Network diagram solved problems also includes CPM problem and crashing.

1. Practice Problem: Chapter 3, Project Management
Problem 1:
The following represent activities in a major construction project. Draw the network to
represent this project.
Activity Immediate Predecessor
A -
B -
C A
D B
E B
F C, E
G D
H F, G
1

2. Problem 2:
Given the following Time Chart and Network Diagram, find the Critical Path.
Activity a m b t Variance
A 2 3 4 3 1/9
B 1 2 3 2 1/9
C 4 5 12 6 16/9
D 1 3 5 3 4/9
E 1 2 3 2 1/9
Problem 3:
What is the variance in completion time for the critical path found in Problem 2?
Problem 4:
A project has an expected completion time of 40 weeks and a standard deviation of 5
weeks. It is assumed that the project completion time is normally distributed.
(a) What is the probability of finishing the project in 50 weeks or less?
(b) What is the probability of finishing the project in 38 weeks or less?
(c) The due date for the project is set so that there is a 90% chance that the project will
be finished by this date. What is the date?
2

3. Problem 5:
Development of a new deluxe version of a particular software product is being
considered. The activities necessary for the completion of this project are listed in the
table below along with their costs and completion times in weeks.
3
Activity Normal
Time
Crash
Time
Normal
Cost
Crash
Cost
Immediate
Predecessor
A 4 3 2,000 2,600 -
B 2 1 2,200 2,800 A
C 3 3 500 500 A
D 8 4 2,300 2,600 A
E 6 3 900 1,200 B, D
F 3 2 3,000 4,200 C, E
G 4 2 1,400 2,000 F
(a) What is the project expected completion date?
(b) What is the total cost required for completing this project on normal time?
(c) If you wish to reduce the time required to complete this project by 1 week, which
activity should be crashed, and how much will this increase the total cost?

4. ANSWERS:
4
Problem 1:
Problem 2:
Critical path: ACDE = 14
Problem 3:
Total variance   variances of activities on critical path
Total variance = 1/9 + 16/9 + 4/9 + 1/9 = 2 2/9 = 2.44
And σ = = 1.6

5. 5
Problem 4:
(a)
50 40
Z 2
5
X 

 
  
Therefore: P(X  50)  P(Z  2)  0.97725
(b)
X  
2
Z    
0.4
5


Therefore: P(X  38)  P(Z  0.4)  0.34458
(c) 90% Z 1.28  ( -) /    40/ 5
Therefore:  1.28*5 40  46.4weeks
Problem 5:
(a)
Project completion time is therefore t t t t t A D E F G      4  8 6 3 4  25
(b) Total cost  $2,000$2200$500$2,300$900$3,000 $1,400  $12,300
(c) Crash D 1 week at an additional cost of
$2,600 $2,300 $300
 
$75

8 
4 4