stuart had wickedly designed totally to subvert the ancient and
fundamental laws of this nation, and in their place to introduce an
arbitrary and tyrannical government; that he had levied and
maintained a cruel war against Parliament and kingdom; and that
new commotions had arisen from the remissness of Parliament to
prosecute him. Wherefore that for the future “no chief officer or
magistrate whatsoever may presume to imagine or contrive the
enslaving or destroying of the English nation, and to expect impunity
for trying or doing the same,” the persons whose names followed
were appointed to try the said Charles Stuart. On the 19th of
January, the King was brought from Windsor to St. James’s, guarded
by troops of horse.
Ever since the eighth, the commissioners for the King’s trial had
been meeting in the Painted Chamber to settle their procedure. But
nearly half of those named refused to accept the duty laid upon them.
Some had fears for their own safety; some, political objections;
others objected to the constitution or authority of the court.
Algernon Sidney told his colleagues that there were two reasons why
he could not take part in their proceedings. First, the King could not
be tried by that court; secondly, that no man could be tried by that
court. “I tell you,” answered Cromwell, with characteristic scorn of
constitutional formulas, “we will cut off his head with the crown
upon it.”
Nevertheless, the question of their authority was a question to which
the court was bound to agree upon an answer. If a story told at the
trial of the Regicides may be trusted, the commissioners were still at
a loss for a formula on the morning of the 20th of January, when the
trial began. As they sat in the Painted Chamber, news was brought
that the King was landing at the steps which led up from the river.
“At which Cromwell ran to the window, looking on the King as he came up the
garden; he turned as white as the wall ... then turning to the board said thus: ‘My
masters, he is come, he is come, and now we are doing that great work that the
whole nation will be full of. Therefore I desire you to let us resolve here what
answer we shall give the King when he comes before us, for the first question he
will ask us will be by what authority and commission we do try him?’ For a time no
one answered. Then after a little space, Henry Marten rose up and said, ‘In the
name of the Commons in Parliament assembled and all the good people of
England.’”
About one o’clock the court adjourned to Westminster Hall. At the
upper or southern end of the Hall, a wooden platform had been
constructed, covering all the space usually occupied by the Courts of
Chancery and King’s Bench. A wooden partition rising about three
feet above the floor of this platform divided the court itself from the
body of the Hall. On the lower side of this partition, running across
the Hall from side to side, was a broad gangway fenced in by a
wooden railing, and a similar gangway ran right down the Hall to the
great door. Along the sides of the gangways, with their backs to the
railings, stood a line of musketeers and pikemen, whose officers
walked up and down the vacant space in the middle of the passages.
The mass of the audience stood within the railed spaces between the
sides of the Hall and the gangways, but on each side of the court
itself, and directly overlooking it, were two small galleries, one above
the other, reserved for specially favoured spectators. At the back of
the court, immediately under the great window, sat the King’s
judges, about seventy in number, ranged on four or five tiers of
benches which were covered with scarlet cloth. They wore their
ordinary dress as officers or gentlemen. In the back row, on each side
of the scutcheon bearing the arms of the Commonwealth of England,
sat Cromwell and Harry Marten. In the centre of the front row of the
judges, at a raised desk, sat Serjeant John Bradshaw, the president of
the court, and on each side of him his assistants, Lisle and Say,
dressed in black lawyer’s gowns. About the middle of the floor of the
court was a table where the two clerks were seated, and on the table
lay the mace and the sword of State. In the front of the court, at the
very edge of the platform, were three compartments, somewhat like
pews, the backs of which were formed by the low partition separating
the court from the Hall. In the central one were a crimson-velvet
arm-chair, and a small table covered with Turkey carpet, on which
were an inkstand and paper. Here sat the King, and in the partition
on his right were the three lawyers who were counsel for the
Commonwealth. The King had his face turned towards the president
and his back to the crowd in the body of the Hall. As the floor of the
court was higher than the floor of the Hall, the spectators stood, as it
were, in the pit of a theatre, but the partition somewhat intercepted
their view of the interior of the court. Yet they could see the King’s
head and shoulders above it.
Charles kept his hat on his head, and showed no sign of respect to
the court.
“The prisoner,” says the official account, “while the charge was reading, sat down
in his chair, looking sometimes on the High Court, and sometimes on the galleries,
and rose again, and turned about to behold the guards and spectators, and after sat
down, looking very sternly, and with a countenance not at all moved, till these
words ‘Charles Stuart to be a tyrant,’ traitor, etc., were read; at which he laughed,
as he sat, in the face of the court.”
Throughout the trial, as the King’s judges had anticipated, he
declined to admit the jurisdiction of the court. On each of the three
days when he appeared before it, on the 20th, the 22d, and the 23rd
of January, he maintained his refusal to plead. “Princes,” he had said
in a declaration published in 1629, “are not bound to give an account
of their actions but to God alone,” and he now consistently repeated
that “a king cannot be tried by any superior jurisdiction on earth.”
What excited more sympathy, however, was his association of the
rights of his subjects with his own, and his claim to be defending
both against the arbitrary power of the army.
“It is not my case alone,” he said; “it is the freedom and liberty of the people of
England; and do you pretend what you will, I stand more for their liberties. For if
power without law may make laws, may alter the fundamental laws of the
kingdom, I do not know what subject he is in England that can be sure of his life, or
anything that he calls his own.”
On Tuesday, the 23rd, after Charles had for a third time refused to
plead, the court adjourned to the Painted Chamber, and the more
determined members resolved to treat the King as contumacious,
and proceed to pronounce judgment against him. Others opposed
this course, and the next two days were spent in hearing evidence at
private meetings of the court in the Painted Chamber—partly in
order to gain time whilst the recalcitrant members of the court were
being converted. One after another, a number of witnesses deposed
that they had seen the King in arms against the Parliament. One had
seen the royal standard set up at Nottingham. Another had seen the
King at Newbury, in complete armour with his sword drawn, and had
heard him exhort a regiment of horse to stand by him that day, for
that his crown lay upon the point of the sword. A third swore that he
heard Charles encourage his soldiers to strip and beat their prisoners
when Leicester was stormed. Documents were also brought to prove
the King’s invitations to foreign forces to enter England. At length,
on the evening of Thursday, the 25th, a vote that the court would
proceed to sentence Charles Stuart to death was procured, and on
the morning of the 26th, sixty-two commissioners agreed to the
terms of the sentence which their committee had drawn up. It was
resolved, however, that the King should be brought before the court
to hear his sentence, instead of being condemned in his absence, and
this was doubtless done in order to give him a chance to plead, in
case he should repent of his contumacy.
On the afternoon of Saturday, January 27th, sixty-seven
commissioners took their seats in Westminster Hall, headed by
Bradshaw, who had now donned a scarlet gown in which to deliver
sentence. Once more Charles refused to plead, requesting that before
sentence was given he might be heard before the Lords and
Commons assembled in the Painted Chamber. He had something to
say, he declared, which was “most material for the welfare of the
kingdom and the liberty of the subject.... I am sure on it, it is very
well worth the hearing.” It was afterwards rumoured that he meant
to propose his own abdication, and the admission of his son to the
throne upon such terms as should have been agreed upon. The court
after a brief deliberation refused the request, and Bradshaw, after
setting forth the prisoner’s crimes and exhorting him to repentance,
ordered the clerk to read the sentence. The King strove to speak.
“Your time is now past,” replied Bradshaw, and bade the clerk read
on. After the sentence was read, all the commissioners stood up to
testify their assent. Once more Charles endeavoured to obtain a
hearing. “Sir, you are not to be heard after sentence,” was the
answer. He still struggled to be heard. “Guard, withdraw your
prisoner,” ordered the president. “I am not suffered to speak,” cried
the King. “Expect what justice other people will have.”
As the King was led from the Court, the soldiers gave a great shout,
crying fiercely, “Execution, execution!” Others, it was said, reviled
him as he passed by them, and blew their tobacco smoke in his face.
But outside, in the street, as he went from Westminster to Whitehall,
“shop-stalls and windows were full of people, many of whom shed
tears, and some of them with audible voices prayed for the King.” It
was clear that the feeling of the people was on the King’s side, and
that consideration, if no other, might well have induced the army
leaders even at the last to draw back. But even had they wished it, the
army would not have permitted them to do so. Moreover, Cromwell
all through the trial never wavered or hesitated, and his influence
kept the Regicides together. When the King’s judges came to be tried
for their own lives, some strove to represent themselves as acting
under coercion. One said that Cromwell and Ireton laid hold of him
and compelled him to take his place in the court; others described
Cromwell as forcing recalcitrant judges to sign the death-warrant,
and bearing down the little minority who wished the King to be
heard after sentence had been pronounced. Colonel Ingoldsby boldly
declared that Cromwell seized his hand and guided his pen, though
the truth is that Ingoldsby’s signature shows no signs of constraint.
Many such legends circulate in contemporary literature, fictitious in
themselves, yet all testifying to a well-founded popular impression.
Cromwell had made up his mind that the King must die, and when
his mind was made up he was inflexible. Against that will, all efforts
to save the King were futile. Fairfax was applied to by Prince Charles,
but while steadfastly refusing to take any part in the trial, he
remained in all other respects a passive tool in the hands of his
council of officers. The Dutch ambassadors appealed to Parliament,
but what remained of Parliament was helpless or obdurate.
The commissioners of the Scottish Parliament presented public
protests and made private appeals to the leaders of the army. They
argued with Cromwell, telling him that the Covenant obliged both
nations to preserve the King’s person, and that to proceed to
extremities against him was to break the league between England
and Scotland. Cromwell answered them by a discourse on the nature
of the regal power, asserting that a breach of trust in a king ought to
be punished more than any other crime. As to the Covenant, its end
was the defence of the true religion; if the King was the greatest
obstacle to the establishment of the true religion, they were not
bound to preserve him. “It pledged them,” he added, “to bring to
condign punishment all incendiaries and enemies to the cause, and
were small offenders to be punished and the greatest of all to go
free?”
Meanwhile, during Sunday and Monday, Charles prepared himself
for death. He spent much time in prayer with Bishop Juxon, burnt
his papers, distributed the small remains of his personal property,
and took leave of his children. As he feared that the army would
make the Duke of Gloucester king, he charged him in simple
language not to take his “brother’s throne.”
“Sweetheart,” said Charles, taking the child upon his knee, “now they will cut off
thy father’s head [upon which words the child looked very steadfastly upon him];
mark, child, what I say: They will cut off my head, and perhaps make thee a king;
but mark what I say: You must not be a king so long as your brothers Charles and
James do live; for they will cut off your brothers’ heads when they can catch them,
and cut off thy head, too, at the last; and therefore I charge you do not be made a
king by them.”
At which the child, sighing, said, “I will be torn in pieces first.” What
Charles said to his daughter, the Lady Elizabeth herself related:
“He wished me not to grieve and torment myself for him, for it would be a glorious
death that he should die, it being for the laws and liberties of this land, and for
maintaining the true Protestant religion. He told me he had forgiven all his
enemies, and hoped God would forgive them also, and commanded us and all the
rest of my brothers and sisters to forgive them. He bid me tell my mother that his
thoughts had never strayed from her, and that his love should be the same to the
last.”
Then, striving to console her, he bade her again “not to grieve for
him, for that he should die a martyr, and that he doubted not but the
Lord would settle his throne upon his son, and that we should all be
happier than we could have expected to have been if he had lived.”
Monday night the King slept at St. James’s. Two hours before the
dawn of the 30th of January, he rose up, and, calling to his servant
Herbert, bade him dress him with care. “Let me have a shirt more
than ordinary,” said he, “by reason the season is so sharp as probably
may make me shake, which some will imagine proceeds from fear. I
would have no such imputation; I fear not death. Death is not
terrible to me. I bless my God I am prepared.”
About ten o’clock, Colonel Hacker came to fetch the King to
Whitehall. Attended by Herbert and Juxon, he walked through St.
James’s Park. A guard of halberdiers surrounded him, and
companies of foot were drawn up on each side of his way. “The
drums beat, and the noise was so great as one could hardly hear what
another spoke.” It was a cold, frosty morning, and the King walked,
as his custom was, very fast, and calling to his guard “in a pleasant
manner,” told them to march apace. When he reached Whitehall, he
was kept waiting in his bedchamber for two or three hours, perhaps
in order to give Parliament time to pass an act forbidding the
proclamation of any new king. During part of this time, he prayed
with Juxon, and at the bishop’s urging ate a mouthful of bread and
drank a glass of claret. About half-past one, Hacker came again to
summon the King to the scaffold. In the galleries and the Banqueting
House, through which Charles followed him, men and women had
stationed themselves to see the King go by. As he passed “he heard
them pray for him, the soldiers not rebuking any of them, seeming by
their silence and dejected faces afflicted rather than insulting.”
From the middle window of the Banqueting House, Charles stepped
out upon the scaffold. He was dressed in black from head to foot, but
not in mourning, and wore the George and the ribbon of the Garter.
The scaffold was covered with black cloth, and from the railings
round it, which were as high as a man’s waist, black hangings
drooped. In the middle of the scaffold lay the block, “a little piece of
wood, flat at bottom, about a foot and a half long,” and about six
inches high. By it lay “the bright execution axe for executing
malefactors,” which had been procured from the Tower—probably
the very axe which had beheaded Strafford. Near the block stood two
masked men; both were dressed in close-fitting frocks,—like sailors,
said one spectator; like butchers, said another. One of them wore a
grizzled periwig and seemed by his grey beard an old man.
Immediately round the foot of the scaffold stood ranks of soldiers,
horse and foot, and behind them a thronging mass of men and
women. Other watchers filled the windows and the roofs of the
houses round.
Seeing that his voice could not reach the people, Charles addressed
himself to the persons on the scaffold, some fourteen or fifteen in
number. He must clear himself, he said, as a man, a king, and a
Christian. To encroach on the liberties of the people had never been
his intent. The Parliament began this unhappy war, not himself. “But
for all this,” he continued, thinking of Strafford, “God’s judgments
are just. An unjust sentence that I suffered to take effect is now
punished by an unjust sentence upon me.”
Then the King forgave the causers of his death, and stated in a few
words his conception of the cause for which he died.
“For the people, I desire their liberty and freedom as much as anybody
whomsoever; but I must tell you that their liberty and freedom consists in having
government, in those laws by which their life and goods may be most their own. It
is not their having a share in government; that is nothing pertaining to them.... If I
would have given way to have all changed according to the power of the sword, I
needed not to have come here; and therefore I tell you (and I pray God it be not
laid to your charge) that I am the martyr of the people.”
CHARLES I.
(From an old
engraving.)
O horrable Murder
But lo a Charg is drawne, a day is set
The Silent Lamb is brought, the Wolves are met;
And where’s the Slaughterhouse? Whitehall must be,
Lately his Palace, now his Calvarie
And now ye Senators, is this the thing
So oft declard Is this your glorious King?
Religion vails her self; and Mourns that she
Is forc’d to own such Horrid Villanie.
When he had done, the King put his long hair under his cap, helped
by Juxon and the grey-bearded man in the mask, and spoke a few
words with Juxon. He took off his cloak and doublet, gave his
George[7]
to the bishop, and bade the executioner set the block fast.
Then, as he stood, he said two or three words to himself, with hands
and eyes lifted up, and lying down, placed his neck on the block. For
a moment he lay there praying; his eye shining, said one of those
who watched, as brisk and lively as ever he had seen it. Suddenly, he
stretched forth his hands, and with one blow the grey-bearded man
severed his head from his body. It was now, noted another spectator,
precisely four minutes past two.
The other masked man took the King’s head, and without a word
held it up to the people. A groan broke from the thousands round the
scaffold,—“such a groan,” writes Philip Henry, “as I never heard
before, and desire I may never hear again.” Thereupon he saw two
troops of horse, one marching towards Westminster, the other
towards Charing Cross, roughly dispersing the crowd, and was glad
to escape home without hurt.
The King’s body was placed in a plain wooden coffin, covered with a
black-velvet pall, then, after embalming, enclosed in an outer coffin
of lead, and conveyed to St. James’s. His servants wished to bury him
at Westminster, in Henry the Seventh’s Chapel, amongst his
ancestors, but this was denied, because “it would attract infinite
numbers of people of all sorts thither, which was unsafe and
inconvenient.” Windsor seemed safer, and the Parliament authorised
Herbert to bury his master there, allowing
five hundred pounds for the expenses of the funeral. Leave was given
to the Duke of Richmond, the Earl of Southampton, and two other
noblemen to attend it. They selected a vault in St. George’s Chapel,
where Henry VIII. and Jane Seymour were interred, and laid the
King’s body there on Friday, the 9th of February. No service was read
over him, for the governor would not allow Juxon to use the service
in the Prayer-book, saying that the form in the Directory was the
only one authorised by Parliament. To the mourners, however, it
seemed that heaven gave a token of their dead sovereign’s innocence.
“This is memorable,” writes Herbert, “that at such time as the King’s body was
brought out of St. George’s Hall the sky was serene and clear; but presently it
began to snow, and fell so fast, as by that time they came to the west end of the
royal chapel, the black velvet pall was all white, the colour of innocency, being
thick covered with snow.”
England mourned, but the army and its partisans rejoiced. At last the
blood shed in the Civil War was expiated by the death of its author.
“Blood defileth the land,” quoted Ludlow, “and the land cannot be
cleansed of the blood that is shed therein, but by the blood of him
that shed it.” The publicity and formality of the proceedings against
the King, which seemed to most men an insulting mockery of justice,
was to the Regicides themselves a source of exultation. “We did not
assassinate, nor do it in a corner,” said Scot. “We did it in the face of
God, and of all men.” A tradition, supported by some contemporary
stories, tells that Cromwell himself came by night to see the body of
the dead King in the chamber at Whitehall, to which it had been
borne from the scaffold. He lifted up the coffin lid, gazed for some
time upon the face, and muttered “Cruel necessity.” A royalist poet
represents him as haunted on his death-bed by “the pale image” of
the martyred monarch. Poetical justice required such retribution, but
history knows nothing of Cromwell’s repentance. He had been one of
the last men of his party to believe the King’s death a necessity, but
having persuaded himself that it was a just and necessary act he saw
no reason for remorse. It seemed to him that England had freed itself
from a tyrant “in a way which Christians in after times will mention
with honour, and all tyrants in the world look at with fear.”
T
CHAPTER XII
THE REPUBLIC AND ITS ENEMIES
1649
he execution of Charles I. was followed by the abolition of
monarchy. On February 6, 1649, the House of Commons voted
that the House of Lords was useless and dangerous, and that it ought
to be abolished. On February 8th, it resolved that the office of a king
was unnecessary, burdensome, and dangerous to the liberty, safety,
and public interest of this nation. Acts abolishing both followed, and
on May 19th a third Act established the English Republic. “England,”
it declared, “shall henceforth be governed as a Commonwealth, or a
Free State, by the supreme authority of this nation, the
representatives of the people in Parliament, and by such as they shall
appoint and constitute as ministers under them for the good of the
people.” Henceforth all writs were to run in the name of the Keepers
of the Liberty of England, and the Great Seal was to bear the picture
of the Parliament with the legend, “In the first year of Freedom by
God’s blessing restored.”
Exactly what they meant by “a Free State” the founders of the
Republic did not explain. Hobbes and Harrington agreed in defining
the new government as an oligarchy. A pamphleteer praised it as an
aristocracy. But the principles on which it was ostensibly based were
the principles of democracy. In their resolutions of January 4, 1649,
the House of Commons had declared that the people were, under
God, the original of all just power, and had based their claim to
override the Lords on that ground. In their declaration of the reasons
for establishing a republic, they asserted that kings were officials,
instituted by agreement amongst the people they governed, whom
the people had therefore a right to dethrone in case of
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  • 2. We believe these products will be a great fit for you. Click the link to download now, or visit testbankdeal.com to discover even more! Operations Management 12th Edition Stevenson Test Bank https://testbankdeal.com/product/operations-management-12th-edition- stevenson-test-bank/ Operations Management 11th Edition Stevenson Solutions Manual https://testbankdeal.com/product/operations-management-11th-edition- stevenson-solutions-manual/ Operations Management 13th Edition Stevenson Solutions Manual https://testbankdeal.com/product/operations-management-13th-edition- stevenson-solutions-manual/ Essentials of Political Analysis 5th Edition Pollock III Solutions Manual https://testbankdeal.com/product/essentials-of-political-analysis-5th- edition-pollock-iii-solutions-manual/
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  • 5. Chapter 08 - Location Planning and Analysis 8-1 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. CHAPTER 08 LOCATION PLANNING AND ANALYSIS Teaching Notes Facility location refers to the location of a service or manufacturing facility with respect to customers, suppliers, and other existing facilities such that it allows the company to gain a competitive and/or strategic edge. In making a location decision, both tangible costs (e.g., cost of operating the facility; cost of land (if it applies); cost of labor, taxes, and utilities; cost of inbound and outbound transportation) and intangible costs (e.g., availability of qualified labor and labor climate) must be considered. Because the location decision usually involves making a large capital investment, it not only affects the firm’s ability to compete but also has long-term strategic implications. Therefore, in making the location decision, we should consider issues related to marketing, production, transportation and other relevant costs as well as the strategy of the organization. The importance of various factors in relation to the location decision will vary between service and manufacturing organizations and from industry to industry as well. Reading: Innovative MCI Unit Finds Culture Shock in Colorado Springs 1. The most severe fallouts from the move to Colorado were: a. Numerous key executives and engineers, and hundreds of the division’s minority population refused to relocate, or fled Colorado Springs soon after relocating. b. The move isolated engineers from top management and from marketing colleagues at headquarters, undermining collaboration. c. The professionals whom Mr. Liebhaber hoped to recruit proved difficult and expensive to woo to Colorado Springs. d. Thousands of workers (more than expected) took advantage of the relocation package, undercutting plans to recruit lower-cost employees in Colorado. e. The move cost more than $200 million, far more than anticipated, and most of the expected savings never materialized. 2. Mr. Liebhaber should have sought out more information by conducting surveys of workers, managers, and engineers asking them for the following information: how likely they were to move, ratings of factors that would affect their decision to move, ratings of factors that they valued about their current work environment, and ratings about factors that they considered important for quality of life issues. Mr. Liebhaber seems to have considered his own quality of life and work issues only. Reading: Site Selection Grows Up: Improved Tech Tools Make the Process Faster, Better 1. Tech tools have improved the process of site selection by providing in-depth market research analyzing traffic volumes, concentration of other retail businesses, and demographic data. In addition, some of these tools provide aerial photographs of proposed sites and surrounding areas. Some tools allow users to plug in the site characteristics criteria and a proposed location and then push a button to receive output such as maps, reports, and models. Other tools provide market optimization software that informs the user on how best to carve out territories, helping to eliminate encroachment and cannibalization. 2. Franchisors also can use geoVue and other similar tools to analyze changes in performance, demographics, or other factors that would warrant closing or relocating a facility.
  • 6. Chapter 08 - Location Planning and Analysis 8-2 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Answers to Discussion and Review Questions 1. Location decisions can have an impact on access to markets, costs (including materials, labor, rent, construction, and transportation), quality of work life (e.g., community-related factors), and growth potential. 2. The fact that similar businesses are located widely underscores the futility of searching for that “one best” location. However, it does not necessarily follow that little attention is needed in finding a suitable location. Many organizations that have not been successful are no longer in business (e.g., service stations in poor locations, motels bypassed by an expressway, and so on). Moreover, others currently in operation might be much more profitable in another location. For some businesses (e.g., restaurants) regional factors are not particularly significant, and even community-related factors are of little importance. However, site-related factors are extremely important. Similarly, there are numerous examples of firms that are less affected by community or site factors than they are by regional factors (i.e., nearness to market, labor, or raw materials). 3. Important community factors include size of the community, public transportation, schools, recreational facilities, libraries, restaurants, shopping centers, cultural and entertainment selections, and so on. 4. Manufacturing and non-manufacturing organizations tend to approach location decisions in a similar way, but the factors that are important to each tend to differ. Although both tend to take costs and profits into consideration, manufacturing firms are often concerned with location of raw materials, transportation costs, availability of energy and water, and similar factors. Non- manufacturing firms often are more concerned with convenience, access to markets, traffic flow, and the like. 5. Foreign locations may offer lower taxes, access to markets, availability of raw materials, lower transportation costs (due to nearness to market), and lower labor costs than a comparable domestic location. Potential drawbacks often relate to the political and economic stability of the host country and attitudes of the populace towards a particular nation, industry, or firm. 6. Location rating, or factor rating, is a qualitative technique used to develop an overall composite index for an alternative, which can be used to compare location alternatives. It involves identifying relevant factors, assigning relative weights to the factors, and rating each alternative with respect to the factors. 7. The first step is to decide on the criteria to use to evaluate location alternatives (e.g., cost, profits, community service, etc.). The second step is to identify any important factors that will dominate the decision. The third step is to develop location alternatives (country, general region, small number of community alternatives, and site alternatives among the community alternatives). The fourth step is to evaluate the alternatives and make a selection. 8. Locational breakeven analysis generally assumes the following: a. Fixed costs are constant for the range of probable output. b. Variable costs are linear for the range of probable output. c. The level of output that will be required can be estimated within a narrow range. d. A single product is involved. 9. Recent trends include the location of foreign manufacturing plants in the United States, having smaller factories located close to markets, choosing nearby suppliers, low-cost labor is becoming less of a factor in many industries, and advances in information technology make it less important to have design, engineering, etc. close to the factory. Taking Stock 1. Due to economies of scale, the centrally located large facility will be more efficient. The scheduling and coordination between the large facility and suppliers or customers will be
  • 7. Chapter 08 - Location Planning and Analysis 8-3 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. simplified. However, due to distance, transportation/distribution costs to or from the large facility will be much higher than those costs would be when using several smaller dispersed facilities instead. Having several smaller dispersed facilities will not only reduce the transportation cost but also increase the flexibility of the firm in terms of being able to reduce distribution lead time, thus resulting in faster deliveries or receipts of goods or merchandise. 2. Unlike the process design decision, the facility location decision is a macro decision and thus requires the involvement of top-level management. The larger the facility, the higher the level of involvement of the company personnel will be. In terms of various functions or departments within the company, manufacturing (or operations), logistics and distribution, marketing, and strategic planning must be involved. Depending on the type of facility considered, other groups may also need to be included in making this important decision. 3. Due to the advancement of data mining and data warehousing, and the related improvements in computers’ ability to store and exchange data, we can generate much more useful information to make the facility location decision. Critical Thinking Exercises 1. The company does have some social responsibility. Because the company employs such a large percentage of the city’s workforce, its leaving is certain to have a major impact on town businesses. It is likely that unless new sources of employment emerge, some residents may be forced to move away, and many businesses may fail, or barely get by. Thus, the company must weigh the projected benefits of the move against the actual and social costs of the move. It also must factor in the primary reasons for the move. These might include high taxes, adverse weather conditions, a shift in its markets, poor public relations, labor strife, an aging facility that has to be replaced, an insufficient supply of essential labor skills, and a need to be closer to a major customer. 2. Trade-offs involved would include: a. The nature of current, and more importantly, the forecasted future demand. b. Current demographics and the future expected changes in demographics for this area. c. The nature and type of competition for this area. We will need to predict what our competitors will be doing in the short-term as well as in the long-term. d. We need to divide the area into several sub-areas and consider the advantages and disadvantages of opening a store in each of the sub-areas. e. What is the projected impact of the new location(s) on the sales of the existing locations? If the demand is too low and we decide to open more than one site, we will have to experience the cost of closing at least one of the existing locations and perhaps absorb the loss of sales in our existing store. On the other hand, if the demand is higher than we expected, and we opened up a store only on one site, we will have to consider the opportunity cost of lost sales and profit.
  • 8. Chapter 08 - Location Planning and Analysis 8-4 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3. Options Pros Cons Avoid such locations. Avoid the problem completely. Miss out on potential business. Locate there and deal with it. Potential business. Need to make sure workers know and abide by the policy. Risk cheating and possible consequences. When in Rome … (assuming “bribes” are more like “tips” to service people). Potential business. Probably a fine line between tipping and bribing, very risky. 4. Student answers will vary. Some possible answers follow: a. If a company located a manufacturing facility that creates heavy pollution adjacent to an elementary school or a retirement home, this action would violate the Common Good Principle. b. If the CEO of a corporation accepted a bribe to locate a new facility in a city, this action would violate the Virtue Principle. c. If an executive asked a subordinate to alter some numbers in a factor-scoring model so that the executive’s location choice came out on top, this action would violate the Rights Principle and the Virtue Principle. Solutions 1. Given: We have the following information shown below for two plant location alternatives: Omaha Kansas City R $185 $185 v $36 $47 Annual FC $1,200,000 $1,400,000 Expected annual demand (units) (Q) 8,000 12,000 Determine the expected profits per year for each alternative: Profit = Q(R – v) – FC Omaha: 8,000($185 – $36) – $1,200,000 = -$8,000 Kansas City: 12,000($185 – $47) – $1,400,000 = $256,000 Conclusion: Kansas City would produce the greater profit.
  • 9. Chapter 08 - Location Planning and Analysis 8-5 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 2. Given: We have the following information shown below for three potential locations for a new outlet: A B C R $2.65 $2.65 $2.65 v $1.76 $1.76 $1.76 Monthly FC $5,000 $5,500 $5,800 a. Determine the monthly volume necessary at each location to realize a monthly profit of $10,000 (round to 1 decimal). 𝑄 = 𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑒𝑑 𝑝𝑟𝑜𝑓𝑖𝑡+𝐹𝐶 𝑅−𝑣 Location A Volume: 𝑄 = 𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑒𝑑 𝑝𝑟𝑜𝑓𝑖𝑡+𝐹𝐶 𝑅−𝑣 = 10,000 + 5,000 2.65−1.76 = 16,853.9 𝑢𝑛𝑖𝑡𝑠 Location B Volume: 𝑄 = 𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑒𝑑 𝑝𝑟𝑜𝑓𝑖𝑡+𝐹𝐶 𝑅−𝑣 = 10,000 + 5,500 2.65−1.76 = 17,415.7 𝑢𝑛𝑖𝑡𝑠 Location C Volume: 𝑄 = 𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑒𝑑 𝑝𝑟𝑜𝑓𝑖𝑡+𝐹𝐶 𝑅−𝑣 = 10,000 + 5,800 2.65−1.76 = 17,752.8 𝑢𝑛𝑖𝑡𝑠 b. Determine the expected profits at each facility given the expected monthly volumes: A = 21,000 per month, B = 22,000 per month, & C = 23,000 per month. Profit = Q(R – v) – FC Location A: 21,000($2.65 – $1.76) – $5,000 = $13,690 per month Location B: 22,000($2.65 – $1.76) – $5,500 = $14,080 per month Location C: 23,000($2.65 – $1.76) – $5,800 = $14,670 per month Conclusion: Location C would yield the greatest profits.
  • 10. Chapter 08 - Location Planning and Analysis 8-6 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 3. Given: There are two alternatives for which costs and revenue are listed below: A B R $17,000 $17,000 v $14,000 $13,000 Annual FC $800,000 $920,000 a. Find the volume at which the two locations have the same total cost (TC). TC = FC + VC TC = FC + (Q x v) TC (Location A) = $800,000 + $14,000Q TC (Location B) = $920,000 + $13,000Q Set the two cost equations equal and solve for Q: $800,000 + $14,000Q = $920,000 + $13,000Q $14,000Q – $13,000Q = $920,000 – $800,000 $1,000Q = $120,000 Q = $120,000 / $1,000 Q = 120 units b. Range over which A and B would be superior: Location A has the lowest fixed costs; therefore, it is preferred at lower volumes. Conclusion: Location A Preferred: 0 < 120 units Location B Preferred: > 120 units 4. Given: There are three alternatives for which costs are given below: A (new) B (sub) C (expand) v $500 $2,500 $1,000 Annual FC $250,000 --- $50,000 a. Step 1: Determine the total cost equation for each alternative. TC = FC + VC TC = FC + (Q x v) A: TC = $250,000 + $500Q B: TC = $2,500Q C: TC = $50,000 + $1,000Q
  • 11. Chapter 08 - Location Planning and Analysis 8-7 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Step 2: Graph the alternatives. Step 3: Determine over what range each alternative is preferred. Looking at the graph, we can tell that Alternative B is preferred over the lowest range, Alternative C is preferred over the middle range, and Alternative A is preferred over the highest range. First, we find the indifference (break-even) point between Alternatives B & C by setting their total cost equations equal to each other and solving for Q. B: TC = $2,500Q C: TC = $50,000 + $1,000Q $2,500Q = $50,000 + $1,000Q $2,500Q – $1,000Q = $50,000 $1,500Q = $50,000 Q = $50,000 / $1,500 Q = 33.33 units Second, we find the indifference (break-even) point between Alternatives C & A by setting their total cost equations equal to each other and solving for Q. C: TC = $50,000 + $1,000Q A: TC = $250,000 + $500Q $50,000 + $1,000Q = $250,000 + $500Q $1,000Q – $500Q = $250,000 – $50,000 $500Q = $200,000 Q = $200,000 / $500 Q = 400 units A (new location) C (expansion) B (sub- contract) 33.3 100 200 300 400 500 400 300 200 100 0 TC ($000) B C A [250] [50] No. of Boats/yr.
  • 12. Chapter 08 - Location Planning and Analysis 8-8 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Conclusion: Alternative B preferred: < 33.33 units Alternative C preferred: > 33.33 units to < 400 units Alternative A preferred: > 400 units b. Expected volume of 150 boats: Based on the graph, Alternative C would yield the lowest total cost (TC) at a volume of 150 boats. c. Other factors that might be considered when deciding between the expansion and subcontracting alternatives include subcontracting costs will be known with greater certainty, subcontracting provides a secondary (backup) source of supply, and expansion offers more control over operations. 5. Rework Problem 4b using this additional information: Alternative A (New Location) will have an additional $4,000 in fixed costs per year. Alternative B (Subcontracting) will have $25,000 in fixed costs per year. Alternative C (Expansion) will have an additional $70,000 in fixed costs per year. Step 1: Change the costs in the table. A (new) B (sub) C (expand) v $500 $2,500 $1,000 Annual FC $254,000 $25,000 $120,000 Step 2: Determine the total cost equation for each alternative. TC = FC + VC TC = FC + (Q x v) A: TC = $254,000 + $500Q B: TC = $25,000 + $2,500Q C: TC = $120,000 + $1,000Q Step 3: Find TC for 150 units. A: TC = $254,000 + $500(150) = $329,000 B: TC = $25,000 + $2,500(150) = $400,000 C: TC = $120,000 + $1,000(150) = $270,000 Conclusion: Alternative C (Expand) would yield the lowest total cost for an expected volume of 150 boats.
  • 13. Chapter 08 - Location Planning and Analysis 8-9 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6. Given: Expected annual volume (Q) = 10,000 units. There are three lease alternatives for which costs are given below: Memphis Biloxi Birmingham Lease building & equipment $40,000 $60,000 $100,000 Transportation $50,000 $60,000 $25,000 v $8 $4 $5 Step 1: Determine fixed cost (FC) for each alternative & add FC to table. FC = Lease cost + transportation cost. Memphis Biloxi Birmingham Lease building & equipment $40,000 $60,000 $100,000 Transportation $50,000 $60,000 $25,000 Annual FC $90,000 $120,000 $125,000 v $8 $4 $5 Step 2: Determine the total cost equation for each alternative. TC = FC + VC TC = FC + (Q x v) Memphis: $90,000 + $8Q Biloxi: $120,000 + $4Q Birmingham: $125,000 + $5Q Step 3: Find TC for 10,000 units. Memphis: $90,000 + $8(10,000) = $170,000 Biloxi: $120,000 + $4(10,000) = $160,000 Birmingham: $125,000 + $5(10,000) = $175,000 Conclusion: The Biloxi alternative yields the lowest total cost for an expected annual volume of 10,000 units.
  • 14. Chapter 08 - Location Planning and Analysis 8-10 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7. Given: There are two alternative shop locations for which costs are shown below: City Outside R $90 $90 v $30 $40 Monthly FC $7,000 $4,700 a. (1) Monthly profit for Q = 200 cars: Step 1: Determine total profit equation for each alternative. Total profit = Q(R – v) – FC City: Q($90 – $30) – $7,000 Outside: Q($90 – $40) – $4,700 Step 2: Determine total profit for each alternative at the expected monthly volume. City: 200($90 – $30) – $7,000 = $5,000 Outside: 200($90 – $40) – $4,700 = $5,300 Conclusion: Outside location yields the greatest profit if monthly demand is 200 cars. (2) Monthly profit for Q = 300 cars: City: 300($90 – $30) – $7,000 = $11,000 Outside: 300($90 – $40) – $4,700 = $10,300 Conclusion: City location yields the greatest profit if monthly demand is 300 cars. b. Determine the indifference (break-even point) between the two locations. Set their total profit equations equal to each other and solve for Q: Q($90 – $30) – $7,000 = Q($90 – $40) – $4,700 $60Q – $7,000 = $50Q – $4,700 $60Q – $50Q = -$4,700 – (-$7,000) $10Q = $2,300 Q = $2,300 / $10 Q = 230 cars
  • 15. Chapter 08 - Location Planning and Analysis 8-11 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8. Given: We are provided the location factors below for four different types of organizations. Factor Local bank Steel mill Food warehouse Public school Convenience for customers Attractiveness of building Nearness to raw materials Large amounts of power Pollution controls Labor cost and availability Transportation costs Construction costs Student answers will vary regarding how they rate the importance of each factor in terms of making location decisions using L = low importance, M = moderate importance, and H = high importance. One possible set of answers is given below. Factor Local bank Steel mill Food warehouse Public school Convenience for customers H L M–H M–H Attractiveness of building H L M M–H Nearness to raw materials L H L M Large amounts of power L H L L Pollution controls L H L L Labor cost and availability L M L L Transportation costs L M–H M–H M Construction costs M H M M–H
  • 16. Chapter 08 - Location Planning and Analysis 8-12 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 9. Given: We are given factors, weights, and factor rating scores for three locations. Scores range from 1 – 100 (best). Location Score Factor Wt. A B C Convenience .15 80 70 60 Parking .20 72 76 92 Display area .18 88 90 90 Shopper traffic .27 94 86 80 Operating costs .10 98 90 82 Neighborhood .10 96 85 75 1.00 Multiply the factor weight by the score for each factor and sum the results for each location alternative. Weight x Score Factor Wt. A B C Convenience .15 .15(80) = 12.00 .15(70) = 10.50 .15(60) = 9.00 Parking .20 .20(72) = 14.40 .20(76) = 15.20 .20(92) = 18.40 Display area .18 .18(88) = 15.84 .18(90) = 16.20 .18(90) = 16.20 Shopper traffic .27 .27(94) = 25.38 .27(86) = 23.22 .27(80) = 21.60 Operating costs .10 .10(98) = 9.80 .10(90) = 9.00 .10(82) = 8.20 Neighborhood .10 .10(96) = 9.60 .10(85) = 8.50 .10(75) = 7.50 1.00 87.02 82.62 80.90 Conclusion: Based on composite score, Location A seems to be the best.
  • 17. Chapter 08 - Location Planning and Analysis 8-13 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10. Given: We are given factors, weights, and factor rating scores for three locations. Scores range from 1 – 100 (best). Location Score Factor Wt. East #1 East #2 West Initial Cost 8 100 150 140 Traffic 10 40 40 30 Maintenance 6 20 25 18 Dock space 6 25 10 12 Neighborhood 4 12 8 15 Multiply the factor weight by the score for each factor and sum the results for each location alternative. Weight x Score Factor Wt. East #1 East #2 West Initial Cost 8 8(100) = 800 8(150) = 1200 8(140) = 1120 Traffic 10 10(40) = 400 10(40) = 400 10(30) = 300 Maintenance 6 6(20) = 120 6(25) = 150 6(18) = 108 Dock space 6 6(25) = 150 6(10) = 60 6(12) = 72 Neighborhood 4 4(12) = 48 4(8) = 32 4(15) = 60 1518 1842 1660 Conclusion: Based on composite score, Location East #2 seems to be the best.
  • 18. Chapter 08 - Location Planning and Analysis 8-14 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 11. Given: We are given factors and factor rating scores for three locations. Scores range from 1 – 10 (best). Location Score Factor A B C Business services 9 5 5 Community services 7 6 7 Real estate cost 3 8 7 Construction costs 5 6 5 Cost of living 4 7 8 Taxes 5 5 4 Transportation 6 7 8 a. Assume that the manager weights each factor equally. Because there are seven factors, each factor will have a weight of 1/7. Therefore, we can sum the scores and divide by 7 to determine the weighted score for each alternative. Factor A B C Business services 9 5 5 Community services 7 6 7 Real estate cost 3 8 7 Construction costs 5 6 5 Cost of living 4 7 8 Taxes 5 5 4 Transportation 6 7 8 Total 39 44 44 Total / 7 5.57 6.29 6.29 Conclusion: Location B or C is best, followed by Location A.
  • 19. Chapter 08 - Location Planning and Analysis 8-15 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. b. Two of the factors (business services and construction costs) are given weights that are double the weights of the other factors. We will give these two factors weights of 2/9 and the other five factors weights of 1/9. Then, we will multiply each factor’s rating by that factor’s weight. Factor Location Score Weight Weight x Score Business Services 9 5 5 2/9 18/9 10/9 10/9 Community Services 7 6 7 1/9 7/9 6/9 7/9 Real Estate Cost 3 8 7 1/9 3/9 8/9 7/9 Construction Costs 5 6 5 2/9 10/9 12/9 10/9 Cost of Living 4 7 8 1/9 4/9 7/9 8/9 Taxes 5 5 4 1/9 5/9 5/9 4/9 Transportation 6 7 8 1/9 6/9 7/9 8/9 1.0 53/9 55/9 54/9 Conclusion: Location B is best, followed by Location C, and then Location A. 12. Given: A toy manufacturer produces toys in five locations and will ship raw materials from a new, centralized warehouse. The monthly quantities to be shipped to each location are identical. The coordinates for all five locations are shown below. Location X Y A 3 7 B 8 2 C 4 6 D 4 1 E 6 4 We know that the quantities to be shipped to each location are identical so we can eliminate quantities from consideration. The correct formulas for the center of gravity are shown below: 𝑥̅ = ∑ 𝑥𝑖 𝑛 𝑦 ̅ = ∑ 𝑦𝑖 𝑛
  • 20. Chapter 08 - Location Planning and Analysis 8-16 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Sum the values in each coordinate’s column. Location X Y A 3 7 B 8 2 C 4 6 D 4 1 E 6 4 Sum 25 20 n = 5 locations. 𝑥̅ = ∑ 𝑥𝑖 𝑛 = 25 5 = 5.0 (round to 1 decimal) 𝑦 ̅ = ∑ 𝑦𝑖 𝑛 = 20 5 = 4.0 (round to 1 decimal) Conclusion: The new warehouse should be located at 5.0, 4.0. 13. Given: A clothing manufacturer produces clothes at four locations. The manufacturer must determine the location of a central shipping point. The coordinates and weekly shipping quantities to the four locations are shown below. Location X Y Weekly Quantity (Q) A 5 7 15 B 6 9 20 C 3 9 25 D 9 4 30 The correct formulas for the center of gravity are shown below: 𝑥̅ = ∑ 𝑥𝑖𝑄𝑖 ∑ 𝑄𝑖 𝑦 ̅ = ∑ 𝑦𝑖𝑄𝑖 ∑ 𝑄𝑖 Sum the values in the quantity column. Location X Y Weekly Quantity (Q) A 5 7 15 B 6 9 20 C 3 9 25 D 9 4 30 Sum 90
  • 21. Chapter 08 - Location Planning and Analysis 8-17 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 𝑥̅ = ∑ 𝑥𝑖𝑄𝑖 ∑ 𝑄𝑖 = 5(15)+6(20)+3(25)+9(30) 90 = 6.0 (round to 1 decimal) 𝑦 ̅ = ∑ 𝑦𝑖𝑄𝑖 ∑ 𝑄𝑖 = 7(15)+9(20)+9(25)+4(30) 90 = 7.0 (round to 1 decimal) Conclusion: The central shipping point should be located at 6.0, 7.0. 14. Given: A company handling hazardous waste wants to minimize shipping cost for shipments to a disposal center from five stations that it operates. The coordinates for each of the five stations and the volumes shipped to the new disposal center are shown below. Location X Y Volume in Tons per Day (Q) 1 10 5 26 2 4 1 9 3 4 7 25 4 2 6 30 5 8 7 40 The correct formulas for the center of gravity are shown below: 𝑥̅ = ∑ 𝑥𝑖𝑄𝑖 ∑ 𝑄𝑖 𝑦 ̅ = ∑ 𝑦𝑖𝑄𝑖 ∑ 𝑄𝑖 Sum the values in the quantity column. Location X Y Volume Tons per Day (Q) 1 10 5 26 2 4 1 9 3 4 7 25 4 2 6 30 5 8 7 40 Sum 130 𝑥̅ = ∑ 𝑥𝑖𝑄𝑖 ∑ 𝑄𝑖 = 10(26)+4(9)+4(25)+2(30)+8(40) 130 = 6.0 (round to 1 decimal) 𝑦 ̅ = ∑ 𝑦𝑖𝑄𝑖 ∑ 𝑄𝑖 = 5(26)+1(9)+7(25)+6(30)+7(40) 130 = 6.0 (round to 1 decimal) Conclusion: The disposal center should be located at 6.0, 6.0.
  • 22. Chapter 08 - Location Planning and Analysis 8-18 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 15. Given: A company is considering two locations for a distribution center: L1 & L2. The five shipment destinations and the monthly shipments (Q) to all five destinations are shown below. Destination Q D1 900 D2 300 D3 700 D4 600 D5 1200 Step 1: Use the map to determine the coordinates of each destination (use a ruler if necessary). Add those coordinates to the table. Then, sum the values in the quantity column. Destination X Y Q D1 1 2 900 D2 2 4 300 D3 3 1 700 D4 4 2 600 D5 5 3 1200 Sum 3700 Step 2: Determine the center of gravity for the optimal location for the distribution center. The correct formulas for the center of gravity are shown below: 𝑥̅ = ∑ 𝑥𝑖𝑄𝑖 ∑ 𝑄𝑖 = 1(900)+2(300)+3(700)+4(600)+5(1200) 3700 = 3.2 (round to 1 decimal) 𝑦 ̅ = ∑ 𝑦𝑖𝑄𝑖 ∑ 𝑄𝑖 = 2(900)+4(300)+1(700)+2(600)+3(1200) 3700 = 2.3 (round to 1 decimal) Step 3: Use the map to determine the coordinates for L1 & L2. Use a ruler if necessary. L1 coordinates ≈ 2.6, 2.4 L2 coordinates ≈ 3.5, 2.5 Step 4: Determine the distance between each proposed location and the center of gravity. Distance between two points = |Difference in X coordinates| + |Difference in Y coordinates| Distance between L1 & Center of Gravity |2.6 – 3.2| + |2.4 – 2.3| = 0.6 + 0.1 = 0.7 Distance between L2 & Center of Gravity |3.5 – 3.2| + |2.5 – 2.3| = 0.3 + 0.2 = 0.5 Conclusion: L2 is closer to the center of gravity and is the better site.
  • 23. Chapter 08 - Location Planning and Analysis 8-19 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Case: Hello Walmart? [This is a good case for in-class discussion. Three groups can be formed: one to take the position of residents, one to take the position of small businesses, and one to take the position of Walmart.] 1. Owners of small businesses: Pro: Restaurants and other businesses that do not compete directly with Walmart generally would welcome the additional traffic that Walmart would attract. Con: Businesses that compete directly would not fare well unless they provided a product or service value that would offset Walmart’s lower price. 2. Residents: Pro: Another shopping option, lower prices, and other, non-competing businesses that would be attracted by the increased traffic that Walmart would generate. Con: Increased traffic and noise, construction inconveniences, loss of small-town atmosphere, and loss of local businesses and jobs. Walmart responses: The company would be a “good neighbor,” supporting the community and providing jobs for low-skilled and handicapped workers. Construction would create construction jobs and generate taxes and revenues for the community. Shoppers would benefit from Walmart’s low prices. In addition, there would be an increase in the tax base. Enrichment Module A. Distance Measurement B. Center of Gravity Method with Predetermined Sites C. Factor Scoring Model D. Emergency Facility Location A. Distance Measurement The companies measure distance when making two important decisions: 1. Facility Layout Decision: Distances are estimated/measured in determining the best layout of equipment or departments within a manufacturing facility such as a plant, a distribution facility such as a warehouse, or a service facility such as a department store. Distance is an important input in determining the best possible layout that minimizes the total distance traveled between departments or workstations. 2. Facility Location Decision: Distance measurement also is a very important input measure in determining the best location for a new service or a manufacturing facility, relocation of an existing facility, or elimination of an existing facility. In most instances, distance measurements are used to estimate the distances between existing warehouses or plants and the newly proposed potential location sites. The estimated distance measures then are used to estimate the transportation costs. Transportation cost is considered a critical factor in the facility location decision.
  • 24. Chapter 08 - Location Planning and Analysis 8-20 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Distance Measurement Methods: There are four methods of measuring distance: 1. Empirical Method 2. Rectilinear Method 3. Euclidean Method 4. Weighted Average Method 1. Empirical Method: The empirical method is the most accurate distance measure. Using the empirical method, distance can be measured in one of two ways. The first type of empirical measurement is the actual recorded travel distance, where a driver records the distance based on a vehicle odometer reading. The second type of empirical measurement of distance is estimation from a map. When there are no actual travel data available, then the map estimation can be very useful. However, the actual travel data obviously provides a more accurate measure of distance than the map estimation. The main advantage of using either empirical method is that they generally provide the most accurate distance measures. On the other hand, the disadvantage is that it can be very time consuming to gather the data and use it as a part of a computerized layout or a location technique, especially if there are many existing and/or proposed locations. 2. Rectilinear Method This mathematical method is very easy to compute and lends itself to easy implementation of computerized layout or location techniques. Rectilinear method requires the use of a two dimensional space with a horizontal axis, X, and a vertical axis, Y. Rectilinear distance often is called “Manhattan” distance because it requires going around the block when no straight- line route is available. If A and B are the locations in question, the Rectilinear distance between A and B is given by the following formula: Dr = B A B A Y Y X X − + − Where: Dr = Rectilinear distance measure between location A and location B; XA = X coordinate of location A; XB = X coordinate of location B; YA = Y coordinate of location A; YB = Y coordinate of location B.
  • 25. Chapter 08 - Location Planning and Analysis 8-21 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Example Problem—Calculation of the Rectilinear Distance: When answering this question, refer to textbook, Chapter 8, Problem 13. a. Determine the Rectilinear distance between location A and B. b. Determine the Rectilinear distance between location A and D. c. Determine the Rectilinear distance between location B and D. Solution to Example Problem—Measurement of Rectilinear Distance: a. The Rectilinear distance between location A and B is: Dr = B A B A Y Y X X − + − Dr = 3 9 7 6 5 = − + − b. The Rectilinear distance between location A and D is: Dr = D A D A Y Y X X − + − Dr = 7 4 7 9 5 = − + − c. The Rectilinear distance between location B and D is: Dr = D B D B Y Y X X − + − Dr = 8 4 9 9 6 = − + − The main advantage of this method is the ease of calculations, while the disadvantage is that it generally overestimates the distance. Because of its propensity to overestimate distance, Rectilinear distance is sometimes referred to as the pessimistic distance measurement method. Rectilinear measure of distance is more commonly used in solving facility layout problems. 3. Euclidean Method This mathematical method is based on the Pythagorean Theorem. Euclidean distance measures distance “as the crow flies” and is most applicable when a straight-line route is possible. The following formula for the hypotenuse of a right triangle provides us with the Euclidean distance: C2 = A2 + B2 or C = 2 2 B A + C is the side of a right triangle opposite the right angle, and A and B are the right degree sides of a right degree triangle. The Euclidean distance method also requires the use of a two dimensional space with a horizontal axis, X, and a vertical axis, Y. If F and G are the locations in question, then the Euclidean distance between F and G is given by the following formula:
  • 26. Chapter 08 - Location Planning and Analysis 8-22 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. ( ) ( )2 2 G F G F e Y Y X X D − + − = Where: De = Euclidean distance measure between location F and location G; XF = X coordinate of location F; XG = X coordinate of location G; YF = Y coordinate of location F; YG = Y coordinate of location G. Example Problem—Calculation of the Euclidean Distance: Refer to textbook, Chapter 8, Problem 13. a. Determine the Euclidean distance between location A and B. b. Determine the Euclidean distance between location A and D. c. Determine the Euclidean distance between location B and D. Solution to Example Problem—Calculation of the Euclidean Distance: a. b. c. The Euclidean distance is the direct or the shortest distance between two given sites. Therefore, for any given pair of sites, the Euclidean distance provides the most direct or the straight-line connection. In most cases, however, there is no straight route between a pair of locations. Therefore, the Euclidean measure provides an optimistic measure of distance and in most cases underestimates the true distance. ( ) ( ) ( ) ( ) 236 . 2 5 9 7 6 5 2 2 2 2 = = − + − = − + − = e e B A B A e D D Y Y X X D ( ) ( ) ( ) ( ) 5 25 9 16 4 7 9 5 2 2 2 2 = = + = − + − = − + − = e e e D A D A e D D D Y Y X X D ( ) ( ) ( ) ( ) 831 . 5 34 25 9 4 9 9 6 2 2 2 2 = = + = − + − = − + − = e e e D B D B e D D D Y Y X X D
  • 27. Chapter 08 - Location Planning and Analysis 8-23 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 4. Weighted Average Method As we discussed in the previous sections, the Rectilinear method is a conservative, pessimistic measure of distance, and the Euclidean method is an optimistic measure of distance. Both Euclidean and Rectilinear measures of distance are frequently the only standard distance options used as a part of many layout and location software programs. However, some managers prefer the weighted average method that provides a compromise distance between the optimistic Euclidean and the pessimistic Rectilinear methods. If A and B are the locations in question, then the weighted average distance between A and B is given by the following formula: ) ( ) ( ) ( ) ( r r e e wa D w D w D  +  = Where: Dr = Rectilinear distance measure between location A and location B; De = Euclidean distance measure between location A and location B; wr = weight associated with the Rectilinear distance; we = weight associated with the Euclidean distance. 0 1  i i i w w =  Example Problem—Calculation of the Weighted Average Distance: Refer to textbook, Chapter 8, Problem 13 and the two examples given earlier in this section. Assume that the pessimistic (Rectilinear) weight is 0.4 and the optimistic (Euclidean) weight is 0.6. a. Determine the weighted average distance between location A and B. b. Determine the weighted average distance between location A and D. c. Determine the weighted average distance between location B and D. Solution to Example Problem—Weighted Average a. The weighted average distance between location A and B is: DWA = (0.4)(3) + (0.6)(2.236) = 2.5416 b. The weighted average distance between location A and D is: DWA = (0.4)(7) + (0.6)(5) = 5.8 c. The weighted average distance between location B and D is: DWA = (0.4)(8) + (0.6)(5.831) = 6.7
  • 28. Chapter 08 - Location Planning and Analysis 8-24 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Exercise Problems 1. Refer to textbook Problem 15 in Chapter 8, and measure the Rectilinear distance between destination 1 and destination 5. 2. Refer to textbook Problem 15 in Chapter 8, and measure the Euclidean distance between destination 1 and destination 5. 3. Refer to textbook Problem 15 in Chapter 8, and measure the Weighted Average distance between destination 1 and destination 5 (wr = 0.3 and we = 0.7). 4. Refer to textbook Problem 15 in Chapter 8 and measure the Rectilinear distance between destination 1 and destination 3. 5. Refer to textbook Problem 15 in Chapter 8, and measure the Euclidean distance between destination 1 and destination 3. 6. Refer to textbook Problem 15 in Chapter 8, and measure the Weighted Average distance between destination 1 and destination 3 (wr = 0.5 and we = 0.5). Solutions to Exercise Problems 6181 . 2 ) 2361 . 2 )( 5 . 0 ( ) 3 )( 5 . 0 ( . 6 2361 . 2 5 . 5 3 1 2 3 1 . 4 3862 . 4 ) 1231 . 4 )( 7 . 0 ( ) 5 )( 3 . 0 ( . 3 1231 . 4 17 . 2 5 3 2 5 1 . 1 = + = = = = − + − = = + = = = = − + − = WA e r WA e r D D D D D D B. Center of Gravity Method with Predetermined Sites: (Weighted Distance Technique) The center of gravity method in its original form identifies a central location relative to its distance to other existing locations and the amount of goods shipped to and from other existing locations. However, the center of gravity method in its original form is unable to evaluate specific location alternatives. If we have narrowed the choice of the new location to a few known specific sites, then the weighted distance technique can evaluate these known locations. For each candidate site, a weighted distance value is computed using the following formula: i n i id w WD  = where:
  • 29. Chapter 08 - Location Planning and Analysis 8-25 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. WD = weighted distance value for a given site wi = weight associated with existing location i di = the distance between existing site i and the proposed location For a typical facility location problem, wi (weight) represents the amount of goods or units shipped between the proposed location and the existing location i. For a facility layout problem, wi (weight) represents the number of trips between the existing location i and the proposed location. Distance is calculated using either Rectilinear, Euclidean or Weighted Average methods. The site with the lowest weighted-distance would be selected, because the lowest weighted-distance usually results in the lowest transportation costs. Problem 1 Based on the destination locations and quantities given in textbook problem 15, the company is considering two locations for a new plant. The coordinates of the first plant location are: (x = 2, y = 3) and the coordinates of the second location are: (x = 4, y = 3). a. Determine the Euclidean distance from the first proposed plant location to all of the destination locations. b. Determine the Rectilinear distance from the first proposed plant location to all of the destination locations. c. Determine the Euclidean distance from the second proposed plant location to all of the destination locations. d. Determine the Rectilinear distance from the second proposed plant location to all of the destination locations. e. Determine the Weighted Distance value for the first and second proposed plant locations based on Euclidean distance and decide where the new plant should be located. f. Determine the Weighted Distance value for the first and second proposed plant locations based on Rectilinear distance and decide where the new plant should be located. Solution to Problem 1 Destination X coordinate Y coordinate Q D1 1 2 900 D2 2 4 300 D3 3 1 700 D4 4 2 600 D5 5 3 1200
  • 30. Chapter 08 - Location Planning and Analysis 8-26 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. a. Plant Site 1—Euclidean Distance From Plant Site 1 (P1) to Destination j (Dj) 3 9 ) 3 3 ( ) 5 2 ( ) ( Distance Euclidean 236 . 2 5 ) 2 3 ( ) 4 2 ( ) ( Distance Euclidean 236 . 2 5 ) 1 3 ( ) 3 2 ( ) ( Distance Euclidean 1 1 ) 4 3 ( ) 2 2 ( ) ( Distance Euclidean 414 . 1 2 ) 2 3 ( ) 1 2 ( ) ( Distance Euclidean 2 2 5 1 2 2 4 1 2 2 3 1 2 2 2 1 2 2 1 1 = = − + − = − = = − + − = − = = − + − = − = = − + − = − = = − + − = − D P D P D P D P D P b. Plant Site 1—Rectilinear Distance From Plant Site 1 (P1) to Destination j (Dj) 3 3 3 5 2 ) ( Distance r Rectilinea 3 2 3 4 2 ) ( Distance r Rectilinea 3 1 3 3 2 ) ( Distance r Rectilinea 1 4 3 2 2 ) ( Distance r Rectilinea 2 2 3 1 2 ) ( Distance r Rectilinea 5 1 4 1 3 1 2 1 1 1 = − + − = − = − + − = − = − + − = − = − + − = − = − + − = − D P D P D P D P D P c. Plant Site 2—Euclidean Distance From Plant Site 2 (P2) to Destination j (Dj) 1 1 ) 3 3 ( ) 5 4 ( ) ( Distance Euclidean 1 1 ) 2 3 ( ) 4 4 ( ) ( Distance Euclidean 236 . 2 5 ) 1 3 ( ) 3 4 ( ) ( Distance Euclidean 236 . 2 5 ) 4 3 ( ) 2 4 ( ) ( Distance Euclidean 162 . 3 10 ) 2 3 ( ) 1 4 ( ) ( Distance Euclidean 2 2 5 2 2 2 4 2 2 2 3 2 2 2 2 2 2 2 1 2 = = − + − = − = = − + − = − = = − + − = − = = − + − = − = = − + − = − D P D P D P D P D P
  • 31. Chapter 08 - Location Planning and Analysis 8-27 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. d. Plant Site 2—Rectilinear Distance From Plant Site 2 (P2) to Destination j (Dj) 1 3 3 5 4 ) ( Distance r Rectilinea 1 2 3 4 4 ) ( Distance r Rectilinea 3 1 3 3 4 ) ( Distance r Rectilinea 3 4 3 2 4 ) ( Distance r Rectilinea 4 2 3 1 4 ) ( Distance r Rectilinea 5 2 4 2 3 2 2 2 1 2 = − + − = − = − + − = − = − + − = − = − + − = − = − + − = − D P D P D P D P D P e. Weighted Distance Values Based on Euclidean Distances P1 = Plant 1 P2 = Plant 2 k = # of existing locations  = k i i id w 1 WDP1 = 900(1.414) + 300(1) + 700(2.236) + 600(2.236) + 1,200(3) = 8,079.4 WDP2 = 900(3.162) + 300(2.236) + 700(2.236) + 600(1) + 1,200(1) = 6,881.8 Because 6,881.8 < 8,079.4, choose proposed Plant Location 2. f. Weighted distance values based on Rectilinear distances WDP1 = 900(2) + 300(1) + 700(3) + 600(3) + 1,200(3) = 9,600 WDP2 = 900(4) + 300(3) + 700(3) + 600(1) + 1,200(1) = 8,400 Because 8,400 < 9,600, choose proposed Plant Location 2. C. Factor Scoring Model This simplistic selection procedure has many areas of application. The two most common areas of application are: 1) Facility Location; 2) Product Selection. Factor Scoring is a very flexible method that considers both tangible and intangible factors. It has the capability to consider multiple decision criteria simultaneously. Steps of the Factor Scoring Model: 1. Develop a list of (factors) criteria to be considered. The decision maker should consider these factors important in evaluating each decision alternative. 2. Assign a weight to each factor that describes the factor’s relative importance.
  • 32. Chapter 08 - Location Planning and Analysis 8-28 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Let wi = the weight for factor i, where i = 1, 2, ….., F F = the number of factors considered. The higher the weight, the more important the criterion. We will use a five-point scale to establish the relative importance of the factors considered. The following table provides an interpretation of the weight scale: Factor Weight Interpretation Table Importance Weight Very important 5 Somewhat important 4 Average importance 3 Somewhat unimportant 2 Very unimportant 1 For example, if a factor has a weight of 4, it is somewhat more important than the average factor. If a factor has a weight of 1, relative to the other factors being considered, the factor in question is very unimportant. 3. Determine a list of decision alternatives. Let dj = decision alternative j and assign a rating for each factor/decision alternative combination. Let rij = the rating for factor i and decision alternative j. Where j = 1, 2,……, D and D = number of decision alternatives considered.
  • 33. Chapter 08 - Location Planning and Analysis 8-29 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. For the purposes of rating each decision alternative/factor combination, we use the following 9-point scale. Level of Satisfaction Rating Extremely High 9 Very high 8 High 7 Slightly High 6 Average 5 Slightly Low 4 Low 3 Very Low 2 Extremely Low 1 For example, a score of 7 for a given decision alternative would indicate that the decision maker (manager) rates this decision alternative (location) high with respect to a given factor. 4. Compute the factor score for each decision alternative. Let Sj = factor score  = F i ij i j r w S 5. Sequence the decision alternatives from the highest score to the lowest score. The decision alternative with the highest factor score is the recommended decision alternative. The decision alternative with the second highest factor score is the second choice decision alternative and so on. Three popular areas of application for the Factor Scoring model are product selection, facility location, and job selection. Product selection and facility location are company-related problems while the job selection is an individual problem. An example for each of the three applications is provided in the following pages. PRODUCT SELECTION EXAMPLE An appliance manufacturing company is considering expanding its product line. It has sufficient capital to introduce only one of the three following products: 1. Microwave Ovens 2. Refrigerators 3. Stoves Management thinks that the following decision criteria should be used in selecting the product: 1. Manufacturing capability/cost
  • 34. Chapter 08 - Location Planning and Analysis 8-30 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 2. Market demand 3. Unit profit margin 4. Long term profitability/growth 5. Transportation costs 6. Useful life The company has determined the following weights for the decision criteria (factors): FACTOR WEIGHT Manufacturing capability/cost 4 Market demand 5 Unit profit margin 3 Long term profitability/growth 5 Transportation costs 2 Useful life 1 The decision factor ratings for each criteria are given in the following table: DECISION FACTOR RATINGS FACTOR MICROWAVE REFRIGERATOR STOVE 1 4 3 8 2 8 4 2 3 6 9 5 4 3 6 7 5 9 2 4 6 1 5 6 Based on the information provided, determine the factor scores for all three products. What is the best choice for the appliance manufacturing company? What is the second best choice?
  • 35. Other documents randomly have different content
  • 36. offered by the highest bidder. If negotiation failed, escape to France would not be difficult. For six months Charles had succeeded in playing off Parliament against Army, and Army against Parliament. But the result had been to make him thoroughly distrusted by both, and his flight from Hampton Court united them against him. The King had hoped much from the divisions of the army, but simultaneously with his arrival at Carisbrooke Cromwell and Fairfax reduced their troops to obedience again. On November 8th, Cromwell carried a vote for the temporary suspension of the sittings of the Council, and sent Agitators and officers back to their regiments. A week later Fairfax held a general review of the army, dividing it into three brigades, which met at three different places. At each review he solemnly engaged himself to the soldiers to stand by them in securing the redress of their military grievances and the reform of Parliament, exacting from them in return a signed pledge to obey the orders of the General and council of war. At the first rendezvous, which took place near Ware on November 15th, there was some opposition. The Levellers tried to convert it into a general demonstration in favour of the “Agreement of the People.” Two regiments came there unsummoned, wearing the “Agreement of the People” in their hats, with the motto, “England’s Freedom, Soldiers’ Rights.” They had driven away their own officers, called on other regiments to do the like, and planned the seizure of Cromwell as a traitor to the cause of the people. But when he rode up to the mutineers none dared to lay hands on him. “Lieutenant- General Cromwell’s carriage, with his naked waved sword, daunted the soldiers with the paper in their hats, and made them pluck it out and be subjected to command.” One soldier was tried, and shot on the field; others, including several officers, were reserved for the judgment of a future court-martial. On November 19th, Cromwell was able to report to Parliament that the army was very quiet and obedient, and received the thanks of the Commons for his services. Meanwhile the King sent a message to Parliament from the Isle of Wight, offering various concessions and asking to be admitted to a personal treaty at London. He applied also to the army leaders, urging them to support his request, to which they coldly replied that they were the Parliament’s army, and must refer those matters to it. Parliament, equally distrustful of Charles, answered his overtures by
  • 37. drawing up an ultimatum, consisting of four bills, to which his assent was required before any treaty should begin. Their chief demand was the direct control of the militia for the next twenty years, and a share in its control when that period ended. Other constitutional questions might be left to discussion, but they must make sure that the King could never use force to impose his will upon the nation. Driven to extremity by this demand, Charles turned once more to the Scottish Commissioners, who had now arrived at Carisbrooke. He found them ready enough to sacrifice the liberties of Englishmen, and they promised him restoration to all the rights of his crown in return for the three years’ establishment of Presbyterianism in England, the rigid suppression of Independents and other heretics, and certain privileges for Scotland and the Scottish nobility. If Parliament refused to disband its forces and to treat with the King in London, an army was to cross the border and replace Charles on his throne (December 27, 1647). “The Engagement,” as this treaty was termed, was wrapped in lead and buried in the castle garden till it could be safely smuggled out of the island. The next day the King definitely rejected the ultimatum of the English Parliament, and prepared to effect his escape to the continent. It was too late. As soon as the King’s answer was delivered, his guards were doubled and he was made a close prisoner. The two Houses were well aware that his refusal of their terms was due to some agreement with the Scots, although they were ignorant of its precise nature. “The House of Commons,” wrote Cromwell to Hammond, “is very sensible of the King’s dealings and of our brethren’s in this late transaction. You should do well, if you have anything that may discover juggling, to search it out, and let us know it. It may be of admirable use at this time, because we shall I hope go upon business in relation to them tending to prevent danger.” On January 3, 1648, the House of Commons voted that they would make no further addresses to the King, and receive no more messages from him. Cromwell and Ireton, who had opposed the resolution to that effect which Marten had brought forward in the previous September, now spoke earnestly in its favour. “It was now expected,” said Cromwell, “that the Parliament should govern and defend the kingdom by their own power, and not teach the people any longer to expect safety and government from an obstinate man
  • 38. whose heart God had hardened.” In such a policy, he added, the army would stand by the Parliament against all opposition: but if the Parliament neglected to provide for its own safety and that of the nation, the army would be forced to seek its own preservation by other means. Events had thus driven Cromwell to be the foremost advocate of that policy of completely setting aside the King which he had long so stubbornly opposed. Yet, though convinced that the King could not be trusted, he was not prepared to abandon monarchy. At a conference on the settlement of the government which took place early in 1648, the “Commonwealth’s-men,” as the republicans were termed, pressed for the immediate establishment of a free commonwealth and the trial of the King. Ludlow noted with great dissatisfaction that Cromwell and his friends “kept themselves in the clouds, and would not declare their judgments either for a monarchical, aristocratic, or democratic government; maintaining that any of them might be good in themselves, or for us, according as Providence should direct us.” When he pressed Cromwell privately for the grounds of his objection to a republic, Cromwell replied that he was convinced of the desirableness of what was proposed, but not of the feasibility of it. There is evidence that during the spring of 1648 the Independent leaders discussed a scheme for deposing Charles I., and placing the Prince of Wales or the Duke of York upon the throne. But the unwillingness of the Prince and the escape of the Duke to France frustrated this plan. While seeking to find some compromise which would prevent a new war, Cromwell endeavoured to unite all sections of the parliamentary party to meet it, if it came. The reunion of the army had already been effected. It was completed in a series of council meetings held at London during December, 1647, in which the officers under arrest for insubordination were pardoned, and a personal reconciliation took place between Cromwell and Rainsborough. In February and March, 1648, Cromwell made conciliatory overtures to the Presbyterians of the City, but as nothing short of the restoration of the King to his authority would content them, the negotiations failed. As little could Cromwell succeed in overcoming the distrust and hostility which the advanced party amongst the Independents now felt towards him. On January 19, 1648, John Lilburn, at the bar of
  • 39. the House of Lords, publicly accused him of high treason. Nor was it only his dealings with the King that made him the object of suspicion. During the last year his political attitude had continually altered. In April, he had urged the army to disband peaceably; in June, he had headed its revolt; in November, he had forced it into obedience to the Parliament again. And besides his apparent inconsistency, he was notoriously indifferent to principles which Levellers and Commonwealth’s-men held all-important. To them a republic meant freedom and a monarchy bondage. For him the choice between the two was a question of expediency, and dependent upon circumstances. In open council he had declared that he “was not wedded or glued to forms of government,” and in private he was said to have avowed that it was lawful to pass through all forms of government to accomplish his ends. It was not surprising, therefore, that men to whom his opportunism was unintelligible thought self- interest or ambition the natural explanation of his conduct, and that charges of hypocrisy and apostacy were freely made against him. Through this cloud of detraction Cromwell pursued his way unmoved. Sometimes he answered his accusers with blunt defiance. “If any man say that we seek ourselves in doing this, much good may it do him with his thoughts. It shall not put me out of my way.” At other times he referred to these slanders with a patient confidence that justice would be done to him in the end. “Though it may be,” he wrote in September, 1647, “for the present a cloud may lie over our actions to those not acquainted with the grounds of them; yet we doubt not but God will clear our integrity from any other ends we aim at but His glory and the public good.” Neither loss of popularity, misrepresentations, nor undeserved mistrust could diminish Cromwell’s zeal for the cause. “I find this only good,” he wrote on his recovery from a dangerous illness in the spring of 1648: “to love the Lord and His poor despised people, to do for them, and to be ready to suffer with them, and he that is found worthy of this hath obtained great favour from the Lord.” Not Cromwell’s utterances only but his acts testify to the integrity of his motives. In March, 1648, Parliament settled an estate upon him as a reward for his services, to which he responded by offering to contribute a thousand a year, out of the seventeen hundred it brought in, to be employed in the recovery of Ireland. And so little
  • 40. did he dream of ever becoming himself the ruler of England, that at the very moment when fortune had opened the widest field to ambition, he began negotiations for the marriage of his eldest son to the daughter of a private gentleman of no great influence or position.
  • 41. T CHAPTER X THE SECOND CIVIL WAR 1648 he Second Civil War broke out in Wales. It began with a revolt of officers and soldiers who had fought zealously for the Parliament throughout the first war. In February, 1648, Colonel Poyer, the governor of Pembroke Castle, refused to hand his charge over to the officer whom Fairfax had appointed to succeed him. In March, he openly declared for the King, and the troops of Colonel Laugharne, followed soon afterwards by their leader, joined Poyer’s forces. In April, it became known in London that the Scots were raising an army to invade England, and at the end of the month parties of English Royalists, by Scottish help, seized Berwick and Carlisle. To meet these two dangers Fairfax sent Cromwell to suppress the Welsh insurgents and prepared to march north himself against the Scots. At the beginning of May, Cromwell left London, taking with him two regiments of horse and three of foot. Poyer was full of confidence. He had won several small victories, and told his men that he would meet Cromwell in fair field, and that he would be himself the first man to charge “Ironsides,” adding that if Cromwell “had a back of steel and a breast of iron, he durst and would encounter with him.” But before Cromwell reached Wales, Colonel Horton defeated the boastful Poyer at St. Fagans, on May 8th, and when Cromwell arrived the war became a war of sieges. Chepstow was stormed by Colonel Ewer on May 25th, and Tenby surrendered to Colonel Horton at the end of May, but Pembroke Castle held out for over six weeks. Its walls were strong and its garrison desperate. Cromwell had no heavy artillery with him, and though he “scraped up,” as he said, a few little guns, and made a breach, his assaults were repulsed with loss. The hostility
  • 42. of the country people and want of provisions added to the difficulties of the besiegers. “It’s a mercy,” wrote Cromwell to Fairfax, “that we have been able to keep our men together in such necessity, the sustenance of the foot for the most part being bread and water.” The besieged, however, were in worse straits, and at last, on the 11th of July, starvation forced Poyer and Laugharne “to surrender themselves to the mercy of the Parliament” and give up town and castle. Three days before Pembroke fell, Hamilton and the Scottish army crossed the border, and Fairfax was not there to face them. London was seething with discontent: there were riots in the city and in the eastern counties, and mass petitions from Essex, Kent, and Surrey urged Parliament to come to terms with the King and to disband the army. At the end of May a royalist rising broke out in Kent, and the fleet in the Downs declared for the King. PEMBROKE CASTLE. (From a photograph.) Fairfax collected eight or nine thousand men and set out for Kent. On June 1st, he forced his way into Maidstone, where the main body of the Kentish Royalists had posted themselves, and, after hard fighting in the barricaded streets, mastered the town, and broke up the insurgent army. A part of them, under old Lord Norwich, marched towards London, but found the city gates closed against
  • 43. them, and dispersed. Norwich himself, with five or six hundred horse, crossed the Thames, and called the Royalists of Essex to arms. Ere long four thousand men gathered round him, and Fairfax, leaving detachments to complete the subjugation of Kent, hurried to Essex to suppress this new rising. Norwich threw himself into Colchester, and a bloody battle took place in the suburbs, in which the raw levies of the Royalists repulsed Fairfax’s veterans with great loss. The parliamentary general, seeing that he could not carry the town by a coup de main, was obliged to sit down to a regular siege, which ultimately developed into a blockade. Forts were built round Colchester, and connected by lines of intrenchments, to cut off all supplies and prevent any escape. The militia of Suffolk and Essex swelled Fairfax’s small force of regulars and completed the investment. The besieged fought well and made vigorous sallies, but unless help came from without the end was inevitable. When the siege began, such relief seemed very probable. All over England little local risings were incessantly breaking out which threatened to become general unless they were at once suppressed. In June, there were risings in North Wales, Northamptonshire, and Nottinghamshire. At the beginning of July, Lord Holland and the young Duke of Buckingham gathered about six hundred Cavaliers at Kingston in the hope of relieving Colchester. But they were hunted from place to place by Fairfax’s cavalry, and could never stay long enough anywhere to collect their partisans. The few who kept together were captured at St. Neots, in Huntingdonshire, on July 10th. At the end of July, Prince Charles and the revolted ships blockaded the Thames, hoping to persuade London to declare for the King by threatening its trade. But a fleet alone could not relieve Colchester, for Fairfax had occupied Mersea Island and cut off the town from the sea. Moreover, London remained quiet, for, though strongly Presbyterian in feeling, it had no desire to see the King restored unconditionally. The only hope of the besieged lay in the advance of Hamilton and the Scottish army. In the north of England the Parliament had no force afoot strong enough to stop the Scots from marching southwards. Major-General Lambert, the commander-in-chief in the northern counties, with three or four regiments of regular horse and the local levies of Yorkshire and Lancashire, more than held his own against the
  • 44. English Royalists under Langdale and Musgrave, defeating them in the field and reducing the garrison of Carlisle to extremities. But when Hamilton advanced to relieve his allies, Lambert could only fall back, stubbornly skirmishing, into north Yorkshire, leaving the Scots to overrun Cumberland and the north. He, too, was hampered by risings in his rear, for early in June Pontefract Castle had been surprised by the Royalists, and later in the month Scarborough had declared for the King. On the 8th of July, when Hamilton entered England, he brought with him no more than ten thousand or eleven thousand men, but additional forces followed later, and including the English Royalists under Langdale and Musgrave he had, by the next month, about twenty-four thousand men under his command. He marched slowly in order to give time for his reinforcements to come up, and spent some time in besieging Appleby and other northern castles. It was only about the middle of August that he resumed his advance and determined to push south through Lancashire. Meanwhile, Cromwell was hurrying north to Lambert’s aid. Even before Pembroke fell he had sent a portion of his horse northwards. As soon as it surrendered, he set out at once with the rest of his horse and the infantry. His men had not been paid for months, but his iron discipline kept them from plundering. The most part of his foot were shoeless and in rags, but boots were provided to meet them at Leicester. Marching by way of Gloucester and through the midlands, Cromwell reached Leicester on August 1st, Nottingham on August 5th, and joined Lambert near Knaresborough in the West Riding on Saturday, August 12th. Some regiments had to be left to besiege Pontefract and Scarborough, so that their united forces came to no more than about eight thousand five hundred men, of whom about three thousand were horse. But three quarters of this army were old soldiers, and, as one of Cromwell’s officers wrote, it was “a fine, smart army, fit for action.” Cromwell had hitherto been under the impression that the Scots intended to advance through Yorkshire, and, relieving Pontefract on their way, to march straight for London. He now learnt that Hamilton had chosen the Lancashire route, and was already on his way through that county. Accordingly, on Sunday, August 13th, he set out to cross the hills which separate Lancashire from Yorkshire, and to attack the invaders. On Monday night, he quartered at
  • 45. Skipton; on Tuesday night, at Gisburn. On Wednesday, he marched down the valley of the Ribble into Lancashire. Two courses were now open to him. He might cross by Hodder Bridge to the southern bank of the Ribble, and seek to bar Hamilton’s advance southwards by placing himself somewhere in his path; or he might keep along the northern bank of the river and engage Hamilton somewhere near Preston itself. Cromwell chose the second course, and he did so with a full consciousness of the importance of the choice. “It was thought,” he wrote, “that to engage the enemy to fight was our business,” and to march straight upon Preston was more likely to bring about a battle because it seemed probable that Hamilton would stand his ground there. There was also a second reason. If he put himself to the south of Hamilton, a defeat would throw Hamilton back upon his supports in Westmoreland and on the road to Scotland. If he defeated Hamilton at Preston, he might be able to drive him southwards, separating him from his supports, and cutting off his line of retreat. Under such circumstances, a defeat would lead to the annihilation of the Scottish army instead of merely forcing it to retire to Scotland. It was for these reasons, and not by any happy accident, that Cromwell adopted the second plan. As he explained a couple of years later, “Upon deliberate advice we chose rather to put ourselves between their army and Scotland.” All Wednesday, therefore, he continued his march down the northern bank of the Ribble, and camped his army for the night at Stonyhurst, about nine miles from Preston.
  • 46. Meanwhile, Hamilton’s army was marching through Lancashire as carelessly and loosely as if Cromwell were fifty miles away. Hamilton himself, with ten thousand foot and perhaps fifteen hundred horse, was at Preston. The Earl of Callendar and General Middleton, with the bulk of the Scottish horse, were at Wigan, fifteen miles ahead of the infantry, while thirty miles in the rear, at Kirby Lonsdale, in Westmoreland, lay Major-General Monro, with about three thousand veteran horse and foot drawn from the Scottish army in Ulster, and two or three thousand English Royalists under Sir Philip Musgrave. Between Cromwell and Preston, covering Hamilton’s flank, was Sir Marmaduke Langdale’s division of English Royalists, numbering three thousand foot and six hundred horse. Hamilton had been warned of the enemy’s approach by Langdale, but discredited his information, and believed he was threatened merely by some Lancashire militia forces. Early on Thursday, the 17th of August, Cromwell fell upon Langdale’s division with tremendous vigour, and beating his foot from hedge to hedge drove them towards Preston. Langdale sent pressing appeals to Hamilton, but the Duke gave him no adequate support. Instead of helping him, he drew the Scottish foot out of Preston and to the south of the Ribble, in order to facilitate their junction with the cavalry at Wigan. To defend Preston, he kept merely a couple of brigades of foot, and the fifteen hundred or sixteen hundred horse of
  • 47. his rearguard. Against forces so divided, Cromwell’s attack was irresistible. At nightfall on Thursday, Preston was in his possession, and not only the town but the bridge over the Ribble, and the second bridge over the Darwen, a mile or so to the south of it. His whole army was solidly planted between Hamilton and Scotland. Langdale’s division had ceased to exist, and of Hamilton’s two brigades of foot hardly a man had escaped. A thousand had fallen in the fight, Cromwell had four thousand prisoners, and his cavalry had chased Hamilton’s flying horse ten miles on the road to Lancaster. In the Scottish camp there was great distraction and depression. Hamilton’s forces were still superior in number to Cromwell’s, for he had six or seven thousand foot on the south side of the river, who had scarcely fired a shot, besides Middleton and the vanguard of cavalry at Wigan. But the Duke, who had shown plenty of personal courage, was weak and irresolute in council. Major-General Baillie, who commanded his foot, urged him to make a stand where he was until Middleton and the horse rejoined them. The Earl of Callendar, Hamilton’s second in command, proposed that the foot should march away as soon as it was dark, to join Middleton, and Callendar’s proposal was accepted. It involved the abandonment of Hamilton’s train, for they had no horses left to draw the waggons; and all the ammunition except what the men carried in their flasks fell into Cromwell’s hands. All night the Scottish infantry marched. “Our march,” says one of them, “was very sad, the way being exceeding deep, the soldiers both wet, hungry, and weary, and all looked on their business as half ruined.” They had lost many stragglers when they arrived at Wigan. On Friday morning, Cromwell, leaving the Lancashire militia to guard Preston and his prisoners, set out in pursuit of Hamilton with three thousand foot and twenty-five hundred horse. The fighting on Friday was mainly between the horse of the two armies. While the Scottish infantry were marching to Wigan to join Middleton, Middleton was marching to Preston to join them, and as he went by a different road they failed to meet. On reaching the camp of the infantry, he found nothing but deserted fires and a few stragglers, and turned back to follow Hamilton’s track to Wigan. Cromwell’s horsemen were at his heels all the way, “killing and taking divers,” though Colonel Thornhaugh, who commanded Cromwell’s van, was killed by a Scottish lancer.
  • 48. Hamilton’s army, when the horse joined, drew up on the moor, north of Wigan, as if to give battle, but, judging the ground disadvantageous, Hamilton retreated into the town before Cromwell came up. “We lay that night in the field,” says Cromwell, “close by the enemy, being very dirty and weary, and having marched twelve miles of such ground as I never rode in my life, the day being very wet.” There was no rest, however, for the Scots in Wigan. Their commanders resolved to make another night march to Warrington, intending to break down the bridge, and put the Mersey between themselves and their pursuer. On Saturday, Cromwell’s cavalry found the Scottish foot posted in a good position at Winwick, about three miles from Warrington. “We held them in dispute,” wrote Cromwell, “till our army came up, they maintaining the pass with great resolution for many hours, ours and theirs coming to push of pike and very close charges, which forced us to give ground; but our men by the blessing of God quickly recovered it, and charging very home upon them, beat them from their standing. We killed about a thousand of them, and took, as we believe, about two thousand prisoners.” This was the last stand the Scots made. When Cromwell reached Warrington the same Saturday evening, General Baillie and the rest of the Scottish infantry surrendered as prisoners of war. Hamilton and Callendar, with two or three thousand horse escaped into Cheshire, intending to join Lord Byron who was in arms for the King, but their fate was not long delayed. Cromwell sent Lambert with four regiments of horse in pursuit, and called on the neighbouring counties to send all the horses they could muster after the fugitives. “They are so tired, and in such confusion, that if my horse could but trot after them I could take them all. But we are so weary we can scarce be able to do more than walk after them. My horse are miserably beaten out—and I have ten thousand of them prisoners.” Skirmishing incessantly with the country people and the local militia, Hamilton made his way as far as Staffordshire, party after party of his followers dropping off by the way, either to surrender or to escape in disguise. With the few who remained, he capitulated to Lambert at Uttoxeter, on Friday, August 25th. On the Monday following, Colchester surrendered to Fairfax, and the Second Civil War was practically over.
  • 49. After the capitulation at Warrington, Cromwell turned northwards again as soon as his soldiers could march. Monro and his six thousand men were still undisposed of, and he feared an attack from them upon the forces left at Preston. Colonel Ashton, who commanded at Preston, had under his charge prisoners more in number than his troops, and like Henry V. at Agincourt Cromwell had ordered Ashton to put the prisoners to the sword if he were attacked. But nothing was farther from Monro’s mind than an advance. On the news of the defeat at Preston, he retreated at once, marched through Durham, and re-entered Scotland. Garrisons were left in Berwick and Carlisle, which Cromwell summoned as soon as he came up, and when they refused to surrender he made a formal application to the Scottish Committee of Estates for their restoration. To give force to his demand he marched his army across the Tweed, protesting at the same time that he had no quarrel with the Scottish nation. If he entered Scotland it was simply to overthrow the faction which had instigated the late invasion. “We are so far from seeking the harm of the well affected people of Scotland, that we profess as before the Lord, that we shall use our endeavours to the utmost that the trouble may fall upon the contrivers and authors of this breach, and not upon the poor innocent people, who have been led and compelled into this action, as many poor souls now prisoners to us confess.” A revolution in Scotland facilitated Cromwell’s policy. The rigid Presbyterians of the west country, who abhorred any union with Episcopalians and Malignants, and cared more for the Kirk than the Crown, had risen in arms and seized Edinburgh. Argyle and his Highlanders backed them, and on September 26th the Hamiltonian faction, who formed the Committee of Estates, agreed to send Monro’s force back to Ireland, to disband their men, and to give up power to their rivals. Argyle’s party was only too glad to come to terms with Cromwell, and to procure the support of his army against their opponents, till they could organise a substantial force of their own. Orders were sent for the immediate surrender of Carlisle and Berwick, and Cromwell came to Edinburgh to treat with Argyle. “Give assurance,” demanded Cromwell, “that you will not admit or suffer any that have been active in or consenting to the engagement against England, to be employed in any public place or trust whatsoever. This is the least security I can demand.” There was nothing the rival faction would more willingly do, and by an Act of
  • 50. the Scottish Parliament “the Engagers,” as Hamilton’s partisans were called, were permanently excluded from political power. Cromwell left three regiments in Scotland for a few weeks to secure the new government, and returned with the bulk of his army to England. Scarborough and Pontefract still remained to be captured, but the Second Civil War was over. Some of Cromwell’s friends amongst the Independent leaders blamed his agreement with Argyle, and saw no security for England in the predominance of a bigoted Presbyterian faction at Edinburgh. They thought that Cromwell should either have exacted more substantial guarantees for future peace, or divided power between the two parties, so that they would balance each other, and be incapable of injuring England. Cromwell answered that the one hope of future peace between the two nations lay in creating a good understanding between English Independents and Scotch Presbyterians, and that he had taken the only course which could produce it. “I desire from my heart—I have prayed for—I have waited for the day to see—union and right understanding between the godly people—Scots, English, Jews, Gentiles, Presbyterians, Anabaptists, and all. Our brothers of Scotland—sincerely Presbyterians—were our greatest enemies. God hath justified us in their sight— caused us to requite good for evil—caused them to acknowledge it publicly by acts of State and privately, and the thing is true in the sight of the Sun.... Was it not fit to be civil, to profess love, to deal with clearness with them for the removing of prejudices; to ask them what they had against us, and to give them an honest answer? This we have done and no more: and herein is a more glorious work in our eyes than if we had gotten the sacking and plunder of Edinburgh, the strong castle, into our hands, and made a conquest from the Tweed to the Orcades; and we can say, through God, we have left such a witness amongst them, as, if it work not yet, by reason the poor souls are so wedded to their Church government, yet there is that conviction upon them that will undoubtedly have its fruit in due time.” He came back to England with the confident hope that peace with Scotland was henceforth secure.
  • 52. W CHAPTER XI CROMWELL AND THE KING’S EXECUTION 1648–1649 hile Fairfax and Cromwell were fighting the armies raised in the King’s name, the Parliament was once more negotiating with Charles I. In spite of the vote for no addresses, passed on January 17, 1648, April was not over before both Houses were discussing the reopening of negotiations. Petition after petition came from the City demanding a personal treaty with the King, and the House of Lords echoed the demand. The Lords were so zealous for a peace that when Hamilton and the Scots invaded England they refused to join the Lower House in declaring them enemies. The Commons, more cautious, insisted that the King should accept certain preliminaries before any treaty began, and refused to allow him to come to London to treat. At last the two Houses arrived at a compromise, and on August 1st it was agreed that there should be a personal treaty with Charles in the Isle of Wight. The Commissioners of Parliament met the King at Newport on September 18th, a couple of days before Cromwell entered Scotland. Charles consented to annul his former declarations against the Parliament, and to admit that they had undertaken the war “in their just and lawful defence.” He promised the establishment of the Presbyterian system for three years, and a limited Episcopacy afterwards. He even offered the control of the militia for twenty years and the settlement of Ireland in such fashion as Parliament should think best. The question whether these concessions were a sufficient basis for lasting peace is one on which modern historians have differed as much as contemporary politicians did. It is certain that the King was not sincere in making them. “To deal freely with you,” wrote Charles to one of his friends, “the great concession I made this day—the Church,
  • 53. militia, and Ireland—was made merely in order to my escape.... My only hope is, that now they believe I dare deny them nothing, and so be less careful of their guards.” The Presbyterian leaders argued and haggled in the hope of obtaining the permanent establishment of Presbyterianism, but the question whether any treaty would bind the King they neglected to take into account. Meanwhile a dangerous excitement was spreading in the army. From an agreement between the Presbyterians and the Royalists, an Independent army had much to fear. The first result of the treaty would be a general disbanding. To be dismissed with a few shillings in his pocket, but without security for his arrears, or indemnity for his acts during the war, was the most a soldier could expect. If any sectary who had fought for the Parliament hoped that it would give him freedom to worship as his conscience dictated, the act against heresy and blasphemy, passed in May, 1648, had shown the futility of his hopes. Whether Episcopacy or Presbyterianism gained the upper hand, toleration would be at an end as soon as he laid down his arms. Add to this, that the soldiers were firmly convinced that the proposed treaty afforded no security for the political liberties of the nation. Once restored to his authority, Charles would, either by force or by intrigue, shake off the restrictions the treaty imposed, and rear again that fabric of absolutism, which it had cost six years’ fighting to overthrow. The renewal of the war had heightened their distrust of Charles, and embittered their hostility to him. The responsibility for the first Civil War had been laid upon the King’s evil counsellors; the responsibility for the second was laid upon the King himself. It was at his instigation, said the officers, that conquered enemies had taken up arms again, old comrades apostatised from their principles, and a foreign army invaded England. In a great prayer-meeting held at Windsor before they separated for the campaign, they pledged themselves to bring this responsibility home to the King. “We came,” wrote one of them, “to a very clear resolution, that it was our duty, if ever the Lord brought us back again in peace, to call Charles Stuart, that man of blood, to an account for the blood he had shed, and mischief he had done to the utmost, against the Lord’s cause and people in these poor nations.” They were equally determined to punish the King’s instruments. At the close of the first war, the army had shown itself more merciful than the Parliament, but the second
  • 54. war made it fierce, implacable, and resolute to exact blood for blood. Fairfax’s execution of Lucas and Lisle, two royalist leaders taken at Colchester, “in part of avenge for the innocent blood they have caused to be spilt,” was a sign of this change of temper. Cromwell shared this vindictive feeling towards the authors of the second war. When he took Pembroke, he excepted certain persons from the terms of the capitulation and reserved them for future punishment. “The persons excepted,” he wrote to Parliament, “are such as have formerly served you in a very good cause; but being now apostatised, I did rather make election of them than of those who had always been for the King; judging their iniquity double, because they have sinned against so much light, and against so many evidences of Divine Providence going along with and prospering a just cause, in the management of which they themselves had a share.” He was equally exasperated against those who had promoted the Scottish invasion. “This,” he said, “is a more prodigious treason than any that hath been perfected before; because the former quarrel was that Englishmen might rule over one another, this to vassalise us to a foreign nation. And their fault that appeared in this summer’s business is certainly double to theirs who were in the first, because it is the repetition of the same offence against all the witnesses that God hath borne.” The moral he drew from his victory at Preston was that Parliament should use it to protect peaceable Christians of all opinions, and punish disturbers of the peace of every rank. “Take courage,” he told them, “to do the work of the Lord in fulfilling the end of your magistracy, in seeking the peace and welfare of this land—that all that will live peaceably may have countenance from you, and they that are incapable, and will not leave troubling the land, may speedily be destroyed out of the land. If you take courage in this God will bless you, and good men will stand by you, and God will have glory, and the land will have happiness by you in despite of all your enemies.” When Cromwell returned from Scotland, he found the Parliament preparing to replace the King on his throne, and to content itself with banishing some dozen of the royalist leaders. Regiment after regiment of Fairfax’s army was presenting its general with petitions against the treaty and demands for the punishment of the authors of the war. Cromwell’s troops imitated their example, and in forwarding their petitions to Fairfax, their leader expressed his complete agreement with his soldiers.
  • 55. “I find,” he wrote, “a very great sense in the officers ... for the sufferings and ruin of this poor kingdom, and in them all a very great zeal to have impartial justice done upon all offenders; and I do in all from my heart concur with them, and I verily think they are things which God puts into our hearts.” On November 20, 1648, the army in the south sent Parliament a “Remonstrance,” demanding the rupture of the negotiations, and the punishment of the King as “the grand author of all our troubles.” Cromwell approved of this declaration, and told Fairfax he saw “nothing in it but what is honest, and becoming honest men to say and offer.” It would have been better, he thought, to wait till the treaty was concluded, before making their protest, but now that it had been made he was prepared to support it. The Newport treaty seemed to him to be a complete surrender to Charles. “They would have put into his hands,” he said later, “all that we had engaged for, and all our security would have been a little bit of paper.” No one knew better than Cromwell that a mere protest would not stop the Parliament, and he was ready to use force if necessary. The arguments by which he justified its employment are fully stated in his letter to his friend, Robert Hammond, whose scruples he sought to overcome. Was it not true that the safety of the people was the supreme law? Was it not certain that this treaty would undo all that had been gained by the war, and make things worse than before the war began? If resistance to authority was lawful at all, was it not as lawful to oppose the Parliament as it was to oppose the King? “Consider,” he urged, “whether this army be not a lawful power called by God to oppose and fight against the King upon some stated grounds; and being in power to such ends, may not oppose one name of authority for those ends as well as another name,—since it was not the outward authority summoning them that by its power made the quarrel lawful, but the quarrel that was lawful in itself.” These, however, were but “fleshly reasonings,” and there were higher arguments. “Let us look into providences; surely they mean somewhat. They hang so together; have been so constant, so clear, unclouded.” The victories God had given could not be meant to end in such a sacrifice of His cause and His people as “this ruining hypocritical agreement.” “Thinkest thou in thy heart that the glorious dispensations of God point to this?” The determination of the army
  • 56. to prevent the treaty was also God’s doing. “What think you of Providence disposing the hearts of so many of God’s people this way? We trust the same Lord who hath framed our minds in our actings is with us in this also.” There were difficulties to be encountered and enemies not few—“appearance of united names, titles, and authorities”; yet they were not terrified, “desiring only to fear our great God that we do nothing against His will.” Briefly stated, Cromwell’s argument was that the victories of the army, and the convictions of the godly, were external and internal evidence of God’s will, to be obeyed as a duty. It was dangerous reasoning, and not less dangerous that secular and political motives coincided with the dictates of religious enthusiasm. Similar arguments might be held to justify not merely the temporary intervention of the army, but its permanent assumption of the government of England. Practical good sense and conservative instincts prevented Cromwell from adopting the extreme consequences of his theory; with most of his comrades the logic of fanaticism was qualified by no such considerations. As Parliament continued the treaty without attending to their Remonstrance, the army determined to employ force. On December 1st, officers sent by Fairfax seized Charles at Newport and removed him to Hurst Castle in Hampshire. The next day, Fairfax and his troops occupied London. Undeterred, the House of Commons resolved by 129 votes to eighty-three that the King’s answers were a ground to proceed upon for the settlement of the kingdom. The same evening, the commanders of the army and the leaders of the parliamentary minority held a conference to decide what was to be done. On their march, the officers had declared their intention of dissolving the Long Parliament, and constituting the faithful minority a provisional government until a new Parliament could meet. But now, in deference to the wishes of their friends in Parliament, they resolved, instead, to expel the Presbyterian majority from the House, and to leave the Independent minority in possession of the name and authority of a Parliament. On December 6th, accordingly, Colonel Pride and a body of musketeers beset the doors of the House of Commons, seized some members as they sought to enter, and turned others back by force. The same process continued
  • 57. on the 7th, till forty-five members were under arrest, and some ninety-six others excluded. Cromwell arrived at London on the night after “Pride’s Purge” began, and took his seat next day amongst the fifty or sixty members who continued to sit in the House. Like the rest of the officers, he had contemplated a forcible dissolution and the calling of a new Parliament. But seeing that a different plan had been adopted by his friends on the spot, he did not hesitate to accept it. He said, “that he had not been acquainted with this design, but since it was done he was glad of it, and would endeavour to maintain it.” On the question of the King, a difference of opinion between Cromwell and the bulk of the officers soon showed itself. He approved of their seizure of Charles, and had no doubt of the justice of bringing him to trial. But he doubted the policy of the King’s trial and condemnation, if any other satisfactory expedient could be devised to secure the rights of the nation. It might be that the King’s deposition would be sufficient, or that he would at last make the concessions which he had hitherto refused. Of the discussions which went on in the council of officers during the next three weeks very little is known. There are vague rumours of a great division of opinion amongst them, of one party sternly insisting on the King’s punishment, of another willing to be content with his deposition or imprisonment. We get glimpses of Cromwell negotiating with lawyers and judges about the settlement of the nation, inspiring a final attempt to come to terms with Charles, and arguing that it would be safe to spare the King’s life, if he would accept the conditions now offered him. All these attempted compromises failed. The King preferred to part with his life rather than with his regal power, and unless he yielded no constitutional settlement was possible. So the military revolution, for a moment arrested in its progress, moved inevitably forward, and Cromwell went with it. On December 23rd, Charles was brought to Windsor. “The Lord be with you and bless you in this great charge,” wrote Cromwell to the governor, sending him therewith minute instructions for the safe- keeping of his captive. On the same day, the House of Commons appointed a committee “to consider how to proceed in the way of justice against the King.” “If any man,” Cromwell is reported to have
  • 58. said, “had deliberately designed such a thing, he would be the greatest traitor in the world, but ‘the Providence of God’ had cast it upon them.” Five days later an ordinance was introduced erecting a tribunal to try the King, to consist of three judges and a jury of 150 commissioners. On January 2, 1649, the ordinance was transmitted to the Lords, with a resolution declaring that “by the fundamental laws of this kingdom it is treason in the King of England for the time being to levy war against the Parliament and the kingdom of England.” The unanimous rejection of this ordinance, and the discovery that the judges would refuse the part assigned to them, did not make the Commons draw back. A new ordinance was brought in, creating a court of 135 commissioners, who were to act both as judge and jury, and omitting the three judges. Fresh resolutions declared the people the original of all just power, the House of Commons the supreme power in the nation, and the laws passed by the Commons binding without consent of King or Lords. This ordinance, or, as it was now termed, act, was passed on January 6, 1649. It set forth that Charles Stuart had wickedly designed totally to subvert the ancient and fundamental laws of this nation, and in their place to introduce an arbitrary and tyrannical government; that he had levied and maintained a cruel war against Parliament and kingdom; and that new commotions had arisen from the remissness of Parliament to prosecute him. Wherefore that for the future “no chief officer or magistrate whatsoever may presume to imagine or contrive the enslaving or destroying of the English nation, and to expect impunity for trying or doing the same,” the persons whose names followed were appointed to try the said Charles Stuart. On the 19th of January, the King was brought from Windsor to St. James’s, guarded by troops of horse. Ever since the eighth, the commissioners for the King’s trial had been meeting in the Painted Chamber to settle their procedure. But nearly half of those named refused to accept the duty laid upon them. Some had fears for their own safety; some, political objections; others objected to the constitution or authority of the court. Algernon Sidney told his colleagues that there were two reasons why he could not take part in their proceedings. First, the King could not be tried by that court; secondly, that no man could be tried by that
  • 59. court. “I tell you,” answered Cromwell, with characteristic scorn of constitutional formulas, “we will cut off his head with the crown upon it.” Nevertheless, the question of their authority was a question to which the court was bound to agree upon an answer. If a story told at the trial of the Regicides may be trusted, the commissioners were still at a loss for a formula on the morning of the 20th of January, when the trial began. As they sat in the Painted Chamber, news was brought that the King was landing at the steps which led up from the river. “At which Cromwell ran to the window, looking on the King as he came up the garden; he turned as white as the wall ... then turning to the board said thus: ‘My masters, he is come, he is come, and now we are doing that great work that the whole nation will be full of. Therefore I desire you to let us resolve here what answer we shall give the King when he comes before us, for the first question he will ask us will be by what authority and commission we do try him?’ For a time no one answered. Then after a little space, Henry Marten rose up and said, ‘In the name of the Commons in Parliament assembled and all the good people of England.’” About one o’clock the court adjourned to Westminster Hall. At the upper or southern end of the Hall, a wooden platform had been constructed, covering all the space usually occupied by the Courts of Chancery and King’s Bench. A wooden partition rising about three feet above the floor of this platform divided the court itself from the body of the Hall. On the lower side of this partition, running across the Hall from side to side, was a broad gangway fenced in by a wooden railing, and a similar gangway ran right down the Hall to the great door. Along the sides of the gangways, with their backs to the railings, stood a line of musketeers and pikemen, whose officers walked up and down the vacant space in the middle of the passages. The mass of the audience stood within the railed spaces between the sides of the Hall and the gangways, but on each side of the court itself, and directly overlooking it, were two small galleries, one above the other, reserved for specially favoured spectators. At the back of the court, immediately under the great window, sat the King’s judges, about seventy in number, ranged on four or five tiers of benches which were covered with scarlet cloth. They wore their ordinary dress as officers or gentlemen. In the back row, on each side of the scutcheon bearing the arms of the Commonwealth of England, sat Cromwell and Harry Marten. In the centre of the front row of the
  • 60. judges, at a raised desk, sat Serjeant John Bradshaw, the president of the court, and on each side of him his assistants, Lisle and Say, dressed in black lawyer’s gowns. About the middle of the floor of the court was a table where the two clerks were seated, and on the table lay the mace and the sword of State. In the front of the court, at the very edge of the platform, were three compartments, somewhat like pews, the backs of which were formed by the low partition separating the court from the Hall. In the central one were a crimson-velvet arm-chair, and a small table covered with Turkey carpet, on which were an inkstand and paper. Here sat the King, and in the partition on his right were the three lawyers who were counsel for the Commonwealth. The King had his face turned towards the president and his back to the crowd in the body of the Hall. As the floor of the court was higher than the floor of the Hall, the spectators stood, as it were, in the pit of a theatre, but the partition somewhat intercepted their view of the interior of the court. Yet they could see the King’s head and shoulders above it. Charles kept his hat on his head, and showed no sign of respect to the court. “The prisoner,” says the official account, “while the charge was reading, sat down in his chair, looking sometimes on the High Court, and sometimes on the galleries, and rose again, and turned about to behold the guards and spectators, and after sat down, looking very sternly, and with a countenance not at all moved, till these words ‘Charles Stuart to be a tyrant,’ traitor, etc., were read; at which he laughed, as he sat, in the face of the court.” Throughout the trial, as the King’s judges had anticipated, he declined to admit the jurisdiction of the court. On each of the three days when he appeared before it, on the 20th, the 22d, and the 23rd of January, he maintained his refusal to plead. “Princes,” he had said in a declaration published in 1629, “are not bound to give an account of their actions but to God alone,” and he now consistently repeated that “a king cannot be tried by any superior jurisdiction on earth.” What excited more sympathy, however, was his association of the rights of his subjects with his own, and his claim to be defending both against the arbitrary power of the army. “It is not my case alone,” he said; “it is the freedom and liberty of the people of England; and do you pretend what you will, I stand more for their liberties. For if power without law may make laws, may alter the fundamental laws of the
  • 61. kingdom, I do not know what subject he is in England that can be sure of his life, or anything that he calls his own.” On Tuesday, the 23rd, after Charles had for a third time refused to plead, the court adjourned to the Painted Chamber, and the more determined members resolved to treat the King as contumacious, and proceed to pronounce judgment against him. Others opposed this course, and the next two days were spent in hearing evidence at private meetings of the court in the Painted Chamber—partly in order to gain time whilst the recalcitrant members of the court were being converted. One after another, a number of witnesses deposed that they had seen the King in arms against the Parliament. One had seen the royal standard set up at Nottingham. Another had seen the King at Newbury, in complete armour with his sword drawn, and had heard him exhort a regiment of horse to stand by him that day, for that his crown lay upon the point of the sword. A third swore that he heard Charles encourage his soldiers to strip and beat their prisoners when Leicester was stormed. Documents were also brought to prove the King’s invitations to foreign forces to enter England. At length, on the evening of Thursday, the 25th, a vote that the court would proceed to sentence Charles Stuart to death was procured, and on the morning of the 26th, sixty-two commissioners agreed to the terms of the sentence which their committee had drawn up. It was resolved, however, that the King should be brought before the court to hear his sentence, instead of being condemned in his absence, and this was doubtless done in order to give him a chance to plead, in case he should repent of his contumacy. On the afternoon of Saturday, January 27th, sixty-seven commissioners took their seats in Westminster Hall, headed by Bradshaw, who had now donned a scarlet gown in which to deliver sentence. Once more Charles refused to plead, requesting that before sentence was given he might be heard before the Lords and Commons assembled in the Painted Chamber. He had something to say, he declared, which was “most material for the welfare of the kingdom and the liberty of the subject.... I am sure on it, it is very well worth the hearing.” It was afterwards rumoured that he meant to propose his own abdication, and the admission of his son to the throne upon such terms as should have been agreed upon. The court after a brief deliberation refused the request, and Bradshaw, after
  • 62. setting forth the prisoner’s crimes and exhorting him to repentance, ordered the clerk to read the sentence. The King strove to speak. “Your time is now past,” replied Bradshaw, and bade the clerk read on. After the sentence was read, all the commissioners stood up to testify their assent. Once more Charles endeavoured to obtain a hearing. “Sir, you are not to be heard after sentence,” was the answer. He still struggled to be heard. “Guard, withdraw your prisoner,” ordered the president. “I am not suffered to speak,” cried the King. “Expect what justice other people will have.” As the King was led from the Court, the soldiers gave a great shout, crying fiercely, “Execution, execution!” Others, it was said, reviled him as he passed by them, and blew their tobacco smoke in his face. But outside, in the street, as he went from Westminster to Whitehall, “shop-stalls and windows were full of people, many of whom shed tears, and some of them with audible voices prayed for the King.” It was clear that the feeling of the people was on the King’s side, and that consideration, if no other, might well have induced the army leaders even at the last to draw back. But even had they wished it, the army would not have permitted them to do so. Moreover, Cromwell all through the trial never wavered or hesitated, and his influence kept the Regicides together. When the King’s judges came to be tried for their own lives, some strove to represent themselves as acting under coercion. One said that Cromwell and Ireton laid hold of him and compelled him to take his place in the court; others described Cromwell as forcing recalcitrant judges to sign the death-warrant, and bearing down the little minority who wished the King to be heard after sentence had been pronounced. Colonel Ingoldsby boldly declared that Cromwell seized his hand and guided his pen, though the truth is that Ingoldsby’s signature shows no signs of constraint. Many such legends circulate in contemporary literature, fictitious in themselves, yet all testifying to a well-founded popular impression. Cromwell had made up his mind that the King must die, and when his mind was made up he was inflexible. Against that will, all efforts to save the King were futile. Fairfax was applied to by Prince Charles, but while steadfastly refusing to take any part in the trial, he remained in all other respects a passive tool in the hands of his council of officers. The Dutch ambassadors appealed to Parliament, but what remained of Parliament was helpless or obdurate.
  • 63. The commissioners of the Scottish Parliament presented public protests and made private appeals to the leaders of the army. They argued with Cromwell, telling him that the Covenant obliged both nations to preserve the King’s person, and that to proceed to extremities against him was to break the league between England and Scotland. Cromwell answered them by a discourse on the nature of the regal power, asserting that a breach of trust in a king ought to be punished more than any other crime. As to the Covenant, its end was the defence of the true religion; if the King was the greatest obstacle to the establishment of the true religion, they were not bound to preserve him. “It pledged them,” he added, “to bring to condign punishment all incendiaries and enemies to the cause, and were small offenders to be punished and the greatest of all to go free?” Meanwhile, during Sunday and Monday, Charles prepared himself for death. He spent much time in prayer with Bishop Juxon, burnt his papers, distributed the small remains of his personal property, and took leave of his children. As he feared that the army would make the Duke of Gloucester king, he charged him in simple language not to take his “brother’s throne.” “Sweetheart,” said Charles, taking the child upon his knee, “now they will cut off thy father’s head [upon which words the child looked very steadfastly upon him]; mark, child, what I say: They will cut off my head, and perhaps make thee a king; but mark what I say: You must not be a king so long as your brothers Charles and James do live; for they will cut off your brothers’ heads when they can catch them, and cut off thy head, too, at the last; and therefore I charge you do not be made a king by them.” At which the child, sighing, said, “I will be torn in pieces first.” What Charles said to his daughter, the Lady Elizabeth herself related: “He wished me not to grieve and torment myself for him, for it would be a glorious death that he should die, it being for the laws and liberties of this land, and for maintaining the true Protestant religion. He told me he had forgiven all his enemies, and hoped God would forgive them also, and commanded us and all the rest of my brothers and sisters to forgive them. He bid me tell my mother that his thoughts had never strayed from her, and that his love should be the same to the last.” Then, striving to console her, he bade her again “not to grieve for him, for that he should die a martyr, and that he doubted not but the
  • 64. Lord would settle his throne upon his son, and that we should all be happier than we could have expected to have been if he had lived.” Monday night the King slept at St. James’s. Two hours before the dawn of the 30th of January, he rose up, and, calling to his servant Herbert, bade him dress him with care. “Let me have a shirt more than ordinary,” said he, “by reason the season is so sharp as probably may make me shake, which some will imagine proceeds from fear. I would have no such imputation; I fear not death. Death is not terrible to me. I bless my God I am prepared.” About ten o’clock, Colonel Hacker came to fetch the King to Whitehall. Attended by Herbert and Juxon, he walked through St. James’s Park. A guard of halberdiers surrounded him, and companies of foot were drawn up on each side of his way. “The drums beat, and the noise was so great as one could hardly hear what another spoke.” It was a cold, frosty morning, and the King walked, as his custom was, very fast, and calling to his guard “in a pleasant manner,” told them to march apace. When he reached Whitehall, he was kept waiting in his bedchamber for two or three hours, perhaps in order to give Parliament time to pass an act forbidding the proclamation of any new king. During part of this time, he prayed with Juxon, and at the bishop’s urging ate a mouthful of bread and drank a glass of claret. About half-past one, Hacker came again to summon the King to the scaffold. In the galleries and the Banqueting House, through which Charles followed him, men and women had stationed themselves to see the King go by. As he passed “he heard them pray for him, the soldiers not rebuking any of them, seeming by their silence and dejected faces afflicted rather than insulting.” From the middle window of the Banqueting House, Charles stepped out upon the scaffold. He was dressed in black from head to foot, but not in mourning, and wore the George and the ribbon of the Garter. The scaffold was covered with black cloth, and from the railings round it, which were as high as a man’s waist, black hangings drooped. In the middle of the scaffold lay the block, “a little piece of wood, flat at bottom, about a foot and a half long,” and about six inches high. By it lay “the bright execution axe for executing malefactors,” which had been procured from the Tower—probably the very axe which had beheaded Strafford. Near the block stood two
  • 65. masked men; both were dressed in close-fitting frocks,—like sailors, said one spectator; like butchers, said another. One of them wore a grizzled periwig and seemed by his grey beard an old man. Immediately round the foot of the scaffold stood ranks of soldiers, horse and foot, and behind them a thronging mass of men and women. Other watchers filled the windows and the roofs of the houses round. Seeing that his voice could not reach the people, Charles addressed himself to the persons on the scaffold, some fourteen or fifteen in number. He must clear himself, he said, as a man, a king, and a Christian. To encroach on the liberties of the people had never been his intent. The Parliament began this unhappy war, not himself. “But for all this,” he continued, thinking of Strafford, “God’s judgments are just. An unjust sentence that I suffered to take effect is now punished by an unjust sentence upon me.” Then the King forgave the causers of his death, and stated in a few words his conception of the cause for which he died. “For the people, I desire their liberty and freedom as much as anybody whomsoever; but I must tell you that their liberty and freedom consists in having government, in those laws by which their life and goods may be most their own. It is not their having a share in government; that is nothing pertaining to them.... If I would have given way to have all changed according to the power of the sword, I needed not to have come here; and therefore I tell you (and I pray God it be not laid to your charge) that I am the martyr of the people.”
  • 66. CHARLES I. (From an old engraving.) O horrable Murder But lo a Charg is drawne, a day is set The Silent Lamb is brought, the Wolves are met; And where’s the Slaughterhouse? Whitehall must be, Lately his Palace, now his Calvarie And now ye Senators, is this the thing So oft declard Is this your glorious King? Religion vails her self; and Mourns that she Is forc’d to own such Horrid Villanie. When he had done, the King put his long hair under his cap, helped by Juxon and the grey-bearded man in the mask, and spoke a few words with Juxon. He took off his cloak and doublet, gave his George[7] to the bishop, and bade the executioner set the block fast. Then, as he stood, he said two or three words to himself, with hands and eyes lifted up, and lying down, placed his neck on the block. For a moment he lay there praying; his eye shining, said one of those who watched, as brisk and lively as ever he had seen it. Suddenly, he stretched forth his hands, and with one blow the grey-bearded man severed his head from his body. It was now, noted another spectator, precisely four minutes past two. The other masked man took the King’s head, and without a word held it up to the people. A groan broke from the thousands round the scaffold,—“such a groan,” writes Philip Henry, “as I never heard before, and desire I may never hear again.” Thereupon he saw two troops of horse, one marching towards Westminster, the other towards Charing Cross, roughly dispersing the crowd, and was glad to escape home without hurt. The King’s body was placed in a plain wooden coffin, covered with a black-velvet pall, then, after embalming, enclosed in an outer coffin of lead, and conveyed to St. James’s. His servants wished to bury him at Westminster, in Henry the Seventh’s Chapel, amongst his
  • 67. ancestors, but this was denied, because “it would attract infinite numbers of people of all sorts thither, which was unsafe and inconvenient.” Windsor seemed safer, and the Parliament authorised Herbert to bury his master there, allowing five hundred pounds for the expenses of the funeral. Leave was given to the Duke of Richmond, the Earl of Southampton, and two other noblemen to attend it. They selected a vault in St. George’s Chapel, where Henry VIII. and Jane Seymour were interred, and laid the King’s body there on Friday, the 9th of February. No service was read over him, for the governor would not allow Juxon to use the service in the Prayer-book, saying that the form in the Directory was the only one authorised by Parliament. To the mourners, however, it seemed that heaven gave a token of their dead sovereign’s innocence. “This is memorable,” writes Herbert, “that at such time as the King’s body was brought out of St. George’s Hall the sky was serene and clear; but presently it began to snow, and fell so fast, as by that time they came to the west end of the royal chapel, the black velvet pall was all white, the colour of innocency, being thick covered with snow.” England mourned, but the army and its partisans rejoiced. At last the blood shed in the Civil War was expiated by the death of its author. “Blood defileth the land,” quoted Ludlow, “and the land cannot be cleansed of the blood that is shed therein, but by the blood of him that shed it.” The publicity and formality of the proceedings against the King, which seemed to most men an insulting mockery of justice, was to the Regicides themselves a source of exultation. “We did not assassinate, nor do it in a corner,” said Scot. “We did it in the face of God, and of all men.” A tradition, supported by some contemporary stories, tells that Cromwell himself came by night to see the body of the dead King in the chamber at Whitehall, to which it had been borne from the scaffold. He lifted up the coffin lid, gazed for some time upon the face, and muttered “Cruel necessity.” A royalist poet represents him as haunted on his death-bed by “the pale image” of the martyred monarch. Poetical justice required such retribution, but history knows nothing of Cromwell’s repentance. He had been one of the last men of his party to believe the King’s death a necessity, but having persuaded himself that it was a just and necessary act he saw no reason for remorse. It seemed to him that England had freed itself
  • 68. from a tyrant “in a way which Christians in after times will mention with honour, and all tyrants in the world look at with fear.”
  • 69. T CHAPTER XII THE REPUBLIC AND ITS ENEMIES 1649 he execution of Charles I. was followed by the abolition of monarchy. On February 6, 1649, the House of Commons voted that the House of Lords was useless and dangerous, and that it ought to be abolished. On February 8th, it resolved that the office of a king was unnecessary, burdensome, and dangerous to the liberty, safety, and public interest of this nation. Acts abolishing both followed, and on May 19th a third Act established the English Republic. “England,” it declared, “shall henceforth be governed as a Commonwealth, or a Free State, by the supreme authority of this nation, the representatives of the people in Parliament, and by such as they shall appoint and constitute as ministers under them for the good of the people.” Henceforth all writs were to run in the name of the Keepers of the Liberty of England, and the Great Seal was to bear the picture of the Parliament with the legend, “In the first year of Freedom by God’s blessing restored.” Exactly what they meant by “a Free State” the founders of the Republic did not explain. Hobbes and Harrington agreed in defining the new government as an oligarchy. A pamphleteer praised it as an aristocracy. But the principles on which it was ostensibly based were the principles of democracy. In their resolutions of January 4, 1649, the House of Commons had declared that the people were, under God, the original of all just power, and had based their claim to override the Lords on that ground. In their declaration of the reasons for establishing a republic, they asserted that kings were officials, instituted by agreement amongst the people they governed, whom the people had therefore a right to dethrone in case of
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