PROJECT SCHEDULING, PLANNING & CONTROL
Homework Assignment #4 and #5
Problem #4:
The city of Bloomington is about to build a new water treatment plant. Once the plant is designed (D) we can
select the site (S), the building contractor (C and the operating personnel (P). Once the site is selected we may
erect the building (B). We can order the water treatment machine (W) and prepare the operations manual (M)
only after the contractor is selected. We can begin training the operators (T) when both the operations manual
and operating personnel selected are completed. When the water treatment and building are finished, we can
install the treatment machine (I). Once the treatment machine is installed and the operators are trained, we can
obtain an operating license (L). The time to complete each activity is assumed to be a normal distribution and the
estimated mean and standard deviation of the time (in months) needed to complete each activity is defined
below:
ACTIVITY
DESCRIPTION
MEAN
D
S
C
P
B
W
M
T
I
L
Design plant
Select site
Select Building Contractor
Select Operating Personnel
Erect Building
Order Water Treatment machinery
Prepare Operations Manual
Train Operators
Install Treatment Machine
Obtain Operator License
6
2
4
3
24
14
3
4
6
3
STANDARD
DEVIATION
1.5
0.3
1.0
1.0
0.6
4.0
0.4
1.0
1.0
6.0
a. Draw the PERT network for the project
b. Calculate the critical path and estimated completion time of the project
c. Using this estimated completion time, determine the probability of completing the project in (1) under 50
months and (2) over 55 months
d. Use simulation to calculate the estimated completion time and to determine the probability of completing
the project in (1) under 50 months and (2) over 55 months (use a monte carlo simulation of 200
repetitions)
e. Explain why the answers to questions (b) and (c ) may differ to that determined in question (d).
f. Use simulation to estimate the probability that B, I and T are critical activities
Problem #5:
Consider the following project:
Activity
Normal Time
(Days)
Crash Time
Normal Cost ($)
Crash Cost ($)
(Days)
Immediate
Predecessors
A
3
2
1,000
1,600
–
B
2
1
2,000
2,700
–
C
2
1
300
600
–
D
7
3
1,300
1,600
A
E
6
3
850
1,000
B
F
2
1
4,000
5,000
C
G
4
2
1,500
2,000
D,E
a) Construct the pert network
b) Determine the critical path and project completion time
c) Determine the cost of crashing the project to 10 days
