Chapter 3, Project Management

Problem 1: The following represent activities in a major construction project.

Activity / a / m / b / Predecessors
A / 2 / 5 / 14 / Start
B / 4 / 7 / 10 / Start
C / 1 / 2 / 9 / A
D / 1 / 2 / 3 / A
E / 2 / 4 / 6 / B
F / 6 / 6 / 6 / B
G / 7 / 9 / 17 / C, E
H / 2 / 8 / 8 / D, F
Activity / a / m / b / T / s2
A / 2 / 5 / 14
B / 4 / 7 / 10
C / 1 / 2 / 9
D / 1 / 2 / 3
E / 2 / 4 / 6
F / 6 / 6 / 6
G / 7 / 9 / 17
H / 2 / 8 / 8

Problem 2: Draw the network to represent this project. Find the Critical Path, expected project completion and variance.


Problem 3:

a.  What is the probability of finishing the project in 24 weeks or less?

b.  What is the probability of finishing the project in 20 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?


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?


Problem 5:

Development of a new software product is being considered. The activities are listed in the table below along with their costs and completion times in weeks.

Activity / Immediate Predecessor / Normal Time / Crash Time / Normal Cost / Crash Cost
A / - / 4 / 3 / 2,000 / 2,600
B / A / 2 / 1 / 2,200 / 2,800
C / A / 3 / 3 / 500 / 500
D / A / 8 / 4 / 2,300 / 2,600
E / B, D / 6 / 3 / 900 / 1,200
F / C, E / 3 / 2 / 3,000 / 4,200
G / G / 4 / 2 / 1,400 / 2,000

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?

Activity / MCA / Crashing cost/week
A
B
C
D
E
F
G

MTR = Maximum time reduction


ANSWERS:

Problem 1:

Problem 2:

Project start / 0
Activity / t / ES / EF / LS / LF / Slack / Critical / s2
A / 6 / 0 / 6 / 2 / 8 / 2 / 0 / 4.00
B / 7 / 0 / 7 / 0 / 7 / 0 / 1 / 1.00
C / 3 / 6 / 9 / 8 / 11 / 2 / 0 / 1.78
D / 2 / 6 / 8 / 12 / 14 / 6 / 0 / 0.11
E / 4 / 7 / 11 / 7 / 11 / 0 / 1 / 0.44
F / 6 / 7 / 13 / 8 / 14 / 1 / 0 / 0.00
G / 10 / 11 / 21 / 11 / 21 / 0 / 1 / 2.78
H / 7 / 13 / 20 / 14 / 21 / 1 / 0 / 1.00
Variance = / 4.22
Project completion time = / 21 / Standard deviation = / 2.05
Completion time of path = / 21

Problem 3:

t = / 24 / 20 / 90%
Z-score = / 1.4600 / -0.4867 / 0.81594
Probability = / 0.9279 / 0.3132 / 22.6766


Problem 4:

(a)

Therefore:

(b)

Therefore:

(c)

Therefore:

Problem 5:

(a)