The network diagram and the corresponding activity cost chart for a manufacturing project at Networks, Inc., are presented below. The numbers in the diagram are the expected times (in days) to perform each activity in the project.The expected time of the critical path is:
Answer(s): B
The critical path is the longest path. The longest path in the diagram is A-D-E, which requires 13 days (5.5 + 7.5) based on expected times.
To keep costs at a minimum and decrease the completion time by 1-1/2 days, Networks, Inc.should crash activity(ies):
Answer(s): A
The critical (longest) path is A-D-E, which has an expected time of 13 days (5.5 + 7.5). However, to decrease the project's completion time by 1.5 days, paths A-B-C-E (4.5 + 1.0 + 6.5 = 12 days) and A-B-D-E (4.5 + .5 + 7.5= 12.5 days) as well as A-D-E must also be shortened. Hence, A-D-E must be reduced by 1.5 days. A-B-C-E by .5 day, and A-B-D-E by 1.0 day. The only way to decrease A-D-E by 1.5 days is to crash activity AD (5.5 expected time - 4.0 crash time = 1.5 days). Crashing DE results in a 1.0-day saving (7.5-6.5) only. Crashing AB is the efficient way to reduce both A-B-C-E and A-B-D-E by the desired amount of time because it is part of both paths. The incremental cost of crashing AB is US $1,000 (US $4,000 crash cost - US $3,000 normal cost) to shorten the completion time by 1.0 day (4.5 - 3.5). The alternatives for decreasing both A-B-C-E and A-B-D-E are more costly.
When making a cost-time trade-off in CPM analysis, the first activity that should be crashed is the activity:
Answer(s): D
When making a cost-time trade-off, the first activity to be crashed (have its completion time accelerated) is one on the critical path. To select an activity on another path would not reduce the total time of completion. The initial activity chosen should be the one with the completion time that can be accelerated at the lowest possible cost per unit of time saved.
In PERT, slack is the:
Slack is the amount of time that commencement of an activity can be delayed without forcing a delay of the entire project.
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