Operations Management: CPM and PERT Sample Problems

BUS 325 Operations Management
CPM & PERT Sample Problems

#1
Suppose that a project requires the following activities and their respective activity times:
1. Complete the chart below (Round numbers to the second decimal place).
Job No.
Immediate Predecessors
Times (weeks)
Expected
Time σ2 To
Tm
Tp

A
-
2
2
2

B
A
1
2
3

C
A
2
4
6

D
B, C
1
3
5

E
D
2
3
4

F
C, D
1
2
3

G
E, F
2
4
6

H
C, F
1
1
1

I
F, G, H
2
2
8

2. Construct the network diagram / Determine ES/EF &LS/LF.

3. Determine the critical path(s).

4. Identify activities that have slack times and also indicate how long the slack times are.

5. What is the probability that the completion of the project takes over 20 weeks?

6. What is the probability that the completion of the project takes over 24 weeks?

#2
Suppose that a project requires the following activities and their respective activity times:
1. Complete the chart below (Round numbers to the second decimal place).
Job
Immediate Predecessors
Times (weeks)
Expected
Time σ2 To
Tm
Tp

A
-
3
4
5

B
A
4
6
9

C
A
5
6
12

D
A
1
3
5

E
B, C
6
9
11

F
C, D
6
9
11

G
E
4
8
12

H
F
2
3
5

I
F
1
3
5

J
I
4
4
10

K
G, H, J
3
6
7

2. Construct the network diagram / Determine ES/EF &LS/LF.

3. Determine the critical path(s).

4. Identify activities that have slack times and also indicate how long the slack times are.

5. What is the probability that the project will take less than 30 weeks to complete?

6. What is the probability that the completion of the project takes over 35 weeks?

#3
Suppose that a project requires the following activities and their respective activity times:
1. Complete the chart below (Round numbers to the second decimal place).
Activity
Immediate Predecessors
Times (Months)
Expected
Time
Activity
Variances
(σ2)

To
Tm
Tp

A
-
2
3
4

B
A
2
4
6

C
A
4
5
12

D
B, C
1
3
5

E
D
3
6
9

F
D
1
3
5

G
E
2
4
6

H
E, F
1
8
9

I
G, H
2
4
12

2. Construct the network