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Magazine Chapter 1: Q16OQ (page 104)
The following CPM network has estimates of the normal time in weeks listed for the activities:
a. Identify the critical path.
b. What is the length of time to complete the project?
c. Which activities have slack, and how much?
d. Here is a table of normal and crash times and costs. Which activities would you shorten to cut two weeks from the schedule in a rational fashion? What would be the incremental cost? Is the critical path changed?
Activity | Normal Time | Crash time | Normal cost | Crash cost |
A | 7 | 6 | \(7,000 | \)8,000 |
B | 2 | 1 | 5,000 | 7,000 |
C | 4 | 3 | 9,000 | 10,200 |
D | 5 | 4 | 3,000 | 4,500 |
E | 2 | 1 | 2,000 | 3,000 |
F | 4 | 2 | 4,000 | 7,000 |
G | 5 | 4 | 5,000 | 8,000 |
Short Answer
Critical Path Method (CPM) is a kind of step-by-step project management process for planning the whole process that determines the critical and non-critical steps.
Step by step solution
(a) Critical Path
A-B-D-F-G = 7+2+5+4+5=23, No
A-B-D-E-G = 7+2+5+2+5=21, No
A-C-D-F-G =7+4+5+4+5=25, Yes
A-C-D-E-G = 7+4+5+2+5=23, No
The critical pathis considered to be the one with the longest time duration and from the above observation, it is clear that the longest time duration is 25.
Thus, the critical routeis A-C-D-F-G.
(b) Length of time to complete the project
Consider these observations to find out the length of time:
- If any activity starts any activity during the forward pass, then the activity having the earliest start time is considered to be the activity of the first finish time.
- Similarly, in the case of backward, if the backward pass succeeds some activities, then the lowest end time will be the late start time for that activity.
- The given yellow cell represents the tasks having no slack and hence is considered vital activities.
The answer will be 25 week period.
(c) Activities with slack
From the above observations given, it is very clear to predict which activity has the slack,
Activity B has the slack2 times and activity E has the slack2 times as well.
(d) The activity that needs to be shortened
Activity C has the least slope amongst all the critical path activities. Hence, activity C will becrashed by1 week at $1200.
Incremental cost
From the above-calculated observations, it is easy to predict the value of the incremental cost,
The incremental cost for activity A is $1,000 and for activity C it is $12,000.
Hence, the total incremental costis $22,000.
The critical path changed
Earlier the critical path was A-C-D-F-G. But for now, the critical path鈥檚 duration has been changed to 23 weeks, which makes about 3 critical paths.
So, the answer would be Yes, the critical pathhas been changed.
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