6/Allocating Resources to the Project
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.
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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 action plan. For example:
o The action 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) needed.
o The action plan may only specify how much of the resource is needed and precedence
between the activities relationships, it may not specify exactly when the PM will need
these resources.
o Although the action 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 tradeoffs 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.
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.
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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:
o The resource’s availability (e.g., days in week available, total hours available per week,
hours available each day).
o Times the resource will not be available (e.g., lunch, weekends, holidays, vacations,
scheduled maintenance), and
o 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 an area) faces a much more daunting problem because a Walt is a scarce
resource that is important to the project’s successful completion and there are no readily
available substitutes for a Walt.
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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.
9. List and describe the three most common criteria by which to evaluate different resource
allocation priority rules.
The three criteria are:
o Schedule slippage … a measure of the delay suffered by projects as a result of the
application of a resource allocation priority rule.
o 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.
o 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 tasks
and activities which represent the jobs.
11. What is meant by the “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.
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Suggested Answers to Discussion Questions
12. 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 be necessary in terms of the
completion time of other projects and perhaps the performance of this and other projects.
13. Discuss the advantages of “labor pools” in a project – oriented company.
The main advantages of “labor pools” versus dedicating workers to specific projects are:
o Less waiting time for key resources.
o The ability to level resource usage, and
o The ability to substitute one worker for another should one become unavailable.
Are there any potential disadvantages with the use of pools?
Potential drawbacks include:
o Workers who do not identify with a particular project.
o Personnel who may not be well trained in specific tasks required by the assignment.
o Fewer opportunities for job enlargement.
All of these may lead to lower levels of job satisfaction, as well as lower morale and
motivation.
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14. 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.
c. The minimum slack priority rule … is used to minimize the number of late activities.
15. 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, psuedoactivities are used to show the 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.
16. 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.
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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.
17. 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 a Type 1 life cycle. Project B’s life cycle is
Type 2. From which (or both or neither) do you borrow the resource? Why?
In this case it would be best to borrow from project A. According to Figure 6-20, as a Type 1
project, fewer resources will have little impact on project A’s performance as it nears
completion. Conversely, as a Type 2 project, taking resources away from project B as it
nears completion will dramatically reduce its performance.
18. 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 really push
the team and 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).
19. Describe as many types of resource allocation problems as you can, based on the
situations described in this chapter.
The chapter identifies three types of resource allocation problems:
o
o
o
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
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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.
Solutions to Problems
20. 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.
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c. Since each resource is assigned 100 per cent to each task, the resource constraints are:
o Resource X is over utilized on the Friday of week 1, Monday of week 2, and Tuesday of
week 3.
o Resource W is over utilized on Tuesday or week 3.
d. After leveling the resources, the project duration is 17 days and the critical path is
A-C-D-F-G.
e. If it is necessary to shorten the project duration without overallocating the resources then
there are two options:
o Adding an additional X resource would shorten the project by 2 days,
o Leveling the W resource would be 15 days.
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The project duration is 13 days when the resources work weekends and after leveling.
21. 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:
4
1
G
D
A
E
3
B
5
H
6
C
F
2
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.
A
4
5
6
7
8
9
10
11
12
13
Activity
a
b
c
d
e
f
g
h
B
Normal
Time
5
4
7
2
3
8
5
6
C
Normal
Cost
$50
$40
$70
$20
$30
$80
$50
$60
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D
Crash
Time
3
2
6
1
E
Crash
Cost
$150
$200
$160
$50
F
Crash
Cost/Day
50
80
90
30
5
4
3
$290
$100
$180
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6/Allocating Resources to the Project
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).
A
1 Deadline:
2 Total Cost:
3
4
5
Activity
6
a
7
b
8
c
9
d
10
e
11
f
12
g
13
h
14
Total
15
16
17
Node
18
2
19
3
20
4
21
5
22
6
B
18
$480
C
D
E
Normal
Time
5
4
7
2
3
8
5
6
Normal
Cost
$50
$40
$70
$20
$30
$80
$50
$60
$400
Crash
Time
3
2
6
1
Crash
Cost
$150
$200
$160
$50
5
4
3
$290
$100
$180
F
G
H
I
Crash
Max Crash
Amt
Crashing
Cost/Day
Amt
to Crash
Cost
50
2
0.0
0.0
80
2
0.0
0.0
90
1
0.0
0.0
30
1
0.0
0.0
0
0.0
0.0
70
3
0.0
0.0
50
1
0.0
0.0
40
3
2.0
80.0
$80
J
Actual
Time
5
4
7
2
3
8
5
4
Event
Time
4
11
13
14
18
The optimal solution using Solver was found in the following way:
o Cell I14 was specified as the target cell to minimize.
o The ranges H6:H13 and B18:B22 were specified as the changing cells.
The following constraints were added:
o
o
o
o
o
o
o
o
o
o
o
o
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.
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.
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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.
f. See solutions to c – e above.
22. 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
B
C
D
4
3
7
5
D
C, D
D
None
D
C, D
D
None
6
0
0
0
a. Using the shortest task first priority rule: 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.
23. 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
D
3
2
F, I
G, H, J
None
H, J
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3
4
8
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6/Allocating Resources to the Project
a. Using the minimum slack rule: Activity D 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 LSof 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.
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:
o 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.
o 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.
o 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:
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6/Allocating Resources to the Project
o Redesign the project plan for this new job to include additional resources to complete the
additional work.
o 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.
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.
Suggested Case Analyses and Solutions
St. Dismas Assisted Living Facility Resource Usage – Part 4
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.
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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 2 nd. The start date used
in these examples is January 2, 2000, to coincide with the year that the case started.
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.
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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”.)
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.
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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.
Or with a more detailed view of the calendar:
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6/Allocating Resources to the Project
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.
Test
5
DB
1
Benchmarking
2
Pla
n
3
Design
4
Pages
Forms
6
8
e
s
t
7
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).
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1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
A
Deadline:
Total Cost:
Activity
Benchmark
Plan
Design
Database
Webpages
Forms
Test
Total
Node
2
3
4
5
6
7
8
B
30
$126,900
Normal
Time
10
5
15
10
10
7
3
C
D
E
F
G
H
I
J
Normal Crash Crash
Crash Max Crash
Amt
Crashing Actual
Cost
Time
Cost Cost/Day
Amt
to Crash
Cost
Time
$15,000
7
$18,750
1250
3
3.0
3750.0
7
$3,750
3
$4,500
375
2
2.0
750.0
3
$45,000
10 $58,500
2700
5
5.0
13500.0
10
$9,000
7
$11,250
750
3
2.0
1500.0
8
$15,000
8
$19,500
2250
2
2.0
4500.0
8
$8,400
7
0
0.0
0.0
7
$4,500
2
$6,750
2250
1
1.0
2250.0
2
$100,650
$26,250
Event
Time
7
10
20
28
28
27
30
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:
o
o
o
o
o
o
o
o
o
o
o
o
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)
83
6/Allocating Resources to the Project
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.
A
B
C
D
E
F
G
1 Deadline:
35
2 Total Cost:
$112,800
3
4
Normal
Normal Crash Crash
Crash
Max Crash
5
Activity
Time
Cost
Time
Cost
Cost/Day
Amt
6
Benchmark
10
$15,000
7
$18,750
1250
3
7
Plan
5
$3,750
3
$4,500
375
2
8
Design
15
$45,000
10
$58,500
2700
5
9
Database
10
$9,000
7
$11,250
750
3
10 Webpages
10
$15,000
8
$19,500
2250
2
11
Forms
7
$8,400
7
0
12
Test
3
$4,500
2
$6,750
2250
1
13
Total
$100,650
14
15
Event
16
Node
Time
17
2
7
18
3
10
19
4
23
20
5
33
21
6
33
22
7
30
23
8
35
84
H
I
J
Amt
Crashing Actual
to Crash
Cost
Time
3.0
3750.0
7
2.0
750.0
3
2.0
5400.0
13
0.0
0.0
10
0.0
0.0
10
0.0
0.0
7
1.0
2250.0
2
$12,150