University Project Management Final Exam Solution Analysis Report

This document presents a comprehensive solution to a project management final exam, addressing various aspects of quantitative methods. The solution includes calculations for mean duration, variance, and standard deviation, along with probability analysis. It provides answers to questions involving critical path identification, Gantt chart creation, resource leveling, and cost/schedule variance analysis. The document also explores decision-making scenarios related to project budget and market trends, offering insights into critical path and resource leveling using Microsoft Project. Furthermore, it presents earned value calculations, including SPI, CPI, and EAC, across different project phases. Finally, the solution provides a network diagram analysis, critical path determination, and cost optimization strategies.

Running head: Quantitative Methods in Project Management
Quantitative Methods in Project Management
Name of the Student
Name of the University
Author Note

1:
For the above given network the Total expected time and variance table is calculated in excel
by suitable formulas given below.
Activity OPT NORMAL PESS TE Var
A 12 15 20 15.33333 1.777778
B 12 15 25 16.16667 4.694444
C 20 25 30 25 2.777778
D 20 25 30 25 2.777778
E 15 20 30 20.83333 6.25
F 6 10 15 10.16667 2.25
Mean 45.83333 10.94444
SD 3.308239

a.
The total expected duration of activity is given by ta+ 4∗tm+tp
6
ta = optimistic time,, tm = normal time, tp = pessimistic time.
Project mean = ∑ mean
The project mean duration is 45.83 ~ 46 days as calculated in excel.
b.
The activity variance V = σ 2=( tp – ta
6 )
2
The project variance = ∑ V
The project variance is 10.94 days.
c. Hence, project standard deviation = √ ∑ V
The project standard deviation is 3.308 days as calculated in excel.
d. Now, project mean μ = 45.83 days.
Project sd = σ = 3.308 days.
Hence, project completion time X follows N(45.83,3.308)
Hence, probability that project will be completed in less than or equal to 50 days will be
P(Z<=(50-45.83)/3.308) = P(Z<=1.2595) = 0.8960 or 89.60%.
Hence, probability that project will be completed in less than or equal to 50 days is 89.60%.
2.
a.

b.
The critical path is A-C-D-E-G and the project will take 14 days.
c.
On Tuesday X is working for an extra 8 hours. In addition to this the same is performed on
Friday and Monday as well for week one and week three respectively. On week 3 Monday W
is working for an extra 8 hours.
d.
The new critical path is now A-B-C-D-E-F-G and it takes 17 days to complete the project.

e. An alternative path is levelling only W and so that the time required is 15 days. The new
critical path would be A-C-D-F-G.
4.
Question 1:
It is more likely that BestSoft’s profit drops by certain percentage while delaying for the
launch of the product by 3 months. This happen due to impatience of the customers and thus
going for alternative brands to buy the product. Increasing the product budget by 30% will
reduce the profit margin but the extra budget will be used in staffs salaries and software
expenses which will be benefitted for BestSoft in future. Thus increasing project budget by
30% is the better alternative.
Question 2:
The other factors that should be considered in addition to profit are
Product relevance in the market:
At the time of launching the product in the market it is best to grab the best timing when the
product is open to huge number of customers. If the company delays for launching the
product then it will not be a good decision for the company.
Competition in the market:
Different companies are launching different products in each day and thus uniqueness of the
product is very less. Hence, the company which is launching the first product type will
always have the advantage over other similar products as people are going to remember the
product by that company’s name.
Question 3:

The main focus of the company should be releasing the product as per the schedule as this
will keep the relevance of the product in the current market and then to increase the sales and
the profit.
Question 4:
The above discussion is generalized by the market trends and completion which is common
to any type of companies launching products in the market. However, in the first question the
scenario is analysed with profit percentage extension of the current budget and it is compared
with delay of the launch of the product.
5.
The tables of excel calculation is shown below.
EV= Budget * %Complete
Actual Cost
Cost Variance (CV)
Formula: Cost variance = EV – AC
Schedule Variance (SV)
Formula: SV = EV – PV
Cost Performance Index (CPI)
Formula: CPI = EV/AC
Schedule Performance Index (SPI)
Formula: SPI=EV/PV
Budget at Completion (BAC) = $65,000
Estimated to Completion (ETC) = (BAC-EV)/CPI
Estimated at Completion (EAC)= ETC +AC
PV = budget - % planned
Week 1
% Complete 100%
Actual Cost (AC) $4,500
Planned Value (PV) end
of week 1
$3,000

Earned Value (EV) $3,000 * 100% = $3,000
SPI= EV/PV 3000/3000 = 1
CPI = EV/AC 3000/4500= .667
ETC= (BAC-EV)/CPI (65,000-3000)/.667 = 92,953.52
EAC = ETC + AC or
EAC= BAC/CPI
92,953.52 + 4500 = 97,453.52
or 97,451.28
Week 3
% Complete 33.33% (5/15)
Actual Cost (AC) $4500 + $28,000= 32,500
Planned Value (PV) end
of week 3
$3,000 + (66.66%*$45,000) =
$33,000
Earned Value (EV)
33.33%*45,000 = 15,000
+3000= 18,000
SPI= EV/PV 18,000/33,000= .545
CPI = EV/AC 18000/32,500 = .553
ETC= (BAC-EV)/CPI
($33000-18000)/.553 =
27,154.77
EAC = ETC + AC or
EAC= BAC/CPI
27,174.77+ 32,500 = $59674.5

Project End
% Complete 100%- work is complete
Actual Cost (AC) $65,000
Planned Value (PV) at
completion
65,000
Earned Value (EV) 100%*$65,000=65,000
SPI= EV/PV 1
CPI = EV/AC 65,000/65,000=1
ETC= (BAC-EV)/CPI 65,000-65,000/1=0
EAC = ETC + AC or
EAC= BAC/CPI
0+65,000
=65,000
EAC =65,000
a. i) SPI = 1
ii) CPI = 0.667
iii) EAC = 97451.28
b. i) SPI = 0.545
ii) CPI = 0.553
iii) EAC = $59674.5
c. i) SPI = 1
ii) CPI = 1
iii) EAC = 65000

6.
a. The AOA network of the tasks are given below.
b. The critical path of the network is A, C, E, F as the norm t is maximum in the case.
c. The duration of the network is 3 + 5 + 7 +3 = 18
d. The normal without crashing cost is $1300
e. The minimum duration is 11.
f. The new price is $ 2000.
7.
a. True
b. False
c. True
d. False
8.
c. Budget constrained
9.
c. $5000
A
B D
F
C E

10.
a. True
b. True
c. True
d. False
11.
b. $1,150