Describe how CPM handles the trade-offs between time and cost in the scheduling of a project.

Question

What will be an ideal response?

Answer 1

In this question, it is assumed that the some or all of the activity times may be reduced by incurring an additional cost. For such activities, normal time, crash time, normal cost, crash cost and hence approximate cost (non-linearity of costs may prevent an exact cost calculation) to reduce time by one unit may be calculated. In order to reduce the overall project time, one would have to reduce one or more activity times in the critical path. The procedure is to pick the activity or combination of activities on the critical path (if there is more than one critical path, make sure that all critical paths are reduced) that may be reduced by one unit time which will in turn reduce the length of the critical path by one unit. If there are choices, choose the combination that has the lowest total cost for reducing the project completion time (all critical paths) by one unit. Reduce the project time and mark all the new activity times and the total project completion time. Repeat this process by picking an activity or a combination of activities on the critical path (critical paths) which reduces the project time by one unit and which costs the lowest among all combinations generating one unit time reduction in the project completion time. Continue this until the desired amount of project time reduction is achieved or there is no feasible combination to reduce the project time.

Feedback: This question can elicit a variety of responses. The "most correct" answers will deal with the issues set forth under the heading "Minimum-Cost Scheduling" and should include, as a minimum, the idea that each activity has a normal cost, normal time, crash cost, and crash time specified; that the critical path is computed; that only activities on the critical path should be considered as candidates to "crash"; that the critical path should be shortened at the least cost; and that the new solution should be checked to determine whether the critical path has changed.