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6/Allocating Resources to the Project
6-1
Chapter 6
Allocating Resources to the Project
This chapter extends the previous one on scheduling into the area of allocating resources
among the activities of a project, or among multiple projects competing for the same resources.
The chapter begins with a discussion of expediting project completion times and highlights that
by selectively choosing which activities to crash and by how much, we can determine the
minimum cost for all possible project completion time. The use of Excel’s Solver optimization
routine to facilitate this analysis is also presented. Next, the chapter moves on to the topic of
resource loading and in particular highlights the problems of over scheduling resources. The
topics of resource leveling and resource allocation naturally follow in the subsequent sections.
Finally, the chapter concludes with an overview of several of the concepts Goldratt raises in his
provocative book Critical Chain.
Cases and Readings
A case appropriate to the subject of this chapter is:
Harvard: 9-613-020 Space Constructors, Inc. This 3-page case involves a simple project where
partial crashing has already been planned but more, and less, crashing is also to be considered.
The network has some special characteristics that offer some worthwhile lessons for the
student.

6-2
Answers to Review Questions
1. Given the fact that a project’s resource requirements are clearly spelled out in the
project’s action plan, why are PMs so concerned with resource allocation?
There can be a variety of reasons why resource allocation is of concern to the PM despite
having a properly completed project plan. For example:
• The project plan only lists general categories of resource requirements such as
engineering, purchasing, marketing, and production. In these cases, the project
manager must still arrange to get the specific resources (e.g., personnel, equipment)
needed.
• The project plan may only specify how much of the resource is needed and the
precedence between the activities’ relationships; it may not specify exactly when the
PM will need these resources.
• Although the project plan specifies the amount of a resource needed for a particular
project, there may not be a mechanism in use that balances the load of resources
across multiple projects. This can lead to conflicts and the creation of bottleneck
resources.
2. Explain the difference between a project that has a fixed delivery day and one that has a
fixed limit on resource usage.
A project with a fixed delivery date can vary the level of resources used to meet a firm
project completion date.
A project with a fixed limit on resource usage cannot obtain additional resources but can
possibly delay the project completion date.
Why might a PM be interested in this difference?
The reason this distinction is important is that it specifies which of the fundamental trade-
offs the project manager can exercise. In the case of projects with fixed delivery dates, only
performance and cost (resource usage) can be varied. In projects with fixed resource usage
levels, only schedule and performance can be varied.
3. What does it mean to “fast track” a project?
Fast-tracking is a technique whereby key stages of the project are overlapped.

6-3
In the construction industry, this might entail beginning construction before the design and
planning are finished. In the pharmaceutical industry this may entail developing the
production process as the new drugs are being developed and tested.
4. List as many things as you can think of that should be entered into a specific resource’s
calendar.
Information that should be entered into a resource’s calendar include:
• The resource’s availability (e.g., days in week available, total hours available per
week, hours available each day).
• Times the resource will not be available (e.g., lunch, weekends, holidays, vacations,
scheduled maintenance), and
• Resource cost (e.g., cost per unit of usage, cost for overtime and overuse, known
changes in future resource cost).
5. Explain why project-oriented firms require excess resource capacity.
In project oriented firms there is much more uncertainty about the timing of resource
needs since the resources primarily move between projects rather than moving between
projects and a functional department. Therefore, extra resource capacity is needed as a
buffer given the greater level of uncertainty present.
6. The arrival and departure times of commercial aircraft are carefully scheduled. Why,
then, is it so important to have excess capacity in the airport control tower?
Although the arrival and departure times may be carefully scheduled, we all know that
actual arrivals and departures often deviate significantly from these schedules. Therefore, a
significant amount of uncertainty is present and greatly complicates the ability of the
airport control system to handle arrivals and departures.
Indeed unplanned events (e.g., weather delays, equipment malfunctions, late flight crews,
and so on) often cascade through the system further compounding the problem. Therefore,
excess capacity in control towers is needed as a buffer given this level of uncertainty.
Clearly, the cost of not having this capacity greatly exceeds the cost of some idle capacity.
7. Explain the difference in the problems faced by a PM who is short of secretarial resources
and one who is short of a “Walt.”
The PM that is short of secretarial resources does not face that great of a problem as this
type of resource is relatively abundant and not usually critical to the project’s ultimate
success or failure. The PM that is short of a “Walt” (i.e., an individual with expertise and
knowledge in a critical area) faces a much more daunting problem because a Walt is a

6-4
scarce resource that is important to the project’s successful completion and there are no
readily available substitutes for a Walt.
8. When allocating scarce resources to several different projects at the same time, why is it
important to make sure that all resource calendars are on the same time base (i.e.,
hourly, daily, or weekly …)?
One reason it is important to ensure the resource calendars are on the same time base is
because task duration is not usually dictated by the number of labor hours required to
complete the task, but rather by the calendar time required to complete it. This may involve
waiting for materials (e.g., concrete, glue) to cure, or equipment to warm up, etc.
9. List and describe the three most common criteria by which to evaluate different resource
allocation priority rules.
The three major criteria are:
• Schedule slippage … a measure of the delay suffered by projects as a result of the
application of a resource allocation priority rule.
• Resource utilization … a measure of the total resource cost (including costs such as
the cost of hiring, firing, and maintaining resource inventories) under different
allocation rules.
• In-process inventory … a measure of the cost of unfinished work in the system.
10. Why is the problem of allocating scarce resources to a set of projects similar to the
problem of scheduling a job shop?
In a job shop allocating resources (equipment and workers) to jobs or orders is required. In
projects, a similar allocation is required where specific resources must be allocated to
various projects when they are needed, which represent the jobs.
11. What is meant by the term “student syndrome”?
The “student syndrome” refers to situations in which people wait until the last possible
minute to begin a task. Its name is derived from the belief that students often delay the
start of an assignment until just before it is due. This isn’t necessarily a foolish or lazy
decision since often the task will change at the last minute, thus invalidating much of the
work that was earlier spent on it.

6-5
12. Describe in your own words what is meant by Goldratt’s critical chain.
Traditionally, in project management the concept of the critical path is used. More
specifically, the critical path is defined as the path(s) that if delayed will delay the
completion of the entire project.
One shortcoming of the critical path approach is that it only considers task precedence
information and does not consider issues related to resource usage. The critical chain
addresses this concern and considers both technical precedence relationships as well as the
resources that will be used to complete the tasks. Therefore, the critical chain refers to the
longest chain of consecutively dependent events including both technological as well as
resource dependencies.
How does it work?
The critical chain works by defining two sources that can delay the completion of the
project. One source of delay is uncertainty in the tasks that comprise the critical chain. A
project buffer is added to guard against these uncertainties. The second source of delay is
uncertainty in the tasks external to the critical chain. A feeding buffer is added to these
paths to help ensure they do not delay the tasks on the critical chain.
Suggested Answers to Discussion Questions
1. Describe the fundamental trade-offs when deciding whether or not to crash a project.
The fundamental trade-off in crashing a project is between schedule and budget.
Specifically, crashing entails employing additional resources (cost) in order to reduce the
project’s completion time.
If the decision is made to crash, what additional trade-offs must be made?
If it is decided to crash a project other trade-offs may then be necessary in terms of the
completion time of other projects and perhaps the performance of this and other projects.
2. Discuss the advantages of “labor pools” in a project – oriented company.
The main advantages of “labor pools” versus dedicating workers to specific projects are:
• Less waiting time for key resources.
• The ability to level resource usage, and
• The ability to substitute one worker for another should one become unavailable.
Are there any potential disadvantages with the use of pools?

6-6
Potential drawbacks include:
• Workers who do not identify with a particular project.
• Personnel who may not be well trained in specific tasks required by the assignment.
• Fewer opportunities for job enlargement.
All of these may lead to lower levels of job satisfaction, as well as lower morale and
motivation.
3. What purpose(s) might be served by using each of the following priority rules for
allocating scarce resources?
a. As late as possible.
b. Shortest task duration time first.
c. Minimum slack first.
a. Starting a task as late as possible … preserves resources and delays cash flows as long as
possible.
b. Allocating resources to tasks with the shortest durations first maximizes the number of
tasks that can be completed within a certain time period. This tends to get the little
messy tasks out of the way so workers can give their full attention to the bigger, more
important tasks.
c. The minimum slack priority rule is used to minimize the number of late activities.
4. Linking a group of projects together with pseudoactivities creates a sort of superproject.
What does this mean, and why would anyone want to do it?
Just as a project consists of tasks and activities with precedence relationships, a
superproject can be thought of as consisting of a group of projects with precedence
relationships. In the superproject, pseudoactivities are used to show any precedence
relationships among the projects. These precedence relationships may be actual
technological constraints (e.g., the product development project must be completed before
the process development project) or simply a reflection of management’s priorities.
The reason for creating a superproject is to help identify important relationships and
dependencies across the projects and use this information to better plan the usage of key
resources.
5. Projects A and B are both nearing completion. You are managing a super important
project C that requires an immediate input of resource being used by both projects A and
B, but is otherwise unavailable. Project A has an S-shaped life cycle. Project B’s life cycle
is J-shaped. From which (or both or neither) do you borrow the resource? Why?

6-7
In this case it would be best to borrow from project A. In an S-shaped project, fewer
resources will have little impact on project A’s performance as it nears completion.
Conversely, in a J-shaped project, taking resources away from project B as it nears
completion will dramatically reduce its performance.
6. Goldratt suggested that to avoid the student syndrome,” it is a good idea to set the
activity durations so short that there is a high probability that the task will not be finished
on time. On the other hand, it has long been known that setting up people for failure is
strongly demotivating. What should the PM do?
There is a delicate balance between setting goals that people believe are impossible to
achieve and therefore result in demotivating the team versus stretch goals that serve to
motivate the team.
The project manager should not set goals that have extremely low probabilities of success,
but may find it desirable to set goals that do have a reasonable chance of not being met
(say 40 to 60 percent).
7. Describe as many types of resource allocation problems as you can, based on the
situations described in the chapter.
The chapter identifies three types of resource allocation problems:
• Available resources (resource loading).
• Scarce resources – single projects.
• Scarce resources – multiple projects.
Resource loading recognizes the existence of needed resources and ensures that they are
allocated to the project when needed. An example would be a construction site where the
electrical work is subcontracted to an external supplier. The main task is to determine that
the external firm can have the necessary skilled work force on site at the appropriate time.
Scarce resources are those with limited availability and the key elements of the project have
to be scheduled around that availability of the resource - even if a firm has just a single
project. An example of this situation would be the reliance of a construction site on a
specific piece of equipment such as a crane.
The allocation of scare resources becomes far more complex when the same resources are
need on more than one project. In this case, the utilization of the resource on project A will
also have an impact on project B (and, possibly, other projects). As indicated in the chapter,
the company will need to apply one of the six priority rules to determine which project shall
have the first use of the scarce resource.

6-8
Solutions to Exercises
1. This project involves the landscaping of a building site.
a. The Gantt chart for the project.
b. Assuming a five day week, the critical path is: A-C-D-E-G and the project duration is 14 days.

6-9
c. Since each resource is assigned 100 per cent to each task, the resource constraints are:
• Resource X is over utilized on the Friday of week 1, Monday of week 2, and Tuesday
of week 3.
• Resource W is over utilized on Tuesday of week 3.
d. After leveling the resources, the project duration is 17 days and the critical path is
A-B-C-D-E-F-G. Because of the scarcity of resources the critical path now includes all
activities.
e. If it is necessary to shorten the project duration without overallocating the resources then
there are several options:
• Since resource X is required by all activities, it makes the most sense to consider
adding this resource first. Adding an additional X resource would shorten the
project by 2 days which would allow tasks B and C to be done simultaneously.
• Adding an additional X and W would shorten the project by 3 days. The extra X
would allow tasks B and C to be done simultaneously and adding an extra W would
further allow tasks E and F to be done simultaneously.
• Adding an additional Y does not help reduce the time with any combination of
additional X and W resources.
• Other possibilities might involve relaxing the predecessor relationships, reducing the
assigned resources to some of the tasks, and so on.

6-10
The project duration is 13 weekdays when the resources work weekends and after leveling.
2. Provided are the predecessors, normal time, normal cost, crash time and crash cost for an
eight activity (a to h) project.
a. The network for this project is as follows:
The critical path is b-c-e-h. The project duration and cost for the all normal level of project
activity is 20 days and $400, respectively.
b. The crash costs per day for all activities are shown in column F.
1
2
3
4
5
6
a
b c
d
e
g
h
f
4
5
6
7
8
9
10
11
12
13
A B C D E F
Normal Normal Crash Crash Crash
Activity Time Cost Time Cost Cost/Day
a 5 $50 3 $150 50
b 4 $40 2 $200 80
c 7 $70 6 $160 90
d 2 $20 1 $50 30
e 3 $30
f 8 $80 5 $290 70
g 5 $50 4 $100 50
h 6 $60 3 $180 40

6-11
c. The spreadsheet below was created to find the optimal way of getting to an 18-day delivery
time. As shown, the total normal cost is $400 (cell C14) and the total crash cost is $80 (cell
I14) for a total project cost of $480 (cell B2). The 18 day duration was achieved by crashing
activity h 2 days (cell H13).
The optimal solution using Solver was found in the following way:
• Cell I14 was specified as the target cell to minimize.
• The ranges H6:H13 and B18:B22 were specified as the changing cells.
The following constraints were added:
• H6:H13 < G6:G13 (maximum amount each activity can be crashed)
• B18 > J7 (node 2)
• B19 > B18 + J8 (node 3)
• B19 > J6 (node 3)
• B20 > B19 + J9 (node 4)
• B21 > B18 + J11 (node 5)
• B21 > B19 + J10 (node 5)
• B22 > B20 + J12 (node 6)
• B22 > B21 + J13 (node 6)
• B22 < B1 (node 6 – project deadline)
• 6:H13 > 0 and B18:B22 > 0 (all decision variables must be > 0)
• The “Assume linear model” check box was also selected.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
A B C D E F G H I J
Deadline: 18
Total Cost: $480
Normal Normal Crash Crash Crash Max Crash Amt Crashing Actual
Activity Time Cost Time Cost Cost/Day Amt to Crash Cost Time
a 5 $50 3 $150 50 2 0.0 0.0 5
b 4 $40 2 $200 80 2 0.0 0.0 4
c 7 $70 6 $160 90 1 0.0 0.0 7
d 2 $20 1 $50 30 1 0.0 0.0 2
e 3 $30 0 0.0 0.0 3
f 8 $80 5 $290 70 3 0.0 0.0 8
g 5 $50 4 $100 50 1 0.0 0.0 5
h 6 $60 3 $180 40 3 2.0 80.0 4
Total $400 $80
Event
Node Time
2 4
3 11
4 13
5 14
6 18

6-12
d. The optimal 16-day project duration can be found by entering 16 in cell B1 and then
resolving using Solver. The optimal solution calls for crashing activity h 3 days, b 1 day, and
d 1 day. The cost of completing the project in 16 days is $400 + $230 = $630.
e. If all activities are crashed as much as possible, the project can be completed in 14 days.
Entering 14 in cell B1 and resolving, it is discovered that the project can be completed in 14
days at a cost of $400 + $ 400 = $800.
3. Given the following AOA network, what is the first activity to be given extra resource?
The following Table shows the activity, duration, successors, critical followers, and slack
associated with each of the four activities:
Activity Duration Successors Critical Followers Slack
a 4 d d 6
b 3 c,d c,d 0
c 7 d d 0
d 5 None None 0
a. Using the shortest task first priority rule for the critical path: Task b has the shortest
duration.
b. Minimum slack first … Tasks b, c, and d all have zero slack.
c. Most critical followers … Task b has the largest number of critical followers.
d. Most successors … Task b has the largest number of successors.

6-13
4. Given the project shown in Figure 5-10 of Chapter 5 and the fact that the facility used by
activities c and d is scarce, which activity would benefit from each of the rules?
The following Table shows the activity, slack, critical followers, duration, and latest start
time for activities c and d:
Activity Slack Followers Critical Followers Duration Latest Start Time
c 3 f,i None 3 8
d 2 g,h,j h,j 4 7
a. Using the minimum slack rule: Activity dD has the least amount of slack and therefore
would get the facility first using this rule.
b. Most followers … d has the most followers and would get the facility first.
c. Most critical followers … d has the most critical followers and would get the facility first.
d. Shortest task first … c has a smaller duration and would get the facility first.
e. With the “as late as possible” priority rule, the latest start times are used. In this case
activity c has a LS of 8 and d has a LS of 7. In using this rule it only makes sense to assign the
facility to the resource with the earliest LS or activity d.

6-14
5. Consider the following activity information and the constraint that the project must be
completed in 16 weeks.
The above worksheet was used with Excel Solver to find the solution. Solver was set to
minimize N11 by changing cells K4, K7, K9, and K10 subject to the constraints:
• J19 = 16
• K4 ≥ L4
• K7 ≥ L7
• K9 ≥ L9
• K10 ≥ L10

6-15
6. Consider the project network below. Suppose the duration of both activities A and D can be
reduced to 1 day, at a cost of $15 per day of reduction. Also, activities E, G, and H can be
reduced in duration by 1 day, at a cost of $25 per day of reduction. What is the least-cost
approach to crash the project 2 days? What is the shortest “crashed” duration, the new
critical path, and the cost of crashing?
Activity
Normal
Time
Crash
Time
Δ
Time
Slope
$
A 4 1 3 $15
B 3 3 0 $-
C 1 1 0 $-
D 5 1 4 $15
E 4 3 1 $25
F 1 1 0 $-
G 3 2 1 $25
H 5 4 1 $25
I 2 2 0 $-
J 1 1 0 $-

6-16
Least-Cost Crash Options
Activity
New
Time
Crash
Costs
A1,D1 11 $30
A2 11 $30
D2 11 $30
Least-Duration Crash
Activity
New
Time
Crash
Costs
A1,D2,E1,G1,H1 5 $120

6-17
7. The network for shooting a TV commercial as shown in the table has a fixed cost of $90 per day,
but money can be saved by shortening the project duration. Find the least-cost schedule.
The critical path is 1-2-3-4 = 19 days
Can crash 1-2 ($30) or 2-3 ($40) on critical path 1 day (3-4 cannot be crashed). Crashing 1-2 by 1 day
cheapest option and results in net savings of $60 ($90-$30).
Critical path is still 1-2-3-4 (18 days). Can crash 1-2 ($50) or 2-3 ($40) on critical path 1 day. Crashing 2-3
by 1 day cheapest option and results in net savings of $50 ($90-$40).
Critical path is 1-2-3-4 (17 days) and 1-2-4 (17 days). Can crash 1-2 ($50) or 2-3 ($45) on first critical path
by 1 day and crash 1-2($50) or 2-4($35) by 1 day on second critical path. Crashing 1-2 shortens both
paths by 1 day and is cheaper than crashing 2-3 on first path and 2-4 on second path. Therefore
cheapest option is to crash 1-2 and results in net savings of $40 ($90-$50).
Critical path is 1-2-3-4 (16 days) and 1-2-4 (16 days). Can crash 1-2 ($70) or 2-3 ($45) on first critical path
by 1 day and crash 1-2($70) or 2-4($35) by 1 day on second critical path. Crashing 1-2 shortens both
paths by 1 day and is cheaper than crashing 2-3 on first path and 2-4 on second path. Therefore
cheapest option is to crash 1-2 and results in net savings of $20 ($90-$70).
Critical paths are 1-2-3-4, 1-2-4, and 1-3-4 (15 days). Can crash 2-3($45), 2-4($35), and 1-3($60) for total
cost of $140. Since the cost of $140 exceeds savings of $90, crashing the project another day is not
justified.
8. Given the network for an HR training project with normal times and crash times (in parentheses),
find the cost duration history. Assume indirect costs for facilities and equipment are $100 per
day.
There are two paths: 1-2-4 (14 days) and 1-2-3-4 (17 days). At 17 days and $100 per day the normal cost
of the project is $1,700. The options to crash the longer path are: 1-2($30), 2-3($80), and 3-4($25).
Since it is least costly to crash, crash 3-4 by 1 day for savings of $75 ($100-$25). The durations of the
two paths are now 1-2-4 (14 days) and 1-2-3-4 (16 days) and the cost of the project is $1,625 ($1,700 -
$75).
The options for crashing the longer path are: 1-2($30), 2-3($80), and 3-4($60). Since it is least costly to
crash, crash 1-2 by 1 day for savings of $70 ($100-$30). Since 1-2 is on both paths, the durations of the
1 2 3
4

6-18
two paths are now 1-2-4 (13 days) and 1-2-3-4 (15 days) and the cost of the project is $1,625 ($1,700 -
$75).
The options for crashing the longer path are: 1-2($50), 2-3($80), and 3-4($60). Since it is least costly to
crash, crash 1-2 by 1 day for savings of $50 ($100-$50). Since 1-2 is on both paths, the durations of the
two paths are now 1-2-4 (12 days) and 1-2-3-4 (14 days).
The options for crashing the longer path are: 2-3($80) and 3-4($60). Since it is least costly to crash,
crash 3-4 by 1 day for savings of $40 ($100-$60). The durations of the two paths are now 1-2-4 (12 days)
and 1-2-3-4 (13 days).
The only option for crashing the longer path is 2-3($80). Crashing 2-3 by 1 day creates savings of $20
($100-$80). The durations of the two paths are now 1-2-4 (12 days) and 1-2-3-4 (12 days). Path 1-2-3-4
cannot be crashed and further and crashing 1-2-4 would not reduce the time to complete the project
since both paths currently have a duration of the 12 days. The duration-cost history of this is
summarized in the table below.
Duration Cost
17 $1,700
16 $1,625
15 $1,555
14 $1,505
13 $1,465
12 $1,445
9. Given the following highway rerouting project
a. Draw the network.
A C
B
E
D
G
F

6-19
b. Find the ESs. LSs, and slacks.
Activity ES EF LS LF Slack
A 0 4 3 7 4
B 0 6 0 6 2
C 4 6 7 9 2
D 6 12 6 12 6
E 6 9 9 12 3
F 6 9 9 12 3
G 12 17 12 17 5
c. Find the critical path.
Critical path: B-D-G
d. If the project has a 1 ½-year deadline for reopening, should we consider crashing some activities.
Explain.
Completing the project in 1.5 years or 18 months. The expected duration is 17 months. Since
the expected duration is less than the deadline, crashing does not need to be considered at this
time.
10. After entering the resource information, are there any problems with the resources being
overloaded? If so, level the resources so that the resources are not overloaded. What impact
does leveling the resources have on the expected project completion time?
Mike and JR were assigned to the tasks in MSP’s Gantt Chart View as shown below:

6-20
Using the Resource Graph view, it is discovered that Mike is overallocated in the first week:
Using the “Level All” feature resolves resource overallocations. In the case, the overallocations can
be resolved without increasing the duration of the project.

6-21
Incidents for Discussion Suggested Answers
Lab Results, Inc.
Question 1: Do you think Sam’s plan is going to work? Why or why not?
No, Sam’s plan of just adding this work to his current work load without any additional
resources will not work for a number of reasons:
• There is little or no excess capacity in the current operation. If Sam is paying overtime
weekly, his current staff are working beyond normal capacity now. Adding additional
work through this new project will only add to this.
• Sam’s plan does not take into account vacation or sick time for his technicians. Four
months is also a long time to ask the staff to work more overtime on top of what they
are already working.
• There is also no time built in to deal with any issues that may come up, such as increases
in work load from his other clients, problems with equipment, etc.
If he continues with this plan, quality and the ability to meet the scheduled delivery of results
will suffer.
How would you handle the bid on the new project?
Among the steps one could take would be to:
• Redesign the project plan for this new job to include additional resources to complete
the additional work.
• Use this as an opportunity to build excess capacity into the current system.
Focusing on the costs associated with additional resources instead of paying overtime to
already overworked staff would reduce the project cost and improve the chance of meeting the
projects specification for quality and delivery.
Question 2: Would Crystal Ball be useful in assessing Sam’s plan and changing it, if necessary?
If Sam has data on the ebb and flow of demand on this work force across time, he can use
Crystal Ball to simulate the amount of overtime his workforce will be expected to work if he
wins the contract. Further, he can find the amount of system capacity consistent with any
given level of overtime.

6-22
Southern Kentucky University Bookstore
Question 1: Is the minimum slack rule a reasonable way to schedule resources of the Textbook
division? Why or why not?
No. The projects are not combined and the minimum slack on one may receive resources when
its slack is more than the minimum slack on another project.
Question 2: What complication is added by making this project four separate projects?
The interactions between these projects are important and must be accounted for by
scheduling this as a multiproject plan. Peak resource loads need to be determined in advance
and leveled. The overall project schedule should be determined with the resource utilization of
each area in mind.

6-23
Suggested Case Analyses and Solutions
Friendly Assisted Living Facility Resource Usage – Part 6
Teaching Purpose: In this installment students are required to develop Gantt charts for the
resources and prepare a resource calendar using MSP.
Question 1: Prepare a Gantt chart with resources for the action plan Dr. Alison submitted.
Begin this project on January 2. Prepare a resource calendar for Dr. Alison.
The following is the Gantt chart of the action plan presented in the case. This Gantt chart was
prepared using MSP with a resource calendar for Dr. Alison and Dr. Link with a workweek of
Monday through Friday, and a daily schedule of 8 a.m. to 5 p.m. with an hour of non-working
time for lunch.
The resource calendar was applied using the “Change Working Time” under the “Tools” menu
in MSP. (The issue of scheduling the “Test of the assessment tool…” will be addressed in answer
#3 & #4). Note: the case stated to start the project on January 2, if students use the year 2000,
the project will actually begin work on January 3rd, as January 2nd is a non-working day. If
students use January 2, 2001 (or later), the project will start on January 2nd. The start date used
in these examples is January 2, 2000, to coincide with the year that the case started.

6-24
The following is the standard resource calendar used for Dr. Alison for all of the tasks defined
by the action plan. Since the case outlined that a resource scheduling conflict would only
pertain to the task of “Testing the assessment tool”, it is not appropriate to constrain Dr. Alison
on the project for any other tasks. Note: The following printout excerpt was prepared using the
Reports feature in MSP. The issue of how to handle the specific scheduling constraint will be
addressed in answer #3 below.
Question 2: How would you handle Dr. Alison’s resource problem?
The resource issue that Dr. Alison has should be handled by adjusting the project schedule to
allow for the scheduling constraints.
The case states that Dr. Alison can perform all of the project steps within his 8 a.m. to 5 p.m.
normal work week, however he will only be able to perform the “Test of the assessment tool”
during his administrative time on Wednesday’s from 8 a.m. to 12 p.m. Since that step is
important to the success of the project, it is necessary to adjust the project plan to reflect Dr.
Alison’s scheduling conflict. It is not appropriate to add another resource, or overallocate Dr.
Allison to get this task done within the time frame specified.
There are several different ways to set a resource constraint on the “Test the tool” task, Step #4
in the action plan. MSP 2007allows you to create a specific calendar for a step in an action
plan. Simply create a New calendar in the Tools menu, “Change working time” section. In the
new calendar create a schedule that has its working time as Wednesdays, 8 a.m. to 12 p.m., and
all other days as non-working. Then you apply this calendar to step 4 in the action plan. (This is
done by selecting the task information box for Step #4, going to the “Advanced” tab, and
selecting the new calendar you just created. These steps are all outlined in the Help section,
under “Assigning a calendar to a task”.)

6-25
Once you apply the new calendar, MSP will automatically adjust the Gantt chart to reflect the
changes in the schedule. Note: If students are using MSP98, the schedule constraint can be
incorporated into the project by adjusting Dr. Alison’s resource calendar for only the time
period that this step takes place (Jan 19 – Jan 26).]
Question 3: Given Dr. Alison’s availability, how long will it take to complete testing of the
assessment tool?
Based on Dr. Alison’s availability to complete the step “Test of the assessment tool”, Step #4
will now take from January 19, 2000 – January 26, 2000. Please note that the task’s duration
remains at 6 hours, however with Dr. Alison only available to work on the step from 8 a.m. – 12
p.m. one day a week, the step will now take an extra calendar week to complete. Without the
constraint the task could begin as soon as Step #3 was completed, January 14. However, with
the constraint applied, Step #4 cannot begin until the following Wednesday when Dr. Alison is
available, and he can only work 4 hours on that day, so another 2 hours the following
Wednesday is necessary to complete the task.
Question 4: Prepare a Gantt chart for Dr. Alison’s plan incorporating any changes you
recommend.
The Gantt chart below shows the scheduling changes adjusted for the availability of Dr. Alison
to complete step #4 in the action plan.

6-26
Or with a more detailed view of the calendar:

6-27
Charter Financial Bank
Teaching Purpose: This case provides students with opportunity to evaluate alternative crashing
strategies.
Question 1: What is the cost of completing this project if no overtime is used? How long will it
take to complete the project?
The network diagram shown below can be constructed from the information in the case.
The time to complete the project at a normal level of activity is 43 days and the cost is
$100,650.
Question 2: What is the shortest amount of time in which the project can be completed?
What is the cost of completing the project in the shortest amount of time?
When all the activities are crashed their maximum amount, the project is completed in 30 days.
In the spreadsheet below, Solver was used to find the least costly way to crash the project such
that it was finished in 30 days. Column H details the amount each activity was crashed. The
incremental cost required to shorten the project these 13 days is $26,250 (cell I13).
1 2
Benchmarking
3
Pla
n
Design
4 6
5
7
Pages
DB
Forms
Test
8
e
s
t

6-28
Using Solver required the following steps:
o Cell I13 was specified as the target cell to minimize.
o The changing cells included the ranges I6:I12 and B17:B23.
In addition to specifying “Assume linear model” the following constraints were entered:
• H6:H12 < G6:G12 (limit on the amount each activity can be crashed)
• B17:B23 > 0 & H6:H12 > 0 (nonnegativity constraints)
• B17 > J6 (node 2)
• B18 > B17 + J7 (node 3)
• B19 > B18 + J8 (node 4)
• B20 > B19 + J9 (node 5)
• B20 > B21 (node 5)
• B20 > B22 (node 5)
• B21 > B19 + J10 (node 6)
• B22 > B19 + J11 (node 7)
• B23 > B20 + J12 (node 8)
• B23 < B1 (deadline specified)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
A B C D E F G H I J
Deadline: 30
Total Cost: $126,900
Benchmark 10 $15,000 7 $18,750 1250 3 3.0 3750.0 7
Plan 5 $3,750 3 $4,500 375 2 2.0 750.0 3
Design 15 $45,000 10 $58,500 2700 5 5.0 13500.0 10
Database 10 $9,000 7 $11,250 750 3 2.0 1500.0 8
Webpages 10 $15,000 8 $19,500 2250 2 2.0 4500.0 8
Forms 7 $8,400 7 0 0.0 0.0 7
Test 3 $4,500 2 $6,750 2250 1 1.0 2250.0 2
Total $100,650 $26,250
Event
Node Time
2 7
3 10
4 20
5 28
6 28
7 27
8 30

6-29
Question 3: Suppose that the benchmarking study actually required 13 days as opposed to the
10 days originally estimated. What actions would you take to keep the project on a normal
schedule?
The spreadsheet presented in question 2 can be modified such that the benchmarking study’s
normal and crash times are now 13 days implying that this task can no longer be crashed. Then
the spreadsheet can be resolved using Solver and specifying a deadline of 43 days. As shown in
the spreadsheet, below the project can still be completed in 43 days by crashing the Plan task
by 2 days and the Test task by 1 day. The cost of crashing these two tasks will increase the
project cost by $3,000.
Question 4: Suppose the President wanted the website launched in 35 days. What actions
would you take to meet this deadline? How much extra would it cost to complete the project
in 35 days?
The spreadsheet presented in question 2 can again be modified. This time 35 is entered in cell
B1 and the problem resolved with Solver. Column H in the spreadsheet below details the
amounts the various activities should be crashed to meet the 35-day deadline. The extra cost
of reducing this project 8 days (43 – 35) is $12,150.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
A B C D E F G H I J
Deadline: 35
Total Cost: $112,800
Benchmark 10 $15,000 7 $18,750 1250 3 3.0 3750.0 7
Plan 5 $3,750 3 $4,500 375 2 2.0 750.0 3
Design 15 $45,000 10 $58,500 2700 5 2.0 5400.0 13
Database 10 $9,000 7 $11,250 750 3 0.0 0.0 10
Webpages 10 $15,000 8 $19,500 2250 2 0.0 0.0 10
Forms 7 $8,400 7 0 0.0 0.0 7
Test 3 $4,500 2 $6,750 2250 1 1.0 2250.0 2
Total $100,650 $12,150
Event
Node Time
2 7
3 10
4 23
5 33
6 33
7 30
8 35

6-30
Rand Contractors
The PERT chart for the project is shown below:
The figure below provides the Crystal Ball model that was created for the Rand Contractors mini
case:

6-31
1. From the Crystal Ball (CB) above it can be seen that analyzing this situation in the usual
way requires analyzing two paths (ABCEF and ABDEF). Assuming the activity times
follow a Beta distribution and simulating the CB model 10.000 times yielded the
following results:
• Expected project completion time: 25.55 days
• Minimum project completion time: 21.88 days
• Maximum project completion time: 31.04 days
2. The following probabilities were found using the CB model:
• The probability the project is finished in 25 days or less: 35.58%
• The probability the project takes longer than 27 days to complete: 13.74%
• The probability the project is finished between 24 and 26 days: 53.03%
3. The only difference between the two paths is whether the plumbing or electrical work
gets done by Bruce first. Since Bruce does both of these activities, the duration of the
project can be found by summing the durations of all five activities as is shown at the
bottom of the figure above. Simulating the CB model 10,000 times yielded the following
results:
• Expected project completion time: 28.43 days
• Minimum project completion time: 24.24 days
• Maximum project completion time: 34.28 days
4. The following probabilities were found using the CB model:
• The probability the project is finished in 25 days or less: 0.34%
• The probability the project takes longer than 27 days to complete: 83.10%
• The probability the project is finished between 24 and 26 days: 4.21%
5. When the actual resources that will be assigned to each activity are considered, the
expected time of the project increases. The implication to project managers is that not
considering the resources that will be allocated to the activities increases the chances
that the project duration may be underestimated.
6. There are a number of different ways to address this. One way is to find a window for
the project’s duration such that the project has a desired probability of finishing within
this window. For example, there is almost a 95% chance the project will be finished
between 26 and 32 days. Providing a window has the advantage of letting the next
customer know the earliest and latest the project is likely to start. On the other hand,
some customers may only be interested in what the latest the project start date might
be. Using the CB model it can be determined that there is slightly more than a 95%
chance the project will be finished in 31 days. Of course different desired probabilities
could be used.

Another Random Scribd Document
with Unrelated Content

next corner. The man was not in overalls and did not look like a
workman.
Jim hallooed to him and the man looked back. But instead of
stopping he broke into a run.
In a moment Jim was after him like a hare. But the man was now
near the corner, and by the speed he put on showed that he was no
mean runner himself. He reached the corner just as a trolley car,
going at a rapid rate, came dashing down the side street.
With a recklessness that might have cost him his life, the man
made a jump for the rear platform, clutching the rail with his
extended hand. The shock seemed as though it might have
wrenched his arm from its socket. But he held on desperately, and
finally drew himself up on the platform and entered the car.
By the time Jim reached the corner the car was a block away. Jim
shouted and waved his hands, but the conductor was inside,
expostulating with his passenger for the risk he had taken, and did
not see or hear him.
The case was hopeless, and Jim, inwardly raging, gave up the
chase and retraced his steps. Joe, who had come to the front of the
house to see what had caused Jim’s sudden departure, came
forward to meet him.
“What’s the big idea?” Joe asked, in some wonderment.
“The idea,” panted Jim wrathfully, “is that I came near getting my
hands on a big rascal and just missed doing it.”
“A rascal?” exclaimed Joe.
“That’s what I said,” replied Jim. “Come to the back of the house
and I’ll show you what I mean.”
“All right, Jim.”
“You thought,” said Jim, “that when that pile of lumber came
down it was an accident. So did I at first. I thought the scaffold had

given way under the weight. But when I glanced at it I saw, as you
can see now, that the scaffold hadn’t broken.”
Joe looked and saw that Jim was right.
“You mean—” he began slowly.
“I mean,” said Jim, “that somebody pushed that lumber over the
edge of the scaffold. And whoever that somebody was, he meant
that the falling lumber should cripple you.”
Joe looked at his chum with rage and horror dawning in his eyes.
And while the full meaning of the dastardly act was sinking into his
mind, it may be well for the benefit of those who have not read the
preceding volumes of this series to leave him and his chum for a
moment and tell who Joe was and by what steps he had reached his
present position as the greatest pitcher that baseball had ever
known.
Joe Matson’s first experience on the diamond was gained in the
little town of Riverside in a Middle Western State, where he had
been born and brought up. From early boyhood he had loved the
game and displayed a natural aptitude for pitching. His success in
this restricted field soon made him known as one of the best
amateur boxmen of his own and surrounding towns. His early
exploits and the difficulties he had to overcome are narrated in the
first volume of this series, entitled: “Baseball Joe of the Silver Stars;
Or, the Rivals of Riverside.”
In the second volume, “Baseball Joe on the School Nine,” can be
noted the steady progress he was making in pitching skill. The bully
of the school did all he could to throw obstacles in his way. But Joe
throve on opposition and his grit first won and then increased his
reputation.
When, a little later, he went to Yale, he found a larger field for his
prowess in the box. It is a hard thing for a newcomer to break into
the ranks of the veteran upper classmen who have gained glory in
the athletic field. But by a singular chance Joe found his opportunity
when the “Princeton Tiger came down to put some kinks in the

Bulldog’s tail.” It was a sadly bedraggled Tiger, however, that went
back to his lair when Joe had got through with him and had chalked
up a glorious victory for Yale.
But Joe, although he stood well in his studies, was not altogether
happy at the great university. His mother wanted him to study for
the ministry, but Joe, although he respected that noble profession,
felt too strongly the call to the outdoor life. He felt that he had it in
him to make good in the ranks of professional baseball, and finally
gained his mother’s reluctant consent to make the venture. His
chance came when a minor league manager, who had been struck
with his work in the game with Princeton, made him an offer. Joe
promptly accepted, and it was not long before his manager learned
that he had drawn a prize in getting a man on his team who had all
the earmarks of a star. How Joe began to climb in professional
baseball is told in the fourth volume of the series, entitled: “Baseball
Joe in the Central League.”
In these days of keen-eyed scouts no player can long hide his light
under a bushel, and before long Joe, to his great delight, was
drafted by the St. Louis team of the National League and ceased to
be a “busher.” Here he was brought into competition with the
greatest players of the game, and it soon became apparent that he
could hold his own with any of them.
No one realized this sooner than McRae, the famous manager of
the New York Giants. Several books of this series are devoted to his
exciting experiences with this great team, of which he was still the
mainstay when this volume opens. It was his magnificent work in
the box that won for the Giants the championship of the National
League and carried them to victory in several World Series with the
champions of the American League. After one of his greatest years
he went with the team on a tour about the world, in the course of
which he had many hazardous and thrilling adventures.
During this time he was not only showing phenomenal skill as a
pitcher, but was rapidly growing in repute as a batsman. He was a
natural hitter, timing and meeting the ball perfectly and landing on it

so hard that it sought the farthest corner of the field. Before long
the fans began to crowd the grounds not only to see a ball game but
to “see Matson knock out another homer.” How his batting and
pitching combined made him a national baseball idol is narrated in
the preceding volume of this series, entitled: “Baseball Joe, Home
Run King; Or, the Greatest Pitcher and Batter on Record.”
But Joe had also won another victory that he prized above all his
baseball triumphs. He had met and fallen in love with Mabel Varley, a
charming girl whom he had met under romantic circumstances near
her home at Goldsboro, North Carolina. The course of true love did
not run altogether smoothly in his case more than in others, but all
attempts to part them had been triumphantly overcome and at the
close of the previous season on the diamond, Joe and Mabel had
been married. Joe esteemed himself the happiest and luckiest of
men.
Joe had as his closest friend, Jim Barclay, a Princeton graduate
who had entered the ranks of organized baseball and joined the
Giants as a “rookie.” Joe had taken to him at once and they were
speedily on the best of terms. Jim had a great deal of pitching
ability, and under the careful tutelage of Joe he had blossomed out
into a regular member of the pitching staff. At the present time he
stood only second to Joe himself as a twirler, and bade fair to
become one of the great stars of the game.
Jim had met Joe’s sister Clara when the latter had come on to see
her brother pitch in one of the World Series games and had lost his
heart at once. She, for her part, had at once conceived a marked
admiration for the stalwart, handsome friend of her brother, and this
had soon ripened into a deeper feeling. So that when Jim the year
before had asked her the momentous question he had got the
answer he craved, and their marriage was to take place as soon as
the playing season was over.
Now to return to the two chums as they stood beside the pile of
lumber that a few minutes before had so nearly caused the death of
one of them.

“You see then, Jim, that my hunch was right and that what I said
to you a little while ago wasn’t imagination,” said Joe.
“Some one is out to do you, for a fact,” assented Jim soberly. “And
all I ask is that I may get my hands on him for five minutes. Just five
little minutes! I’d make him wish he’d never been born!”
“That fellow you were chasing must have been the one who did
it,” ruminated Joe. “Did you get a good glimpse of him? Had you
ever seen him before?”
“Not that I know of,” replied Jim. “It certainly wasn’t either Hupft
or McCarney, or I should have recognized him at a glance. But that
doesn’t say that he mightn’t have been a tool of theirs. At any rate,
you can be sure that he was the man that actually pushed over that
pile of boards. His very running was a confession of guilt. And, by
the way he ran, I shouldn’t wonder if he were a ball player himself.
I’m not so slow myself, but he almost held his own. What a bit of
bad luck it was that that trolley came along just at that minute.”
“What did he look like?” asked Joe. “Was there anything you could
identify him by if you should happen to meet him again?”
“Well,” said Jim, cudgeling his memory, “I could see that his hair
was light and that his ears stuck out more than most men’s. But I
suppose there are ten thousand men in New York that would answer
that description. He didn’t look like a workman and he didn’t have
overalls on.”
“How did he happen to be Johnny on the spot, I wonder,” mused
Joe. “Do you suppose he’s been following us this morning?”
“Hardly likely,” conjectured Jim. “What is more probable is that he
knew that we were in the habit of practicing in this particular spot. It
hasn’t been any secret, and more than once in the clubhouse I’ve
mentioned what a dandy place we had for morning pitching practice.
That probably led the plotters to reconnoiter about this
neighborhood and get the lay of the land. The scaffold and the pile
of lumber carried their own suggestion. Work on the building has
stopped, and there’s nothing to prevent anybody lurking in the place

ready to take advantage of any chance that might offer itself.
Perhaps that fellow has been hiding in there every day for a week,
figuring that some time in the natural order of things you’d be
standing near that scaffold. And that he didn’t calculate wrongly is
shown by what happened this morning.”
“It was an infernal scheme all right,” said Joe. “A cunning one, too.
If that stuff had really landed on me, it would have been put down
as an accident, and no one would ever have been the wiser.”
“Well,” remarked Jim, “a miss is as good as a mile and some good
Providence must have been watching over you this morning. But it
gives you a desperate feeling to realize that enemies are working
against you in the dark and that you have no way of forcing them
into the open.”
“They’ll overreach themselves yet,” declared Joe confidently.
“There never yet was a crook that didn’t give himself away at some
time or other. In one way I’m glad this happened. It makes a
certainty of what before had been only a probability. Now we know
that somebody is trying to down me, and it will put us doubly on our
guard. But of course I needn’t tell you, Jim, that Mabel and Clara
must never hear a word of this. It would simply drive them crazy
with worry.”
“Trust me,” replied Jim. “We’ll keep this up our sleeves and tell
them nothing about it until we’ve squelched the rascals who have
been trying to get your number. And even then I guess we’d better
keep mum. What they don’t know won’t hurt them.”
“Righto,” assented Joe. “But now I guess we’d better have our
lunch and get ready for the game. We won’t have any more time
than we need to reach the grounds.”
“I’m just as glad that it isn’t the turn of either of us to pitch to-
day,” commented Jim. “I guess we’re both a bit too shaken up to be
in our best form. But if my arm is idle to-day my eyes won’t be, and
you can bet that from this time on I’ll watch Hupft and McCarney like
a hawk.”

“Same here,” responded Joe grimly. “And if I get the goods on
them, may heaven have mercy on them—for I won’t!”

CHAPTER III
UNDER COVER
Joe and Jim ate their lunch that day in a little more thoughtful
mood than usual, and that mood still persisted as they prepared to
go to the grounds.
But the ten minutes of brisk walking in the bracing air soon
dissipated the somber shadow that had tried to settle down upon
them. They were young and vital, the blood coursed strongly
through their veins, and they were soon feeling the sheer joy of
living that was natural to them.
And this feeling grew stronger as they drew near the Polo
Grounds. That famous park held a strong place in their affections. It
was the visible symbol of their profession, the place where they had
won their spurs, where they had gained glorious victories that
thrilled them to the marrow as they recalled them, where they had
fought memorable battles in which every particle of their strength
and manhood had been called into play, where they had listened to
the plaudits of cheering thousands who had lauded them to the
skies when they had pulled some hotly contested game out of the
fire.
Soon they were in the midst of the procession that even at that
early hour was wending its way towards the gates. It was not long
before they were recognized, and admiring comments began to pass
from one to another of the crowd.
“That’s Baseball Joe, the king of them all.”
“Did you see the game he pitched against the Brooklyns
yesterday? It was a corker, all right.”

“Trust him to show those bimbos from over the bridge where they
get off.”
“And that fellow with him is Barclay. There’s nothing slow about
him, either. Has been going great guns all the season.”
“If they only had two more like them the pennant would be
cinched already. The Giants would win in a walk.”
Joe and Jim would not have been human if such comments had
not pleased them. But they were used to hero worship, and, as the
crowd began to close in upon them and hinder their progress, they
were glad enough when they reached the players’ gate and could
slip into the grounds.
Some of the players had preceded them to the clubhouse and
were already getting into their uniforms, and the newcomers
speedily followed their example.
“What’s the matter with your arm, Joe?” asked Larry Barrett, the
second baseman, “Laughing Larry,” as he was called because of his
jolly disposition. “It’s all cut and bruised. Been in a fight?”
“Nothing like that,” replied Joe, making haste to cover the injured
member. “Had a tumble this morning and that arm got the brunt of
it. Little bit sore yet, but it will be all right by to-morrow.”
“Well, for the love of Pete, don’t have any more such tumbles,”
implored Larry. “It might catch your pitching arm next time. And if
anything happened to that wing of yours the Giants would be in the
soup.”
“They’d get out of it again,” countered Joe. “The Giants are too
great a team to be dependent on one man. McRae would simply
have to look around for another pitcher.”
“Sure!” said Larry sarcastically. “Just as simple as that! Look
around for another pitcher! There are plenty of pitchers such as they
are, but there’s only one Matson.”

“And that’s no lie,” broke in Curry, the star left fielder of the team.
“Many’s the time, old boy, that you’ve carried the whole team on
your back. And now that Hughson’s gone we’ll have to rely on you
more than ever if we’re to have a look in for the flag.”
“Good old Hughson,” murmured Joe regretfully. “It won’t seem like
the old team without him. I only hope he’ll prove as great a
manager as he was a pitcher.”
There were murmurs of assent to this from all about him, for
Hughson had been a favorite with every member of the team, as
indeed he had been with players and fans all over the United States.
For many years before Joe had broken into baseball, Hughson had
stood for all that was best and greatest in the game. For more than
ten years he had been recognized as the finest pitcher on the
diamond. Again and again he had led the Giants to the
championship. He had everything that a pitcher should have—speed,
curves, slants, drops, in bewildering variety and profusion. The very
fact that he was slated to pitch against a team was almost enough
for that team to count the day lost. It was not merely the skill and
strength of his pitching arm that inspired terror in his opponents.
Still more formidable was the head set on his sturdy shoulders. He
could outguess the batsman in a way that seemed almost uncanny.
He mixed brains with his work, saving his strength when he could,
letting the eight men behind him do their share of the work. But
when the pinch came, he tightened up, and usually it was all over
but the shouting.
Add to this phenomenal skill that he was a gentleman, on and off
the diamond, genial, kindly, always playing fair, an honor and an
ornament to the national game, and it was not hard to understand
his wonderful popularity.
Joe had especial reason for the warm feeling with which he
regarded Hughson. The latter had greeted him cordially when he
first came to the Giant team. He had realized the marvelous skill
with which Joe was endowed and he knew that the time might come

when he would take his own crown as the greatest pitcher of the
game. Yet there was no trace of jealousy or apprehension in his
treatment of the newcomer. He coached him, corrected his faults,
brought out his strong points and taught him all that he knew
himself, not omitting the secret of the “fadeaway” ball that had
made him famous. He and Joe had become and always remained
the warmest of friends.
An automobile crash in which Hughson had been caught had
injured his pitching arm, and despite an extended course of
treatment its magic had gone forever. Even after that misfortune,
however, he had remained with the Giants for two seasons. But he
was not the Hughson of old. He was able to get by in many games
by favoring his arm and depending chiefly on headwork.
Now he had left the team with which he had been identified for so
many years and accepted the position of manager of the Cincinnati
Reds. The best wishes of all the Giant team had gone with him.
Already under his management the Reds were improving and
seemed to be facing the best season they had had in years.
Only the week before the Cincinnatis had played the Giants on the
occasion of the first invasion of the Western clubs—played, too, with
such vim and spirit that the best the Giants could do was to break
even on the series.
“Yes, the loss of Hughson has put a dent in our chances for the
pennant,” put in Wheeler, the big center fielder. “Even with that lame
wing of his he won more games for us than any others, except you
and Jim. And you two, good as you are, can’t pitch every other day.
McRae ought to have his lines out for a couple more prospects in the
pitching line. The rookies we got this year haven’t made good in the
box. Young Bradley shows promise, but he needs a year or so yet
before he’ll be ready to take his regular turn.”
“You bet the old man isn’t asleep,” said Burkett, the burly first
baseman of the team. “He’s got his scouts out combing the minor
leagues with a fine tooth comb. I hear he has a line on Merton of

the San Francisco Seals. They say he shows all the signs of a top-
notcher. But even if he gets him, he won’t be able to report till the
end of the season, and by that time the pennant will be either lost or
won.”
“How about that Lemblow out in the Middle Western League?”
chimed in Mylert, the Giant catcher. “They say he’s got speed to burn
and a cross-fire delivery that reminds one of Hays of the Yankees.
He’s crazy to break into the big league, and if the old man comes
across with the ‘mazuma’ I’ve no doubt he could get him.”
“He may be a good pitcher,” remarked Iredell, the shortstop of the
team. “But I’ve heard that he has a rather shady past. Not that
they’ve ever been able to hang anything on him. Perhaps he’s too
cunning for that. But there have been all sorts of rumors about him
not being on the level, and where there’s so much smoke there may
be some fire.”
“I heard that he’s been resting up for a couple of weeks lately,”
volunteered Willis, the Giants’ third baseman. “Hurt one of his
fingers or something like that. I saw him pitch once in a barn-
storming tour at the end of last season. He sure can put some
smoke on the ball. Queer looking duck he is, too. Looks like a rube
with his straw-colored hair and big ears sticking out from his head.”
“What’s that you said?” put in Jim quickly.
“I said that he put smoke on the ball,” replied Willis, in some
surprise. “He just burned it over the plate.”
“Yes, yes,” returned Jim impatiently. “But I was talking about his
looks!”
“I was just telling you he wouldn’t take any beauty prize,” replied
Willis. “Big lob ears standing almost at right angles to his head and a
headful of hair that looks like a stack of hay. Tall and thin, too, a
regular beanpole. But what makes you so interested in the fellow’s
looks? He doesn’t have to be an Apollo Cuticura—or is it Belvedere?
—does he, to take his turn in the box?”

“Not a bit of it,” agreed Jim, with a laugh. “That would rule a good
many of us fellows off the diamond. But come along, Joe,” he added
to his friend. “If we stay in here chinning very much longer, McRae
will be after us with a big stick.”
They went out of the clubhouse and made their way across the
field. The bleachers were already full and there were only a few
vacant spots in the grandstand. As Joe and Jim were recognized a
vigorous handclapping rose from the spectators that told of the
place they had in the affections of the fans.
“Did you catch what Willis was saying about Lemblow?” Jim asked
of Joe, as they got out of earshot of the others.
“I got it all right,” replied Joe. “And I tumbled to your question
about his looks. You thought that the description fitted the fellow
that pushed that pile of lumber down on us.”
“Fits him to a dot,” affirmed Jim emphatically. “The same hair and
the same ears. And this fellow, too, was tall and thin. And what did I
tell you about the way he ran? Only a trained athlete could have
legged it that way.”
“It certainly looks as though you’d hit it right,” admitted Joe
thoughtfully. “Under ordinary circumstances it wouldn’t be possible,
for he’d be playing with his team out West. But there’s the fact that
he’s been laying off for a couple of weeks on account of his injured
finger. That would make it possible for him to come on East. And if
he’s so crazy to break into the big league, what would give him a
better chance than to have one of us, or possibly both of us,
disabled? It may all be a coincidence, but if it is, it’s one of the
queerest things that ever happened.”
“Then, too, there’s his reputation,” rejoined Jim. “What Iredell said
about his not being on the level only fits in with what I’ve heard
from others. He got into trouble near the end of last season about
one or two games that looked crooked, and it took a good deal of
hushing up to smooth the thing over. Now, putting all these things

together, doesn’t it look just as clear as that two and two make
four?”
“Not quite so certain as that, perhaps,” replied Joe. “But it
certainly looks as though we were getting a line on what happened
to us this morning. Now if we can only find that there’s some
connection between Lemblow and Hupft and McCarney, a good
many puzzling things will be explained. But there’s McRae beckoning
to us to get up to the plate and knock flies out to the fields in
practice. Just keep your eye peeled, old boy, and I’ll do the same.
There never yet was a skein so tangled that it couldn’t be unraveled
if you only get your hand on the end of the thread. And I think
we’ve got the end in our hands right now.”

CHAPTER IV
LINING IT OUT
The Giants’ opponents that day were the St. Louis Cardinals, the
last of the Western clubs to visit the Polo Grounds on the first round
of the inter-sectional games.
Cincinnati, as has been said, had been able to make an even
break of it with the Giants. The Pittsburghs had done even better, for
the Smoky City boys had left the big town with three scalps hanging
to their belts. The Giants had taken sweet revenge on the Chicagos,
however, having made a clean sweep of the whole four games.
For several seasons, the best the Cardinals could do was to finish
at the tail of the first division or the head of the second. They had
an excellent pitching staff and some of the heaviest batters in either
league. Their fielding was good and their shortstop was such a
phenomenon that the St. Louis owners had refused an offer of two
hundred and fifty thousand dollars for him.
But despite these advantages the team had not been able to win
the championship. They did not work with the smoothness and
perfection necessary for a champion team. Perhaps it was the failure
of efficient management or a case of individual stars playing for their
own records instead of for the good of the team. But whatever the
reason, the record showed that while they had started out each
season like a house afire they had failed at the end to take the
coveted flag.
This year, however, things were different. A new manager had
seemed to be able to put some of his own vim and determination
into the team and they were playing like a machine. The first four
men in the batting order had been dubbed the “Murderers’ Row”

because of the way they were “killing” the ball, and the rest of the
team were not very far behind. It was perfectly clear that this year
the Cardinals were a team to be reckoned with.
Under ordinary circumstances, Joe would have pitched the first
game of the St. Louis series so that the Giants might have a good
chance to get the jump on their opponents by grabbing off the
opening contest. But the day before had originally been an open
date, and the Giants and Brooklyns had taken advantage of it to play
off a postponed game; and as the Brooklyns had usually been a
“Jonah” for the Giants, McRae had thought it advisable to put Joe in
the box. The result had justified his judgment.
Markwith, the portside flinger of the Giants, had been chosen,
therefore, to open the St. Louis series. He was one of the star
pitchers of the league, and during the season could be counted on
to turn in his fair share of victories. His speed was dazzling and he
had a good assortment of curves and slants. The only trouble with
him was that he was an “in and outer.” When he was good he was
very good indeed, practically unbeatable. But if his support were bad
or the opposing batters began to get to him, he was liable to lose his
nerve and be batted out of the box.
This day, however, he showed up well in practice and seemed to
be in fine fettle, so that it was with less misgiving than usual that
McRae put on him the pitcher’s burden.
“Get right after them, Red,” the manager counseled, as the bell
rang for the Giants to take the field. “I want you to show that
Murderers’ Row that you’re some little murderer yourself.”
“I’ll do my best, Mac,” said Markwith, with a grin, as he slipped on
his glove and went to the box.
The first inning was short and sweet. Remley, the lead-off man of
the Cardinals, tried to wait Red out. This was justified perhaps by
the fact that Markwith was a trifle unsteady at the opening and had
difficulty in finding the plate. His first two offerings were balls. He
whipped the third over, however, for a strike and followed it with

another. With two strikes on him, Remley lashed out savagely at the
next ball and missed it.
“You’re out,” called the umpire, as the ball settled in Mylert’s
glove.
Remley threw down his bat in vexation and went grumbling to the
dugout.
McCarthy came next, swinging three bats of which he flung away
two as he toed the line.
“Put it over, kid, and see me kill it,” he called to Markwith, shaking
his bat at him.
Red grinned and floated up a slow one that looked as big as a
balloon as it approached the plate but small as a pea when it
reached it. McCarthy nearly broke his back reaching for it.
“Strike one,” called the umpire.
“Not so much of a killer after all, are you?” taunted Markwith, as
the catcher returned the ball to him.
McCarthy glowered and gritted his teeth as he waited for the next
one.
It came waist high over the plate, and McCarthy caught it on the
end of his bat. It seemed for a moment that he had made his boast
good, for the ball shot on a line toward center. Iredell, however, who
was playing close to second, leaped into the air and speared it with
his gloved hand, while the stands rocked with applause.
Mornsby, the famous shortstop of the Cardinals, was next at bat.
“Oh, see who’s here!” remarked Markwith, with affected surprise.
“Play ball, you clown,” growled Mornsby. “You’re not on the
vaudeville stage now.”
This was a fling at a theatrical venture that Markwith had gone
into the preceding winter.

“So you’re the quarter of a million dollar beauty!” retorted
Markwith, referring to the price that had been offered for Mornsby.
“Just watch me make you look like thirty cents.”
He put over a ball at which Mornsby refused to bite. The next one
he fouled off. The third he struck at too high and the ball dribbled
down to the pitcher’s box. Markwith picked it up with a tantalizing
grin and tossed to Burkett for an easy out at first.
“Thirty cents was too big an offer,” he called to Mornsby, as he
drew off his glove and came into the bench. “I ought to have made
it a dime.”
“We’ll get you yet, you false alarm,” snapped Mornsby. “You’ll curl
up before the game’s half over.”
The Giants in their half made a bid for a run but were unable to
score. Curry poled one out between right and center that Cooper
gathered in after a long run. Iredell raised a twisting Texas leaguer
over second that McCarthy and Weston both tried for but failed to
reach, narrowly missing colliding with each other.
In the mixup, Iredell, by fast running, reached second. Burkett
came next, and with two balls and two strikes called on him lined
out a grasser that Mornsby found too hot to handle. He knocked it
down, however, but recovered it too late to get Burkett at first.
Iredell, who had taken a good lead, had no difficulty in making third.
On the first ball pitched to Wheeler, the next batter, Burkett made
a break for second. His aim was not so much to reach the base as to
draw a throw from the catcher which would enable Iredell to make
for home. The catcher threw the ball, not to second but to the
pitcher, and Iredell, who had started for the plate, was caught and
run down between third and home. Burkett in the meantime had
reached second and was half way down the base line between
second and third, ready to dash for the latter if Iredell should be put
out. A snap throw to Weston, however, the moment that Iredell had
been tagged, caught Burkett between the bags and he was also run
down, making three out. It was a bit of stupidity, or at least

carelessness, on the part of the Giants and of smart playing by the
visitors.
The next four innings produced no tally for either side. Leadows,
the bespectacled pitcher for the Cardinals, was having one of his
best days, and he set the Giants down almost as fast as they came
to the bat. Markwith, too, was pitching well. He was hit harder and
oftener than Leadows, but so far the breaks of the game had been
with him, and he had had spectacular support on the part of the
Giant fielders. Hupft especially made some almost miraculous
catches in the field that shut off sure home runs and McCarney was
guarding third in a way that recalled the days of Jerry Denny.
“Do you see that?” Joe asked in a low tone of Jim, as McCarney
made a superb stop of a hot grounder and relayed it like a bullet to
first. “You didn’t see him doing that kind of playing yesterday when I
was in the box.”
“Right you are,” replied Jim. “And I noted, too, the one that Hupft
picked off the fence in the last inning. Both of them are playing like
fiends.”
In the sixth inning the Giants broke the ice. Burkett laced out a
dandy two-bagger to right. Wheeler laid down a perfect sacrifice
between the pitcher’s box and first that enabled Burkett to get to
third. Willis sent out a long fly to right center that was caught, but
on the throw in Burkett scored by a long slide to the plate. Larry
went out on an assist from Mornsby to Blair and the inning was over.
But the Giants were a run to the good, and at that stage of the
game a single run might prove the winning tally.
In the seventh the Cardinals went them one better. Blair led off
with a sharp single to left. Atkins followed with a grounder that just
touched the end of Iredell’s glove and went for a hit, Blair reaching
third. Munson was set down on strikes and Bixby sent up a high
twisting foul that Mylert caught at the very edge of the dugout.
Remley, however, whaled out a mighty three-bagger to right that

scored both of his mates. Markwith put on extra steam and struck
out McCarthy, leaving Remley on third.
The Giants’ half of the seventh was fruitless and the eighth
opened with St. Louis one run to the good.
It was not any too good a lead, and they started out to put the
game “on ice.” Mornsby offered at the first ball pitched, and sent the
ball crashing into the bleachers for the first home run of the game.
This mighty hit seemed to rattle Markwith and he passed Nealon to
first on four consecutive balls. Ralston rapped out a two-bagger on
which Nealon went all the way to the plate. Leadows struck out, but
Blair made a pretty single on which Nealon reached third. Markwith
passed Atkins and the bases were full. The score now stood 4 to 1 in
favor of St. Louis with three men on bases and one out.
McRae, the Giants’ manager, beckoned to Markwith, and the latter,
drawing off his glove, came in to the bench.
“Wouldn’t give a dime for me, eh?” jeered Mornsby. “I wouldn’t
give a plugged nickel for you. That home run broke your heart,
didn’t it? I told you you were a false alarm.”
Markwith, usually ready with a retort, was too discomfited to make
reply.
“It’s up to you, Joe,” said McRae. “I know you pitched yesterday,
but I’ll have to call on you to save this game if it isn’t already past
saving.”
Joe was not altogether unprepared for the call, for in the previous
inning McRae, seeing that Markwith was faltering, had sent him out
to do a little warming up.
“All right, Mac,” he responded, and walked out to the box.
His coming was the signal for a storm of cheers from stands and
bleachers. It seemed almost hopeless, but they had seen him so
often lead a forlorn hope to victory.

As was his right, Joe tossed up a few balls to Mylert to get the
location of the plate. Then he took his stand in the box as Munson
came to the plate, eager to send his comrades home. Even a single
would probably bring in two of them. A long sacrifice to the outfield
would account for one run. And a sharp two-bagger would clear the
bases.
Joe wound up and shot a fast high one over the plate. Munson
missed it by inches.
“Strike one!” called the umpire, and the crowd cheered
boisterously.
Mylert returned the ball to Joe on the bound. Joe muffed it and it
dropped at his feet.
He stooped carelessly to pick it up. Then like lightning he shot it to
Larry at second, catching Blair flat-footed off the bag.
Nealon on third made a dash for the plate. Larry tagged Blair and
returned the ball in a flash to Joe, who had run over to the third
base line. Joe put the ball on Nealon and the side was out.
It had all happened in the twinkling of an eye. For an instant the
crowd was paralyzed. Then it woke up and a perfect tempest of
cheers swept over the field.
Robson, the rotund assistant manager, fairly shouted with glee as
he brought his hand down with a resounding smack on McRae’s
knee.
“Did you see that, John?” he roared. “Did you see that fake muff?
Did you see that lightning throw? Did you ever see any foxier playing
in all your life?”
“No, I didn’t,” grinned McRae. “But for the love of Mike, Robbie,
keep that ham of a hand off my knee. Yes, that was some playing. I
don’t know which is the greater, that boy’s arm or his head. They’re
both wonders. Joe hasn’t his match in the baseball world.”

Joe came in smiling, to be mauled and pounded by his rejoicing
comrades.
McRae and Robson beamed upon him.
“Great work, Joe,” said McRae. “Now if you hold them down in the
next inning and our boys get busy with their bats we still have a
chance to cop the game.”
But the Giants, although they got two men on bases in their half
of the eighth, were unable to score, and the ninth opened with St.
Louis still three runs ahead.
They made no more, however, for in their half of the ninth Joe
mowed them down in order, and the Giants came in to make their
last stand with three runs to tie and four to win.
Burkett led off with a nicely placed single in short right. Wheeler
followed with a clean hit over second, on which Burkett tried to
reach third. The ball came back too quickly, however, and he had to
turn back to second, which he reached safely only through a muff by
Weston, who was covering the bag. It was a close call and the Giant
rooters breathed a sigh of relief. McCarney, who had already made
two hits and seemed to have his batting clothes on, fell an easy
victim on strikes. Larry came to the rescue with a neat bunt that got
him to first and advanced his comrades each a base.
The bases were now full, and Hupft, who came next to bat, was
implored to give the ball a ride and bring his mates in. But a groan
went up when he raised an easy pop fly to the box that Leadows
caught without moving from his tracks.
Two men were now out and many of the spectators were
beginning to rise from their seats. They sat down suddenly, however,
at the mighty roar that went up when Joe came to the plate.
Leadows looked him over carefully. He had a wholesome respect
for Joe’s prowess, not only as a pitcher, but as a batter. Here was a
foeman worthy of his best.

Leadows took an unusually long time winding up. Then he sent in
a swift incurve that just missed the corner of the plate. Joe remained
motionless.
An outcurve followed, and again Joe let it go by.
The third was a fast one with a hop to it, and came over the plate
half way between knee and waist. Joe met it full on the seam.
There was a resounding crash and the ball started on its journey
to the bleachers.
It started almost on a line, rising steadily as it soared toward right
field. On and on it went as though it had wings. The Cardinal
outfielders started for it and then stopped and threw up their hands
in despair. The ball cleared the field, cleared the bleachers, cleared
the wall. Where it finally landed no one knew, no one cared.
Joe had dropped the bat and started like a deer for first. But as he
rounded the bag on his way to second, a glance at the ball told him
there was no need for hurry. So he jogged around the bases at his
leisure following the three comrades who romped joyously to the
plate, while in his ears were the thunderous cheers of the spectators
like the roaring of the sea.
He had made a homer with the bases full. He had pulled the game
out of the fire. At the very last moment he had snatched victory
from defeat!

CHAPTER V
PLAYING THE GAME
If a visitor from Mars had seen the crowd at the Polo Grounds
when Joe knocked out that homer, he would promptly have set down
the people of this planet as madmen. The people in the stands and
bleachers simply went crazy with delight. Cheer after cheer went up.
Hats were thrown into the air and on the diamond by the hundreds.
Then the throng swept down on the field in the frantic desire to
surround the hero of the game and carry him in triumph on their
shoulders.
But Joe had seen them coming and was off at top speed for the
clubhouse. The crowd thickened about him as he fled, and for the
last hundred feet he had fairly to fight his way through to get away
from the embarrassing attentions of his admirers.
Even in the clubhouse his troubles were not over, for his comrades
were almost as delirious as the outside throng. They wrung his hand
and slapped his back until he was sore.
McRae was all smiles, while Robbie, as Robson was usually called,
fairly hugged him in his delight.
“Man, you’re a wizard in the box and at the bat!” Robbie cried.
“Sure, it’s magic that you use. You’ve put a come-hither on the ball.
You’ve got it bewitched. You go into the box and you put two men
out with only one ball pitched. You whack the ball and it starts for
Kingdom Come.”
McRae, though less exuberant, was none the less delighted.
“Once more you’ve pulled me out of a hole, Joe,” he said
earnestly. “Many’s the time I’ve had to call on you in a tight pinch,

and I’ve never been disappointed yet. You’re my standby and the
standby of the team. You’ve only proved to me again, what needed
no proving, that when the test comes you’re there.”
“I’m glad you feel that way, Mac,” returned Joe. “Although I think
you make too much of what I’ve done. The team’s the biggest thing
on earth to me outside of my home and folks, and it’s always a
pleasure to give it my best efforts.”
There were two notable exceptions to the praise that was heaped
on Joe by his mates. Hupft and McCarney stood aloof, not saying a
single word, and their brows were so black that one might have
thought that St. Louis had won instead of the Giants.
“How sore those spalpeens look,” remarked Larry to Wheeler, as
he finished his dressing. “They’re like corpses at a wedding.”
“I’ve noticed that,” replied Wheeler. “I suppose they’re a little bit
crabbed because they failed to come through in the ninth inning.
They had their chances to send the boys in, but both fell down. I’ve
felt that way myself more than once. They’ll be all over that by to-
morrow.”
The grumpiness of the pair had not escaped Joe and Jim,
although they gave no sign until they were clear of the clubhouse
and on their way home.
“I’ll bet a nickel I know what you’re thinking of,” bantered Jim.
“Too easy,” laughed Joe. “Of course, we’re both thinking of the
same thing and that is the sour looks of that precious pair of
highbinders at the end of the game. Even the other fellows, who
haven’t the reason we have to suspect them, were struck by it. You
heard what Larry said to Wheeler.”
“If they were really foxy they’d have made a bluff at feeling good,
no matter how they felt,” remarked Jim. “There were all the other
fellows fairly out of their heads with delight, and they were as black
as thunderclouds. If they don’t look out, other people will tumble to
the fact that there’s something crooked going on.”

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