Unit v operations mgt

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UNIT V
FACILITY, LAYOUT LOCATION AND
WORK MEASUREMENT
5.1 INTRODUCTION
The unit deals about one of the strategic decision in the operations management
namely plant location decision, the characteristics of different layouts are discussed. The
different techniques available to design the layout are also introduced. Work measurement
technique like time study, work sampling and methods time measurement are elaborated to
fix the standards for organizational activities. The impact of learning curve on the standard
and productivity improvement is also discussed.
5.2 LEARNING OBJECTIVES
1. To comprehend the factors to be considered for selecting the location.
2. To know the characteristics of different types of layout.
3. Understand the techniques to be adopted in designing the layout.
4. To establish the standards for different activities using standard techniques.
5. To construct learning curve and to comprehend the impact of learning curve in
standards and productivity.
5.3 FACILITY LOCATION
Facility location i.e. identifying the best location is a strategic decision in operation
management. This is a decision like any other strategic decisions like identifying the product,
choosing the technology, deciding the capacity etc. It is a long term decision. Once the
resources are committed taken back the resources involves more cost because of change in
the decision later. So you should be careful while identifying the various locations and
choosing the best one.
Need for the Decision
1. Research and development department of an organization come up with a new
product, to manufacture the product you need to incur the decision.
2. For the existing product, there is a lot of market potential so to tap the untapped
market you have to expand the capacity. To expand the capacity, you have to identify
the location.
3. Markets are served in a particular region, more competitions and high escalation of
cost. It is difficult to survive then identifying the location where there is untapped
market in the different regions.
4. Relocation required because of Tsunami, fire, flood, earthquake natural holocaust etc.
5.3.1 Selection of location

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Selection of the best location involves two phases:
5.3.1.1 Phase 1
In the phase I a preliminary feasibility study is carried out to assess the production input,
process technology, infrastructural facilities, social and cultural conditions and legal and
government considerations.

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Production Input:
Raw material:
It is important to assess the availability of raw material. The assessing is to be carried
out in the point of view of the transportation cost and the amount or deposit. Suppose if you
start a cement or aluminium industry the deposit of ore and how long it will be lost, that is to
be assessed. You have to see the present requirements and future requirements and choose
the place where the above conditions are fulfilled. The raw material supplier is for away then
the transportation cost dominates the price that makes you less competitive.
Labour inputs:
When you assess the labour input, the quality of the labour is important. You may find
the labours with fewer wages but the productivity of that labour may be low. So in addition
to bothering about that wages, you should assess then the skill level also.
You can see now more foreign IT companies sources India. The main reasons are those
companies identify abundant IT skills in India at comparatively lesser cost. So they sources
India.
Process Technology:
Some times the technology restricts the choice of location e.g. to start a pulp and paper
mills. You need water for processing so most of the pulp and paper mill industry are started
in the river banks.
Infrastructural facilities:
A study is very much required to asses well connected and land roads, parts, out parts,
railway lines telecommunication facilities etc. This is important because it reduces the
transportation cost and lead time. Lend time reduction show lot of saving in other costs. It
helps the organization to be a cost competitive.
Legal and political considerations:
Governments woo the corporate to start industry in their respective countries or state
through providing free land, exemption of taxes, subsided power tariffs, less cumbersome
licensing procedures. In addition the prospective person has to see that the legal formalities
and complication. He / she has to study the government stipulation about the pollution
standards to be exercised, zoning codes to be adopted import and export regulations
prescribed and construction specifications etc.
Social and cultural conditions:
This is the process of exploring the attitude of the people towards the plant to be started
over there. This study involves the skill availability and accessibility.
This study also involves the study about their demographic variables like the age
distribution, income distribution, their status, their life conditions their tradition. Here you
should explain in detail to make them aware of the usefulness of plant to up lift them both
economically and socially. At present in India since this process not carried out
systematically and scientifically many important projects are stalled by the people in many
states like West Bengal, Orissa, Tamil Nadu, to state a few.

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5.3.1.2 Phase – II
It there is a problem in the first phase, the second phase may not see the lime light.
In the phase 1 macro analysis is over, in the second phase the region, community and site
selection take place. Region include country to country or state-to-state within a country or
within a state different regions. The factors to be considered in the selection of region,
community and site are shown in the table.
The factors are considered under different major heading like infrastructure, market,
supply, and environment and internal. You should note that most of the factors are considered
in all the regional, community and site selection. For example, customer concentration and
trends are considered in all region, community and site selection.
Table 5.1
Regional selection Community Decision Site Decision
Infrastructure
Transportation network and
their costs
Transportation network and
their costs
Proximity to transportation
system
Utilities supply and costs Utilities supply and costs Utilities supply and costs
Market
Customer concentration and
trends.
trends.
trends.
Supply
Materials and supplies
availability & accessibility
Labour availability &
accessibility
Labour availability &
accessibility
Land and construction cost Site availability cost &
construction cost
Size of the site
Site costs
Environment
The intensity of unionization Community attitudes towards
the new facilities
Zoning restrictions
Climate Community service & taxes Proximally to related industry
Banking services Environmental impact
Government SOPS Government SOPS
Environmental regulations Environmental regulations
Internal
Preference of the management

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5.4 PLANT LOCATION SELECTION
The selection of plant is characterized by the subjective factors as well as the objective
factors. But it is very difficult to quantify subjective factors. The plant location evaluation is
done by considering both subjective and objective factors through a subjective evaluation
known as Rating Plan Method. You can see in the following section, how the rating plan is
applied to choose a place, where to start a Bio technology plant, in India.
To start a biotechnology plant what factors you consider and how do you evaluate the same
using rating plan method.
Selection Criteria
The important considerations for selecting a suitable location are given as follows:
a. Natural or climatic conditions.
b. Availability and nearness to the sources of raw material.
c. Transport costs-in obtaining raw material and also distribution or marketing
finished products to the ultimate users.
d. Access to market: small businesses in retail or wholesale or services should be
located within the vicinity of densely populated areas.
e. Availability of Infrastructural facilities such as developed industrial sheds or sites,
link roads, nearness to railway stations, airports or sea ports, availability of
electricity, water, public utilities, civil amenities and means of communications
are important, especially for small scale businesses.
f. Availability of skilled and non-skilled labour and technically qualified and trained
managers.
g. Banking and financial institutions are located nearby.
h. Locations with links: to develop industrial areas or business centers result in
savings and cost reductions in transport overheads, miscellaneous expenses.
i. Strategic considerations of safety and security should be given due importance.
j. Government influences: Both positive and negative incentives to motivate an
entrepreneur to choose a particular location are made available. Positive includes
cheap overhead facilities like electricity banking transport, tax relief, subsidies
and liberalization. Negative incentives are in form of restrictions for setting up
industries in urban areas for reasons of pollution control and decentralization of
industries.
k. Residence of small business entrepreneurs want to set up nearby their homelands
One study of locational considerations from small-scale units revealed that the native
place or homelands of the entrepreneur was the most important factor.
Heavy preference to homeland suggests that small-scale enterprise is not freely mobile.
Low preference for Government incentives suggests that concessions and incentives cannot
compensate for poor infrastructure.
In the rating plan method, ideal rating is considered for the factors, then how much
rating each location scores against each factor is assessed and best location is chosen based
on the highest total point.

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Table 5.2 - Rating Plan Method To Evaluate The Factors For Plant Location:
Factors
 Availability of technically qualified
skilled labor.
 Availability and nearness to the source
of material.
 Market Potential
 Access to the market
 Competitive Analysis
 Site Economics
 Positive Govt. Influences
 Strategic consideration of safety and
security
 Rent or buy the property
TOTAL POINT
Ideal Point
30
20
15
5
5
10
10
2
3
100
Lucknow
25
15
13
4
5
10
10
2
3
87
Bangalore
28
17
11
5
2
5
6
2
2
78
Pune
20
15
10
4
3
6
6
2
1
67
In the above table, Lucknow scores more than the Pune and Bangalore.
5.4.2 Cost analysis method:
In the previous section, you saw how the rating plan method is applied, to choose the
location. In this section, you can see a method, where only the objective factor is considered,
namely the cost factors i.e., to start a plant in a particular location, based on the labour
availability and accessibility, material availability and accessibility, you may have different
variable cost as well as fixed cost for each location. Now based on the estimated fixed cost
and variable cost, you can formulate for each location, a different a total cost equation. Once
the total cost equation is arrived for each location by applying the cost volume profit analysis,
you can estimate the range of production quantity at which the locations are preferred. You
can understand above method through exapmle5.1.
Example 5.1
Consider a corporate office, which wants to identify the best location. They have identified 3
locations after a preliminary survey. They are locations A, B and C. The corporate has
estimated the variable cost and fixed cost and then the total cost for the each location against
the production quantity. This is shown in the table.

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Table 5.3
SITE
Fixed cost
(Rupees in lakhs)
Variable cost
(Rupees per unit)
A 2.5 1000
B 3 750
C 4 500
Solution:
Considering site A and B,
the total cost for site A for ‘x’ quantities = 250000 + 1000x. ---- (1)
the total cost for site B for ‘x’ quantities = 300000 + 750x. ---- (2)
Therefore from (1) and (2),
x = (300000 – 250000)/(1000-750)
= 200 units.
Considering site B and C,
the total cost for site B for ‘x’ quantities = 300000 + 750x. ------ (3)
the total cost for site C for ‘x’ quantities = 400000 + 500x. -------(4)
Therefore from (3) and (4),
x = (400000 – 300000)/(750-500)
= 400 units.
Result,
If ‘x’ < 200 units, select site A as it has minimum fixed value.
If 200 < ’x’ < 400 units, select site B as it has minimum variable cost compared to
A and minimum total cost compared to C.
If ‘x’ > 400 units, select site C as it has the least variable cost.

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Graphical representation:
Figure 5.1
Review Questions
1) Define facility location.
2) When will you go for facility location?
3) What are the phases in the facility location?
4) What the methods used for plant location selection?
5.5 TYPES OF LAYOUT
After selecting plant location, based on the type of production system to be adopted,
the layout has to be decided. The types of layout are
1. Fixed product layout
2. Product layout
3. Group (flexible) layout
4. Process layout
5.5.1 Fixed Product Layout
The fixed product layout is developed by locating the workstations or production centers
on the fixed job. Fixed layout type is used when the job size is large. Logistics are involved in
ensuring that the right processes are brought to the product at the right time and at the right
place. This has been mainly used in electronic industry to support computer systems
integration and test; materials, sub assemblies, components, peripherals are brought to the
single workstation where finished system is built. This type of layout requires generally

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higher number of personnel and equipments than the other types, since the work piece
remains stationary.
Figure 5.2 – Fixed Product Layout
Advantages:
1. This method is highly flexible and any changes in product design and product mix can
be easily accommodated.
2. Since work centers are independent, scheduling results in achieving minimum total
production time
3. The teams of personnel are responsible for continuity of operations.
4. Movement of materials is reduced.
5. Job enlargement could be promoted by allowing individuals or teams to perform the
whole job.
Limitations:
1. Skilled labour is required.
2. Supervision is required.
3. Positioning of material and machinery is costly and complex
4. Equipment duplication may occur.
5. Utilization of equipment is required.
5.5.2 Product Layout
In this layout the machines are arranged according to the processing sequence of the
product. Material flows directly from one workstation to other workstation. Machines are not
shared by the products. This type of layout is used for high volume production. For proper
utilization of machines sufficient production volume is required. Since the processes are

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located closed together in the production sequence, the layout minimizes the distance
between the work center.
Figure 5.3 – Product Layout
Advantages:
1. The total production time is short.
2. The material handling is reduced because of the location of the machines to
minimize the distances between the consecutive operations.
3. Less skilled operator is required. Thus training is simple and short.
4. Less space is occupied by work in transit and temporary storage.
5. The flow is smooth and logical flow line results.
6. Small in process inventory as the work is directly fed from one process to other.
Limitations:
1. The production time is determined by the slowest machine.
2. A general supervision is required.
3. Since identical machines are arranged at various locations, initial investment is high.
4. A change in the product design requires an entire change in the layout.
5. A break down of one machine lead to complete stoppage of entire production.
5.5.3 Group Layout
When production volume is not sufficient for product layout, group layout is used. Here
products are grouped in to logical product families. The groups of processes are called cells.
So it is also called as cellular layout. It is a compromise between product and process layout.
Since products are grouped into families this technology is also called as group technology
with each individual cells are called GT cells.

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Figure 5.4 – Group Layout
Advantages:
1. This supports the use of general purpose equipments.
2. This is a compromise between product and process layout.
3. Shorter travel distances and smoother flow lines than process layout.
4. Team attitude and job enlargement tend to occur.
5. Utilization of each machine is increased.
Limitations:
1. Higher skilled employees are required
2. General supervision is required.
3. It depends on the balanced material flow through the cell otherwise buffers and WIP
storage are required.
5.5.4 Process Layout
In this type the machine are grouped and the product passes from one group to
other group based on the sequence of production. The groups of processes are called cells.
The process layout is used in the rapid changes in the product mix or production volume as
well as when both product and group layout cannot be used. Typically job shop employs
process layout due to the variety of products manufactured and their low production
volume. It has high degree of inter departmental flow.

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Figure5.5 – Process Layout
Advantages:
1. Since the machines are grouped, only fewer machines are required; thus minimum
investment is required
2. Better utilization of machines could be achieved.
3. High degree of flexibility exists.
4. Supervision could be specialized.
5. The working personnel find the job more satisfying and interesting since there is a
diversity of tasks.
Limitations:
1. Highly skilled labour is required.
2. Work in process inventory is increased.
3. Total production time is longer
4. Planning and control of production system turns out to be tedious.
5. Space and capital are tied up by the work in process.
6. Material handling is more expensive because of longer flow line.
5.5.5 Design of Process Layout
To design a process layout there are some computerized techniques available.
Computerized techniques are classified into
 Techniques which select the best process layout based on the material cost
comparison.
 Other computerized techniques which select the best process layout based on the
qualitative factors namely the closeness between the departments.
Closeness ratings are as follows:
A – Absolutely essential
E - Ordinary closeness
I – Important
O – Ordinary importance
U – Un important
X – Not desirable.

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CRAFT (Computerized Relationship Allocation of Facilities Techniques)
CRAFT algorithm was originally developed by Armour and Buffa. CRAFT is more
widely used than ALDEP and CORELAP. It is an improvement algorithm. It starts with an
intial layout and improves the layout by interchanging the departments pairwise so that the
transportation cost is minimized. The algorithm continues until no further interchanges are
possible to reduce the transportation cost. The result given by CRAFT is not optimum in
terms of minimum in majority of applications. Hence, CRAFT is mainly a heuristic
algorithm.Unfortunately, plant layout problem comes under combinatorial category. So,
usage of efficient heuristic like CRAFT is inevitable for such problem.
CRAFT Requirements
1. Initial layout.
2. Flow data.
3. Cost per unit distance.
4. Total number of departments.
5. Fixed departments.
Number of such departments
Location of those departments
6. Area of departments.
CRAFT Procedure
The steps of CRAFT algorithm are summarized below.
Step 1. Input: 1. Number of departments
2. Number of interchangeable departments
3. Intial layout
4. Cost matrix
5. Flow matrix
6. Area of departments
Step 2. Compute centroids of departments in the present layout.
Step 3. Forum distance matrix using the centroids.
Step 4. Given data on flow, distance and cost, compute the total handling cost of the
present layout.
Step 5. Find all the possible pairwise interchanges of departments based on common
border or eqal area criterion. For each possibility, interchange the corresponding
centroids and compute approximate costs.
Step 6. Find the pair of departments corresponding to the minimum handling cost from
among all the possible pairs of interchanges.
Step 7. Is the cost in the previous step less than the total cost of the present layout? If
yes, go to step 8.If not go to step 11.
Step 8. Interchange the selected pair of departments.Call this as the NEW LAYOUT.
Compute centroids, distance matrix and total cost.
Step 9. Is the cost of new layout less than the cost of the present layout?
If yes, go to Step 10.If not, go to Step 11.

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Step 10.The new layout is hereafter considered as the present layout.its data on centroids,
layout matrix and the total cost is retained. Go to step 5.
Step 11. Print the present layout as the FINAL LAYOUT.
Step 12. Stop
LAYOUT:
Figure 5.6
Figure 5.7
Figure 5.8
1) Iteration 1: calculate the distance matrix.
Distance between two departments = |x1-x2| + |y1-y2|
Where,
(X1, y1) is the centre of department 1
Centroids of A,B and C,
A(50,125)
B(25,50)
C(75,50)

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DISTANCE MATRIX:
Figure 5.9
2) Determine the total cost for all possible movements between each department.
Cost between two departments = Distance matrix X Cost matrix
Figure 5.10
3) Re allocation of departments,
In this step the departments are interchanged. For interchanging
1. Both departments should have the same area (or)
2. Both departments should share common boundary
4) After reallocating find the new centroid and repeat step 2 and 3.
ITERATION 2
Interchange A and C (Because A and C have common border and same area)
Therefore new Centroids are,
C (50,125)

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B (25,150)
A (75, 50)
Figure 5.11
DISTANCE MATRIX:
Figure 5.12
COST MATRIX:
Figure 5.13

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ITERATION 3:
Interchange B and C (Because B and C have common border and same area).
Therefore new centroid are,
B (50,175)
C (25, 50)
A (75, 50)
Figure 5.14
DISTANCE MATRIX:
Figure 5.15

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COST MATRIX:
Figure 5.16
TOTAL COST: 975
5) Check total cost for all the possible reallocations and select the layout with
minimum total cost.
6) Repeat the iterations till the least total cost is achieved. This layout is optimum
solution.
In the given problem layout seems to be optimal compared to other two layouts.
Now taking layout 2 as base layout, continue further iterations to find the least cost.
That layout is the optimal solution.
Corelap Algorithm
Input data requirement
1. Relationship chart and closeness rating.
2. Building description is given by maximum length to width ratio.
Objective
1. Maximizing overall closeness rating.
How the software programs works
First he found out the closeness rating between the departments. It has to be placed in
layout. If there is any type select the department which is high in closeness rating. If there
is again tie select the department which is larger in area. If the tie still exists then select
any department randomly.
Output
Computer printout shows final layout.
Determination of placement order of department:

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For the purpose of finding the order of placing the departments the following data are
needed.

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REL- chart and closeness ratings:
REL –chart:
Table 5.4
CLOSENESS VALUES:
A=6, E-5, I=4, O=3, U=2, and X=1
Using the closeness rating TCR (total closeness rating) is calculated thus:
Table 5.5

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The following steps are carried out to select the placement order of the departments.
1. Department with the largest TCR is selected for the first placement. In case of ties,
the department with the largest area is selected. Department 5 is selected.
2. Review the closeness relationship of department 5 with other departments to find
the department that has the highest closeness relationship with department 5.
Table 5.6
Department 6 has the highest closeness relationship with the department 5. So it has
to be placed next to department 5.
3. Check the closeness relationship for both the departments.
Table 5.7
In the above study department 7 has high closeness rating with 6. Thus it has to
be placed in the layout next.
Similarly if there is a tie in closeness rating, then select the department with
highest TCR.
If there is a tie again, then select a department with larger area. In case of tie in both
conditions, then select a department randomly. Order of placement:
5  6  7  2  1  4  3
PLACEMENT OF DEPARTMENTS IN THE LAYOUT:
Table 5.8
5

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1. The first department to be placed is 5. it is placed in the centre of a (7x 15) layout.
Each cell has an area of 6000 sq.mt.
3. The second department from the list is department 6. It is thus placed.
Table 5.9
6 6
5
(Department 6 has two squares. It can be placed thus…)
3. Department 7 has to be placed. It has two squares. It can be placed thus in three ways.
Table 5.10
Table 5.11
Table 5.12
7 7
6 6
5

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In the above case we have to find the weighted rating for each department.
WEIGHTED DEPARTMENT RATING
Table 5.13
6
Closeness
relationship
Weighted rating.
A 243
E 81
I 27
O 9
U 1
X -729

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PLACEMENT RATING:
a. Department 7 with department 6 = E = 81,
Therefore placement rating = 81.
b. Weighted rating of 7 with 6 = 81
Weighted rating of 7 with 5 = 27
----------
Total = 108
----------
Similarly for the other layout also, the rating is 108.
Thus we have to select either b. or c. layouts… let us take c. layout…
4. Next department 2 has to be placed.
Table 5.14
PLACEMENT RATING = (27+1) = 28.
No other allocation has maximum placement rating…
5. Next department 1 has to be placed. It has the following four possibilities.
Table 5.15 Table
5.16
2 6 6
7 7 5

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PLACEMENT RATING:
A. Weighted rating with department 6 and 2 = 82
B. Weighted rating with department 6 and 5 = 10
C. Weighted rating with department 7 and 5 = 10
D. Weighted rating with department 7 and 2 = 82
Table 5.19
The above arrangement is selected randomly (between A. & D.)
6. Next department 4 has to be placed. It has the following five possibilities.
Table 5.20
Table 5.21
1 1
2 6 6
7 7 5
4 1 1
4 2 6 6
7 7 5

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Table 5.22
Table 5.23
Table 5.24
PLACEMENT RATING:
A. Weighted rating with department 1 and 2 = 108
B. Weighted rating with department 2 and 7 = 82
C. Weighted rating with department 7 and 5 = 28
D. Weighted rating with department 6 and 5 = 28
E. Weighted rating with department 1 and 6 = 28
1 1
4 2 6 6
4 7 7 5
1 1 4 4
2 6 6
7 7 5

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Table 5.25
The above arrangement is selected.(A.)
7. The last department to be placed is department 3.
Table 5.26
The above placement of department 3 has maximum placement rating. (Based on REL).
Thus the layout is allocated with all the departments as follows.
Table 5.27
4 1 1
4 2 6 6
7 7 5
4 1 1 3
4 2 6 6
7 7 5

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Total Score Of The Layout:
Total score of the layout is the sum of the products found by multiplying the length
of the shortest path between all departments and the numerical closeness value for the pairs.
Total score = For all pairsCloseness rating x length of shortest path

The path is calculated by the rectilinear distance from the border of one department to
the border of the other one.
Therefore, if two departments are adjacent, they will have common border. The path
length will be zero.
Total score of the above layout is given as follows:
Table 5.28
4 1 1 3
4 2 6 6
7 7 5

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Department
to
Distance Closeness Score
1 2 0 - -
1 3 0 - -
1 4 0 - -
1 5 2 3 6
1 6 0 - -
1 7 1 2 2
2 3 2 2 4
2 4 0 - -
2 5 2 4 8
2 6 0 - -
2 7 0 - -
3 4 2 2 4
3 5 1 2 2
3 6 0 - -
3 7 2 2 4
4 5 3 4 12
4 6 1 2 2
4 7 1 2 2
5 6 0 - -
5 7 0 - -
6 7 0 - -
Total 46

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Thus the procedure to find the total score ends with this step. One can repeat the
procedure with different scales and pick up the best layout with the MINIMUM TOTAL
SCORE…
ALDEP (Automated layout Programming):
ALDEP is a construction type algorithm .This algorithm uses basic data on
facilities and builds a design by successively placing the departments in the layout. After
placing all the departments in the layout, a score is computed .This is nothing but the sum of
the closeness rating values of different neighbouring departments in the layout. This
algorithm is repeated for a prespecified number of times and the best layout is selected
based on the maximum layout score.
The basic data required for this algorithm are listed below.
1. Total number of departments.
2. Area of each department .
3. Length and width of layout.
6. Closeness ratings of various pairs of departments in the form of Relationship Chart.
7. Minimum department preference (MDP) value.
8. Sweep width.
9. Number of iterations to be performed.
10. Location and size of each restricted area in the layout if present.
Steps to be followed:
Step 0.INPUT:
1) Number of departments in the layout.
2) Area of each department.
3) Length and width of the layout.
4) REL-CHART (Relationship chart).
5) MDP value.
6) Sweep width.
7) Number of iterations to be carried (N).
8) Current iteration number(I),1.
9) 9.Locations and sizes of fixed departments if present.
10) 10.score of the current layout (It is assumed as a very high negative value before
performing the first iteration).
Step 1. Select a department randomly and place it in the layout.
Step 2. Scan the relationship (REL) – chart and classify the unselected departments into
two lists, namely List A and List B.
List A contains the unselected departments whose relationship values in relation to the
lastly selected department are less than the MDP value.
List B contains the unselected departments whose relationship values in relation to the lastly
selected department are greater than or equal to the MDP value.

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Step 3. Is the List B empty? If so , go to step 4;otherwise,go to step 5.
Step 4. Select a department randomly from List A and place it in the layout. go to step 6
Step 5. Select a department from List B which has the maximum REL value in relation to the
lastly selected department and place it in the layout.
Step 6. Whether all the departments are placed in the layout? If not go to step 2; if yes, go to
step 7.
Step 7. Compute the score of the layout.
Step 8. Is the score of the layout more than the score of the current best layout? If yes, update
the new layout as the current best layout and store the corresponding score.
otherwise, drop the new layout.
Step 9. Is the current iteration number I =N? if yes, go to step 10; otherwise, increment the
iteration number by one (I =I+1) and then go to step 1.
Step 10. Print the current best layout and the corresponding score.
STEPS OF ALDEP:
1. Get the inputs. (REL chart, Department area, layout plan)
(A=64, E=16, I=4, O=1, U=0, X=-1024)
The REL diagram for a plant with 11 departments is as follows:
Table 5.29
1) Based on the area of all the departments, fix an appropriate scale. Based on the scale
divide the departments in to number of square blocks.
Table 5.30

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DEPARTMENT AREA NO. OF SQUARES
1 600 12
2 400 8
3 350 7
4 150 3
5 350 7
6 150 3
7 200 4
8 800 16
9 200 4
10 350 7
11 5000 50
(SCALE: 1: 50, i.e. each cell in the layout is assumed to be a square of area 50 sq. units).
11. Draw an initial layout based on the layout area or based on the total area of all the
departments. Divide the departments in to the basic number of squares. (Sum of all
department squares).
2) ITERATION-1:
a. Initially assume a closeness rating of “0”.
b. Fix a cut-off value for the department selection. (i.e.) “A” or “E” or “I”...
c. Initially place a department randomly or the department with the max.
area.
d. Then from the candidate (remaining) departments, select a department
with the maximum cut-off value with the previously placed department.
3) Serpent type Allocation:
While allocating/placing each department in the layout, it has to be laid out
in the following sequence. (Each cell is area of 50 in sq. units… based on the
scale).
Table 5.31

34
Table 5.32
11 11 11 9 10 2 2 7 7 0 0
11 11 11 9 10 2 2 7 0 0 0
11 11 11 9 10 2 2 7 0 0 0
11 11 11 9 10 2 2 8 0 0 0
11 11 11 6 10 1 3 8 0 0 0
11 11 11 6 10 1 3 8 0 0 0
11 11 11 6 10 1 3 8 0 0 0
11 11 11 4 5 1 3 8 0 0 0
11 11 11 4 5 1 3 8 0 0 0
11 11 11 4 5 1 3 8 0 0 0
11 11 11 11 5 1 3 8 0 0 0
11 11 11 11 5 1 8 8 0 0 0
11 11 11 11 5 1 8 8 0 0 0
11 11 11 11 5 1 8 8 0 0 0
11 11 11 11 1 1 8 8 0 0 0

35
6) If in there is a tie or no department satisfies the cut-off value during the selection of
candidate department, then place a department randomly.
7) Calculation of TCR (Total Closeness Rating):
a. Once all the departments are placed, then the next step is to calculate TCR.
b. Make a note of all the pair of departments sharing common border with each other.
(Note a pair only once i.e. either 1-3 or 3-1).
c. Now add up all the pairs’ REL points…
d. Then multiply it by 2.

36
Table 5.33
Pairs REL points
11-1 0
11-9 16
11-6 16
11-4 64
11-5 4
9-10 1
9-6 4
6-10 1
6-4 16
4-5 1
10-2 0
10-5 4
5-1 1
2-8 0
2-3 16
2-1 64
1-3 16
1-8 0
3-8 1
7-8 64
2-7 0

37
290
Thus the Total Closeness Rating is (290*2) = 580
7) This is the TCR value for the initial layout.
8) Keeping this as the minimum value continue the steps (4-7) for all the possible layouts
and calculate the TCR value for all the layouts. Once iteration results in a TCR value less
than the immediately previous layout’s TCR value then that layout is the optimal solution.

38
Table 5.34
Total Closeness Rating:
Table 5.35
11 11 11 8 8 6 9 1 1 0 0
11 11 11 8 8 6 9 1 0 0 0
11 11 11 8 8 6 9 1 0 0 0
11 11 11 8 8 4 9 1 0 0 0
11 11 11 8 8 4 3 1 0 0 0
11 11 11 8 8 4 3 1 0 0 0
11 11 11 7 8 5 3 1 0 0 0
11 11 11 7 8 5 3 1 0 0 0
11 11 11 7 8 5 3 1 0 0 0
11 11 11 7 8 5 3 1 0 0 0
11 11 11 11 10 5 3 1 0 0 0
11 11 11 11 10 5 2 2 0 0 0
11 11 11 11 10 5 2 2 0 0 0
11 11 11 11 10 10 2 2 0 0 0
11 11 11 11 10 10 2 2 0 0 0

39
Pairs REL points
11-8 64
11-7 64
11-10 4
8-7 64
8-10 1
8-6 1
8-4 1
8-5 0
10-5 4
10-2 0
6-9 4
6-4 16
4-5 1
4-9 1
4-3 0
5-2 0
5-3 1
9-1 0
9-3 1
3-2 16
3-1 16
1-2 64
319
Thus the Total Closeness Rating is (319*2) = 638.
Thus Iteration 2 shows that layout 2 has high TCR value compared to layout 1. Thus
layout 2 is an optimal one compared to layout 1. Similarly iterations are continued to find
the optimal layout.
5.6 LINE BALANCING
This is a technique applied to design workplace of a plant, which adopts flow
line production system. You know that the productive system of flow line production
produces less variety and standardized products. So the capacity of the system is to be
established first or the no. of units produced per day.

40
Figure 5.17 – Line Balancing
Objective: To design an effective and efficient workplace
Input:
Capacity:
The capacity as it is mentioned already that the capacity is measured through the output.
In an automobile industry it may be number of cars to be produced in a day. To decide the
capacity you need to have the information about the demand for the product. Yearly demand
has been converted into day to day capacity requirement.
Technological constraints:
Technological constraint that means when you are manufacturing a product, there is a
sequence in which the operation on the components is to be carried out then the produced
components are assembled according to the particular sequence. For example in the case of
electric motor manufacturing activity the activities and immediate predecessor activity to be
carried out are given below:
Table 5.36
Activities Immediate
Activities
Min
A Axile manufacturing - 700
B Rotar manufacturing - 800
C Rotar assembly A, B 400
D Stator manufacturing - 200
E Stator cashing manufacturing - 400
F Stator assembly D, E 300
G Protective shield manufacturing - 500
H Final assembly C, E, F 300
The above relationship could be shown in a network form as follows for clear understanding.

41
Figure 5.18
Available Working time:
The available working time is the total working hours available based on the time
frame. Example: if the capacity calculation is done for the day then the available hour’s
calculation is done for day. If there is one shift of 8 hours duration then the available time in
seconds is calculated as 8 x 60 x 60 second.
= 28,800 seconds
Technological constraint continuation:
Each activity is considered to be an element. An element is a distinct that of a
specified job. This is done for the purpose of observation, measurement and analysis.
Against each element the time for completing the activity is also estimated.
Output:
Number of stations:
Based on the available working time per day, the no. of units to be manufactured, and the
total work content, the no. of stations are calculated as follows:
No. of stations = 3600 x 35 units
[Total work content per unit] [Desired no. of units per day]
= -------------------------------------------------------------------------
Total productive time available per day

42
= 8 x 60- x 60
= 4.375
= 5 stations
Maximum allowable time:
From this you can calculate the maximum allowable time for each station
Total available hours
= --------------------------------------
Desired no. of units per day
= 8 x 60 x 60 /35
= 823 seconds.
Minimum Allowable time:
This is the highest elemental time. In this example the highest elemental time is 800
seconds. The maximum and minimum allowable time helps you to assess the efficiency and
effectiveness of the proposed designs.
Assignment of the job elements to the workstations:
A method is to be adopted to assign the jobs to workstations. The method may be an
optimal method or heuristic method. In heuristic method, you may get best solution but there
is no guarantee that you may get a solution. But it helps to get nearer to best solution. One
such a procedure is the longest operation time (LOT) Remaining. Longest Operation time
remaining means after assigning a particular task to a work station. You should find out the
remaining unassigned elements and choose the element with highest operation time. Then
add the element with the already assigned element. You should be careful enough that total
element time in a particular workstation should not exceed the cycle time established.
Suppose the element considered for assigning could not be assigned because the total
elemental time at the workstation increased beyond the cycle time. Then in such case you
should look for the next highest remaining elemental time. The above mentioned caution is
to be followed before assigning the element to the work station. Thus process is continued
till all the elements are assigned.
Assignment of elements for 823 seconds work station cycle time
Table 5.37
B A C & E D & F G &
H
I WS II
WS
III
WS
IV
WS
V
WS

43
WS – Work
Station I:
Consider the highest elemental time. This is element B it could be straight away
assigned to station because it does not have any predecessor. Next 5 highest elemental time
is 700 that is element A. But element A could not be assigned because if you assigned A the
stations sum of elemental time exceeds the time cycle time 823 seconds. This reason holds
good for other remaining elemental times.
Station II:
In Station II you can assign element A. This has elemental time of 700 second. You can
not assign any remaining elements to station II because the total elemental time exceeds the
cycle time.
Station III:
In Station III the remaining highest elemental time is 500 minutes that is of element G.
But before assigning the activities, you should complete other activities as per the
technological constraints. So next highest operational elements are C & E, so C & E are
assigned to station III. No. other elemental could be assigned to station III.
Station IV:
Table 5.38
Line design for 800 seconds
1 2 3 4 5 Effectiveness Efficiency
B A C&D E&F G&H
Goal
accomplishment
Utilization of
employee
Time
required
per unit in
each
station
800 700 600 720 800
28800/800 = 36
Units
3620
Available
time each
work
station
800 800 800 800 800 4000
Utilization
3620/4000
90.5%
Idle time
per cycle
0 100 200 80 0 380
Idle time
380/4100
=9.26%

44
Next highest unassigned element is G. For the same reason spelt out previously. They are
not allotted to station IV then you can go for allocating next highest elements namely D & F.
Station V:
Then In the remaining unallotted elements, element G is allotted first and then H.
The efficiency and effectiveness
The efficiency and effectiveness of the LOT method is shown below:
Suppose if you adopt minimum allowable cycle time 800 seconds. On the basis for the
allocation of elements, then the elements to be assigned will be as shown as below:
Next highest unassigned element is G. For the same reason spelt out previously. They
are not allotted to station IV then you can go for allocating next highest elements namely D &
F.
Station V:
Then In the remaining un allotted elements, element G is allotted first and then H.
The efficiency and effectiveness
The efficiency and effectiveness of the LOT method is shown below:
Suppose if you adopt minimum allowable cycle time 800 seconds. On the basis for the
allocation of elements, then the elements to be assigned will be as shown as below:
Table 5.40
B A C & D E & F G & H

45
I II III IV V
Table 5.41
As you have seen the second design consists of 800, as the cycle time stands better in
terms of efficiency and effectiveness compound to the first design. Employee idleness could
be reduced tasks. Thus results in reduction in no. of the employee.
Till now it is assumed that the elemental time is deterministic but there is a possibility
that the more manual elements involved in the task you can’t get the single elemental time, in
this case usually the elemental time follows certain distribution. You can design the
workplace or product layout by considering the stochastic time elements also.
Line design for 820 seconds
1 2 3 4 5 Effectiveness Efficiency
B A C&E D&F G&H
Goal
accomplishment
Utilization of
employee
Time
required
per unit in
each station
800 700 820 500 800
28800/820 = 35
Units
3620
Available
time each
work
station
820 820 820 820 820 4100
Utilization
3620/4100
88.29%
Idle time
per cycle
20 120 0 320 20 480
Idle time
480/4100
=11.71%

46
Review Question
1. What are the types of layout?
2. What are the techniques used in layout planning?
3. Define line balancing and why it is required?
4. What is minimum allowable time?

47
5.7 TIME STUDY AND WORK MEASUREMENT
Work study consists of two major phases namely method study and work
measurement. In an industry method study is applied with an objective of simplifying the job
and finding the best method of doing work. Method study paves the way to reduce the work
content due to bad working methods, bad layout, wrong selection of tools etc. Work
measurement is applied with an objective to reduce the ineffective time and to set the
standards. Usually in the industry the method study is applied to ensure the correct methods,
process etc. Then, for the best method - the measurement of the method is carried out.
According to ILO, Work measurement is defined as follows:
“Work measurement is the application of techniques designed to establish the time for
a qualified worker to carry out the job at a defined level of performance” Now each key
term requires a kind of explanation:
Who is qualified worker?
Qualified worker is one who has the requisite physical attributes, requisite intelligence
and education, requisite skill and knowledge. With the above mentioned qualities, he can
complete the work to meet the satisfactory standards of safety, quality and quantity.
Average worker:
All the recruited workers are qualified workers. But if you analyze their performance.
The performance may be the time taken per unit by the worker. Assume that there are 500
workers; if you analyze their performance; the performance against the frequency mostly
follows the normal distribution.
Figure 5.19

48
The shaded portion represents the majority of the worker that means more workers take time
to produce one unit between t1 and t2. The no. of employee fall in the region you can
consider as the qualified average workers. The unshaded portions in the left side represent
above average performance and the unshaded portion of the right side represent the below
average performer. Since most of the workers performance falls in the shaded area. The
organization has to set the time standard for the average workers.
Work Measurement Techniques
There are many techniques available to measure the work. The techniques are listed below:
Figure 5.20
Procedures to conduct work measurement technique: According to ILO
SELECT : Select the job to be studied.
RECORD : Record all the relevant facts by direct observations or by means of suitable
recording technique.
EXAMINE : Examine critically the recorded elements.
MEASURE : Measure each element by time measurement.
COMPILE : Arrive at the normal time and standard time by adding allowance.
INSTALL : Implement the established standard time.
5.7.1 Time Study
Select:
First you should select the job to be studied. Situations may lead you to conduct the time
study to fix the time standard.
a) SITUATION:
1. Organization requires time standard to introduce incentive scheme
2. To determine the no. of equipment and no. of workers, you need to conduct work
measurement technique.
3. To fix the standard cost, particularly to determine the labor cost, you need time
standard.
4. To determine the selling price, tender price and to promise the delivery time you need
to have time standard.
Record:

49
After selecting the job you should note down the surrounding conditions like working
place, layout condition and see to that the worker adhere to the methods suggested by the
method study.
Examine:
Next you should divide the job into different elements. Suppose you have to fix time
standard for the job which involves drilling operation. The elements are:
1. Selecting the work piece and placing it in jig.
2. Tightening the screw
3. Advancing the drill towards the work piece
4. Drilling
5. Withdrawing the drill from the operation
6. Loosening the screw
7. Removing piece from jig
8. Removing the chips
The purposes of the dividing jobs into different elements are to time the elements accurately
and also to have a distinguishable starting and ending points for each element.
Measure:
After dividing the jobs into different elements, the no. of observations to be made on
each elements is to be determined. Here a trade off is to be made between the accuracy of the
result and the cost of the time / study. If you take more observations, results in more
accuracy in the result. You can know now, how do you determine the sample size
statistically.
To determine the sample size statistically you have to specify the desired accuracy and
the confidence level. Suppose you need 5 % accuracy result and 95 % confidence level.
Assume that the sampling mean follows normal distribution. t is the mean.
Figure 5.21
Of the elemental time, t is the standard error of the sampling distribution. A 95 %
confidence level and ± 5% accuracy level means that the changes are at least 95 out of

50
100 that the average value for the element will not be in error when you allow more or
less 5 % of true element time.
The above bold statements showed pictorially as below:
From the above figure, you can arrive Z t = (accuracy level) X (t )
At 95% confidence limit and 5% accuracy level, the Z value from the normal distribution is
1.96.
1.96  t = .05 t ----------- 1
You know the relationship between the population standard deviation and standard error of
the sampling distribution.
 t =  / √n ----------- 2
Where n is the sample size, σ is the population standard deviation. Substitute the value of 
t in equation 1.
1.96  / √n = .05 t
1.96  / .05 t = √n
n = (1.96  / .05 t )2
Here usually the population standard deviation is not known. In this case  is estimated from
the pilot study. Suppose the number of samples to be taken is less than pilot study, then you
need not go for further sample collection. But the number of samples to be determined is
more than the pilot study samples, then more sample need to be collected.

51
This process is continued for each element. But there is a possibility that in each
element you may end up with different sample size requirements. In this case you can fix the
number of cycles for the all the elements based on the element which demands the highest
sample size requirement.
Measure:
In this phase, the elemental time is recorded using stop watch which is specifically
designed for the time study.
Rating:
While measuring the time for each element, the time study person has to take note of the
pace in which the operator does the job. The accuracy of the judgment towards the pace of
the operator depends upon the experience and training of the time study person. Rating is
defined as the workers rate of working relative to the time study person’s concept
corresponding to the standard pace.
Rating is an adjustment factor, because when a time study person choose a qualified,
experience, trained worker there is a possibility that the operator may belong to the below
average group of that company in this case he may take more time to complete the element.
So to bring the time related to the average worker, which observed time has to be multiplied
with the adjustment factor i.e. or other wise to lessen the observed time. In this case rating
will be less than 1. This case becomes opposite while the supposed selected operator is
above average worker. In this case the rating factor takes more than 1 to have higher
observed time than what is available.
Rating = Observed rating / standard rating
Standard rating = 100
Compile:
After obtaining the observed time, rating for each element Normal time is calculated.
Normal time for element = observed time for the element x rating factor
All the normal elemental times are added to arrive at the normal time for the operation.
You should not consider this time as standard time because you should add
allowances with the normal time. Because allowances are to be given to compensate for the
energy that the operator spent while doing the job and also allowances are to be added for
meeting his / her personal needs like going for toilets etc. Allowance for these reasons is
beyond his control.
Allowances are personal allowances, fatigue allowances and delay allowances.
Personal allowances for meeting his / her personal needs, fatigue allowances are allowed for
physical exertion. Delay allowances are due to lack of materials, random inspection visits
etc.

52
Now the standard time is arrived as follows:
Standard time = Normal time x 100 / [100 - % allowance]
5.7.2 Work sampling:
Work sampling is another work measurement technique for measuring the following
 To measure & control the percentage of idle time of an activity or productive
resource
 To established the standard time
 To determine the performance index of the operator / department / unit
When do you apply work sampling technique:
 Jobs consists of longer lead time
 To measure the team work
Let us consider the first application namely to measure & control the percentage of idle
time of an activity or productive resources.
Usually in any organization, the management bothers very much about the utilization
of key productive resources. Work sampling study used to identify the percentage of idle
time and it helps the management to correct the excessive idle time. It helps in fixing idle
time control chart so that management can control the idle time percentage of the so called
critical resources every time.
Consider in a hospital X- ray equipment is very critical. The management of the
hospital wants to establish a control chart to monitor & control the idleness of the X- ray
machine.
To fix this standard, first nothing has to determine how many observations to be made.
To determine the no. of observations you should analyze the process of conducting this study.
This study is nothing but a random process. There are two out comes of this random process,
one is the X ray machine is working, and another outcome is X- ray machine is not working.
So there is every possibility that the outcome to follow a binomial distribution. Based on the
percentage of occurrence of activity (in this case idle) ‘P’ and the no. of trails ‘n’ binomial
distribution is approximated into a normal distribution.

53
Figure 5.23
p is the stand error of this sampling distribution
p = √ P (1-P)/n
n = sample size
p = percentage of occurrence of the activity to be measured.
As it is required in the Time study, here also to determine the no. of cycles to be
determined, you need to specify the two parameters namely the confidence interval and
accuracy. Assume 95% confidence limit and 10% accuracy value. ‘P’ is estimated from the
past record that p = 20% suppose ‘P’ is not available, then you should conduct a pilot study to
determine the ‘P’ then the sample size is determined as follows:

54
Figure 5.24
General formula
Z . p = SP
Where S = accuracy level
Z . √ P (1 – p) / n = SP
n = Z2
P (1- p) / P2
S2
= [Z2
/S2
] (1-p) / p
For 95% confidence limit and 10% accuracy value
n = [1.96/.10]2
[1 - .20/.20]
n = 1537 observation
Timing of the activity to be measured
Next you should decide to schedule the timing of the observation to be measured.
For this you should generate random numbers through the computer or random number
tables. Assume that the hospital is working for 16 hours. Then generate three digit random
numbers. Working time of the hospital is given as below.
Table 5.42
Shifts Starting time Break Ending time
I 8 A.M. 12- 1 P.M. 5 P.M.
II 5 P.M. 9- 10 P.M. 2 A.M.

55
First digit represents the number of hours after 8 A.M. Second and third digit help us to
find the minutes. The following table shows the conversion of random numbers in to timing.
Table 5.43
Random Number Hours after start Observation time Chronological order
712 7.12 3.07 3
473 4.73 12.44 Lunch hour
482 4.82 12.49 Lunch hour
116 1.16 9.01 1
311 3.11 11.07 2
You can know how do you convert the random number 712 into 3.07 AM. 7 represents the
time after the starting of the factory. Namely, 8 AM then it is 3’o clock. Second and third
digit represents 1 and 2 represents 0.12 X 60 minutes 7.2 minutes, that means the observer
has to observe the position of X ray machine after 3.07 Hrs. Similarly the no. of random
numbers are converted into observer observable time. Suppose you have got the results as
shown in the table
Table 5.44
Activity No.of observation
X Ray machine is working
X Ray machine is not working
1227
310
Total Observation 1537
The percentage of idle time is calculated as follows
‘p’ = 310/1537 = 20%
In this case you need not go for further observations. Suppose the obtained ‘p’ value is
more than the allowable limit, then you need to rework to find the no. of observations to be
taken. Suppose, if it comes around 1600,m then further (1600 -1537) so 63 observations has
to be taken to fix the standard
Now p =
1537
8.2X
= 0.1
You can fix the control limit using P and p value as follows:

56
Figure 5.25
Upper control limit P + 3 p = 0.23
Mean = P =2
Lower control limit P – 3 p = 17
This is kept as a standard and any particular day, proportion of idle time exceeds the limit you
have fixed, then the reasons has to be analyzed and corrected. Thus the work sampling
techniques used to fix the standard to monitor and control the key resources.
Establishing Time Standard by Work sampling:
Work sampling study in addition to finding the performance index, fixing the control
limits for delay and percentage of utilization of activities, it also used for establishing the
time standard for operation or for the job.
Data required to be collected:
Assume that an operator does a turning operation in a part. By work-sampling study
to determine the time standards the following information is to be collected.
 The percentage of working
 The total working time
 The Number of pieces to be produced.
 The average performance index
 The allowance
The normal time per unit is calculated using the following formula.
Normal Time = (The percentage of working) (Total working time) / No. of Pieces product) x
Average performance index.
Then standard time is calculated follow as:
Standard time
= Normal time (100/100 - % Allowances)

57
E.g.: An operator does a turning operation in a product. An observer collected the following
information.
 The percentage of working = 85%
 The total working time = 480 min.
 The no. of pieces produced = 300 units
 The average performance index = 120
 Allowances from the time study manual is arrived at 15%
Normal time = (0.85 x 480)/300 (120/100)
= 1.632 min.
Standard time = 1.632 x 100/ (100-15) = 1.632 x 100/85
= 1.92 min.
Work Sampling study to establish the performance index:
This study is applied to establish the average performance index. This average
performance index of the labour or department helps the management to control the labour
cost. Let us see how you calculate the average performance index. The work sampling study
may be carried out for many periods for data collection. Then from the data collected you
can calculate the average performance index as follows:
Average Data per period from the data collected during the study.
 Average no. of pieces produced during the period
 Standard time per unit.
 Average working time.
Performance index = [(Average no. of pieces produced during the period x Standard time
per piece in minutes) / Average hours worked during the
period x 60] x 100
E.g. Assume that a drilling operation is carried out on a product. The organization interested
in knowing the average performance index of the operator who does the drilling operation.
Work sampling study has been conducted for several weeks. The average data collected from
the study are given below:
Average no of pieces produced during a week = 1500
Standard time per piece per min. = 5 min.
Average hours worked during the period = 36 hours
Performance index = [500 x 5 /36 x 60] x 100
= 115 %
The average performance index helps the organization to control the labour cost.
5.8 LEARNING CURVE

58
In the case of more labour intensive mass production industry, mostly the labour do
repetitive type of job, that results in more learning due to experience of doing the same job
because of this, the time taken to produce subsequent units gets reduced compared to the
previous units. This phenomenon will not lose for longer period, at some point of the time
this learning effect ceases. After the learning effect ceases, the time required to produce one
unit or one batch will be the same irrespective of the number of units or batches. The
organization has to cash in the relevant range period, the period in which the learning effect is
there. During the learning effect period, the standard time per unit is not constant it varies
depends upon the quantity of the order you get. Since the learning effect has impact on the
standard time that is the reason to study this concept in this section .
Learning Curve Model:
Consider the past data of a company manufacturing Aircraft components. For a particular
component the data are taken for ten situations.
Table 5.45
Using (1) and (3) if you draw the curve, it appears as follows
Figure 5.26
Situation
Quantity
(Q)
Production Time
(tp)
Cumulative
batches (1)
Cumulative
Production Time (2)
Cumulative Average
Time (3)=(2) / (1)
1 20 164 20 164 8.2
2 30 228 50 392 7.84
3 50 340 100 732 7.32
4 80 453 180 1185 6.58
5 120 655 300 1840 6.13
6 150 767 450 2607 5.79
7 210 863 660 3470 5.26
8 260 1115 920 4595 5
9 330 1488 1250 6083 4.86
10 380 1311 1630 7394 4.37

59
Since the nature of the curve is exponential, the general equation for exponential curve is
Y= a × X b
Y= cumulative average time
X= Cumulative production quantity
a = The time required to produce the first quantity
b = Exponent
‘b’ depends upon the operating condition. In the above model, for the particular cumulative
production quantity what will be the cumulative average time? This could be easily
calculated provided, if you know the two parameters namely ‘a’ and ‘b’. Since the curve is
exponential in nature, if you take the logarithm for the X value and Y value then you can get
a linear curve as follows.
Log (Y) = Log (a) + b × Log(X)
Thus the curve is of the form
Y = a + bx
Where
y= Log (Y)
x= Log(X)
So using the simple regression analysis you can find the values of ‘a’ and ‘b’. For the given
data, shown in the table, let us try to estimate the regression model,
Table 5.46
log X log Y
2.995 2.104
3.401 2.059
3.912 1.99
4.382 1.884
4.787 1.813

60
5.01 1.756
5.347 1.66
5.56 1.609
5.799 1.581
5.94 1.513
If we solve
Figure 5.27
log Y = 2.7555 – 0.263 ln x.
Where,
R2
= Coefficient of determination = 0.985
R2
adjusted = 0.983
Since R2
value is approximately 99%, which means 99% of the variations in the original data
have been captured by the estimated regression line. Thus show that the estimated line is the
best fit for the original data.
Cumulative average time
ln Y = 2.7555 – 0.203 ln X
You know that
b = ln learning curve percent / ln2.
-0.203 = ln learning curve percent / ln 2.
ln learning curve percent = ln 2 * (-0.203)
= 0.6931 * (-0.203)
= -0.1407.
Learning curve percent = Antilog of [-0.1407]
= 86.88%
= 87%.

61
The practical meaning of learning effect or the learning curve percent is that if the
production quantity becomes double, then corresponding required time to produce one unit of
that doubled quantity gets reduced to that extent of (1- learning curve percent). This is shown
in the following table for the problem discussed already.

62
Table 5.47
UNIT
Assume 20 units = 1 units
Cumulative average time
(Y = a * b)
20 = 1 units Y = 164 (1-0.203)
40 = 2 units Y = 164 (2-0.203)
60 = 3 units Y = 164 (3-0.203)
80 = 4 units Y = 164 (4-0.203)
From the above table you can easily identify that when the production quantity becomes
double; the average time per unit gets reduced to the extent of 13%. So this is to be taken into
account while calculating the standard time for the product. Thus way the standard time gets
reduced.
Application of learning curve:
As it is mentioned already the reduced standard time could be made use of
estimating the following,
1. Learning curve concept could be applied in pricing the product
2. This concept could be applied in standard costing
3. This is applied in budgeting and production planning.
5.9 PRODUCTIVITY
Productivity is the ratio between the output and input. This is an index, the output
may be sales and input is the recourses utilized for getting the output. Example the output is
sales value and the input is cost of goods sold.
If the Productivity Index is more than one, you can say that the performance of the
organization is good. If it is less than one you can say that the organization is not doing well.
Impact of Learning Curve on the Productivity
Cost of the goods sold is the function of labour, material and overhead cost because of
learning effect the time required to produce one unit in the relevant range decreases as the
number of units produce is more. The result is less labour and variable over heads. So the
denominator decreases that leads to higher productivity. There are many reasons for the
improvement in the productivity. The increase may due to Quality, methods, materials, better
management etc. in addition learning effect also have a source for the productivity
improvement.
Summary

63
This unit would have helped you to know the factors to be considered while selecting
a location. The kind of system design, like layout design, work measurement standards are
exposed with an objective of complete understanding the nuances of the system design
techniques. At last, you are exposed to the construction and the impact of the learning curve
on the productivity.
Review Questions
1. List the various work measurement techniques.
2. List out the procedures to carry out the work measurement.
3. What is time study?
4. Define work sampling?
5. What is impact of learning curve on productivity?

Unit v operations mgt

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