Solution: PMAN635 Quantitative Methods in Project Management Final

This document presents a detailed solution to a final exam in the PMAN635 course, focusing on quantitative methods in project management. The solution encompasses various aspects, including calculating mean duration, variance, and standard deviation for a project network, determining the probability of project completion within a specific timeframe. It also includes a comprehensive analysis of a landscape project, utilizing Gantt charts and resource allocation techniques to identify the critical path, project duration, and resource constraints. The solution further explores resource leveling to optimize project timelines, and addresses issues related to software tools in project reporting, earned value calculations, and project evaluation statements. The document provides answers to multiple-choice questions related to project management principles, and concludes with a bibliography of relevant resources.

1. Solution
Activity Predecessor
s
OPT Normal Pessimistic Mean Variance SD
A 12 15 20 23 1.78 1.33
B 12 15 25 24.25 4.69 2.17
C 20 25 30 37.5 2.78 1.67
D 2 20 25 30 37.5 2.78 1.67
E 2,3 15 20 30 31.25 6.25 2.50
F 3 6 10 15 15.25 2.25 1.50
35 45 60 68.75 9.027778 4.16666667
The probability that the project would be completed in 50 days is 43.19%
2. Solution
a.

ID Task
Mode
Task Name Duration Start Finish Predecessors Resource Names
0 Project 2 14 days Mon 8/13/18 Thu 8/30/18
1 A 2 days Mon 8/13/18 Tue 8/14/18 X,Y
2 B 2 days Wed 8/15/18 Thu 8/16/18 1 X
3 C 3 days Wed 8/15/18 Fri 8/17/18 1 X
4 D 4 days Mon 8/20/18 Thu 8/23/18 2,3 X,Y
5 E 3 days Fri 8/24/18 Tue 8/28/18 4 W,X
6 F 1 day Fri 8/24/18 Fri 8/24/18 4 W,X,Y
7 G 2 days Wed 8/29/18 Thu 8/30/18 5,6 X,Y
X,Y
X
X
X,Y
W,X
W,X,Y
X,Y
S M T W T F S S M T W T F S S M T W T F S
Aug 12, '18 Aug 19, '18 Aug 26, '18
b. The critical path is shown below,
ID Task
Mode
Task Name Duration Start Finish Predecessors Resource Names
1 A 2 days Mon 8/13/18 Tue 8/14/18 X,Y
3 C 3 days Wed 8/15/18 Fri 8/17/18 1 X
4 D 4 days Mon 8/20/18 Thu 8/23/18 2,3 X,Y
5 E 3 days Fri 8/24/18 Tue 8/28/18 4 W,X
7 G 2 days Wed 8/29/18 Thu 8/30/18 5,6 X,Y
X,Y
X
X,Y
W,X
X,Y
S M T W T F S S M T W T F S S M T W T F S
Aug 12, '18 Aug 19, '18 Aug 26, '18
The project overall duration is 14 days.
c. The resources X and W have been over allocated for the activities B, C, E, F.
d. The new critical tasks and the project duration (17 days) have been shown below
ID Task
Mode
Task Name Duration Start Finish Predecessors Resource Names
0 Project 2 17 days Mon 8/13/18 Tue 9/4/18
1 A 2 days Mon 8/13/18 Tue 8/14/18 X,Y
2 B 2 days Mon 8/20/18 Tue 8/21/18 1 X
3 C 3 days Wed 8/15/18 Fri 8/17/18 1 X
4 D 4 days Wed 8/22/18 Mon 8/27/18 2,3 X,Y
5 E 3 days Wed 8/29/18 Fri 8/31/18 4 W,X
6 F 1 day Tue 8/28/18 Tue 8/28/18 4 W,X,Y
7 G 2 days Mon 9/3/18 Tue 9/4/18 5,6 X,Y
X,Y
X
X
X,Y
W,X
W,X,Y
X,Y
S T T S M W F S T T S M W F
Aug 12, '18 Aug 19, '18 Aug 26, '18 Sep 2, '18

e. Inclusion of a new resource would be helpful for retaining the project duration of 14 days
without over allocating any of the resources (X and W).
3. Answer
The using Software Tools for reporting project information might lead to the following
problems,
 Failure in system would result in delay
 Loss of data due to technical errors
 Redundancy Problems
 Interception of information and its misuse
 Manipulation of the information via system server
5. Solution
For 1st Week,
Earned value = $3000
Planned value = $3000
Actual Cost= $4500
SPI= EV/PV =1
SPI= EV/AC = 0.67
EAC= Budget (First task)/CPI = $4500
SPI= Earned Value/Planned Value

Planned value (third week) = $3000 + 66.66% * $45000
=$33,000.00
Earned value (third week) = earned value of first task (first week) + earned value of second task
(third week)
Only 5 mile out of 15 miles of fibres are laid, hence only 33.33% of work has been completed
Earned value of second task (third week) = 33.33% * $45000
=15000
Earned Value (first Week) = $3000
Earned value (third week) = $3000 + $15000
=$18000
SPI = 18000/33000 =0.55
CPI = EV/AC
AC (after third week) = Actual cost (Week 1) + Actual Cost (Week 2)
= $4500 + $28000
= $32500
CPI = $18000/$32500
=0.55
EAC= BAC (third week) /CPI

BAC= Budget (first task) + Budget (second task)
BAC= $3000 + 66.66%*$45000
=$33000
EAC= $33000/0.55
=$59583.33
At the end of project,
EV= EV(1st week) +EV(3rd Week) +EV(5th Week)
EV (5th Week) = 35.5% * 45000 (work done in next two weeks)
=15,973
EV = $3000 + $18000 + $15,973
=33,973
PV (5th Week) = $53,000
AC (5th Week) = AC(1st Week) + AC(3rd Week) + AC(5th Week)
=$4500+$2800+$9165
=$41665
Answer:
After 1
week
EV $3,000.00 SPI 1

PV $3,000.00 CPI 0.67
AC $4,500.00 EAC $4,500.00
BAC $3,000.00
After 3
week
EV $18,000.00 SPI 0.55
PV $33,000.00 CPI 0.55
AC $32,500.00 EAC $59,583.33
BAC $33,000.00
At the end
EV $33,973.00 SPI 0.64
PV $53,000.00 CPI 0.82
AC $41,665.00 EAC $65,000
BAC $53,000.00
6. Answers
a.
b. Critical path is the summation of the shortest time required for the completion of the project
and it includes all the major activities sequentially that cannot be executed simultaneously.
c. The duration of the network is 18 days

d. The normal cost of the project is $1300
e. The minimum (crashed) duration is 11 days
f. The new cost of the project is $2000
7. Identify which of the following statements is true and which is false:
a. The primary purpose of project evaluation is to give feedback to senior management for
decision and control purposes. (True)
b. The original criteria for selecting and funding a project are largely irrelevant for project
evaluation. (False)
c. The timing of an audit depends on the purpose of the audit. (True)
d. It is best for the project manager and the project team to make the termination decision.
(False)
8. A project that cannot go over budget is considered (pick one):
a. Time constrained
b. Schedule constrained
c. Budget constrained (Answer)
d. Performance constrained
9. A task has a normal duration of 9 days and crash duration (the minimum duration) of 7 days.
Its normal cost (total for 9 days) is $4000 and its crash cost is $10000 (total for 7 days).What is
the crash cost per day?

a. $14000
b. $7000
c. $5000
d. $4000
e. $3000 (Answer)
10. Identify which of the following statements is true and which is false:
a. The shortest time to complete a network is equal to the duration of the longest path through the
network. (True)
b. The actual project duration will be known with certainty when the project is completed. (True)
c. The difference between EST and LFT is called slack. (True)
d. The start to finish linkage is normally used in situations where it is desirable for two or more
activities to finish at the same time. (False)
11. A task is expected to take 20 hours of labor at $25 per hour (direct cost).The required
material cost is $500. The organization adds a burden of 30% to all direct labor costs to account
for overhead. It does not add any burden on top of material costs. The total task cost is:
a. $500
b. $1,150 (Answer)
c. $1,250

d. $1,300
e. $1,500

Bibliography
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management journal, 34(4), 12-23.
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Management, 24(2), 136-144.
Czernigowska, A. (2008). Earned value method as a tool for project control. Budownictwo i
Architektura, 3, 15-32.
Dwyer, T., Marriott, K., & Wybrow, M. (2008, September). Dunnart: A constraint-based
network diagram authoring tool. In International Symposium on Graph Drawing (pp.
420-431). Springer, Berlin, Heidelberg.
Sulaiman, T., Barton, B., & Blackburn, T. (2006, July). AgileEVM-earned value management in
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