Chapter Three Part Two Problems
Total Marks = /45
Question #1 â€“ /12 marks
The network below represents a project being analyzed by Critical Path Methods. Activity durations are A = 5, B = 2, C = 12, D = 3, E = 5, F = 1, G = 7, H = 2, I = 10, and J = 6.
a. What task must be on the critical path, regardless of activity durations? (1 mark for reasoning, 1 mark for correct answer)
b. What is the duration of path A-B-E-H-J? (2 marks for showing calculation, 1 mark for correct answer)
c. What is the critical path of this network? (1 mark for correct answer)
d. What is the length of the critical path? (2 marks for calculation, 1 mark for correct answer)
e. If activity C were delayed by two time units, what would happen to the project duration? (2 marks for explanation, 1 mark for correct answer)
Question #2 â€“ /18 marks
Three critical path activities are candidates for crashing on a CPM network. Activity details are in the table below.
Activity |
Normal Time |
Normal Cost |
Crash Duration |
Crash Cost |
A |
9 days |
$8,000 |
7 days |
$12,000 |
B |
5 days |
$2,000 |
3 days |
$10,000 |
C |
12 days |
$9,000 |
11 days |
$12,000 |
a. What is the crash cost per unit time for activity A? (3 marks â€“ 2 for calculation, 1 for correct answer)
b. What is the crash cost per unit time for activity B? (3 marks â€“ 2 for calculation, 1 for correct answer)
c. Which activity should be crashed first to cut one day from the project’s duration; how much is added to project cost? (4 marks â€“ 3 for calculation, 1 for correct answer)
d. Assuming no other paths become critical, how much can this project be shortened at what total added cost? (8 marks â€“ 6 for calculations, 2 for correct answers)
Question #3 â€“ /15 marks
Pirmin’s Bike Shop is behind on a custom bike and needs to crash 8 hours of time from the 8-step project. Given the project table below calculate the crash cost for 8 hours of time-savings (9 marks for calculation, 1 mark for correct answer).
Suppose Pirmin calls the customer and asks for a project extension, reducing the amount of time he needs to crash. Calculate both the maximum time-savings available on a $25 crash budget and the cost to crash four hours of savings (4 marks for calculation, 2 marks for correct answer) .
Activity |
Normal Duration (hours) |
Normal Cost ($) |
Crash Duration (hours) |
Crash Cost (S) |
Immediate Predecessors |
A |
2 |
10 |
2 |
0 |
None |
B |
3 |
15 |
2 |
23 |
A |
C |
5 |
25 |
4 |
30 |
B |
D |
3 |
20 |
1 |
24 |
C |
E |
6 |
30 |
4 |
45 |
C |
F |
1 |
5 |
1 |
0 |
E |
G |
7 |
35 |
6 |
50 |
F |
H |
10 |
50 |
7 |
80 |
D, G |