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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.

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