Good Homes Construction Company is about to begin the construction of a large new home. The company's President, Michael Dean, is currently planning the schedule for this project. Michael has identified the five major activities (labeled A, B, . . . , E) that will need to be performed according to the following project network.
He also has gathered the following data about the normal point and crash point for each of these activities.
These costs reflect the company's direct costs for the material, equipment, and direct labor required to perform the activities. In addition, the company incurs indirect project costs such as supervision and other customary overhead costs, interest charges for capital tied up, and so forth. Michael estimates that these indirect costs run $5,000 per week. He wants to minimize the overall cost of the project. Therefore, to save some of these indirect costs, Michael concludes that he should shorten the project by doing some crashing to the extent that the crashing cost for each additional week saved is less than $5,000.
(a) To prepare for analyzing the effect of crashing, find the earliest times, latest times, and slack for each activity when they are done in the normal way. Also identify the corresponding critical path(s) and project duration.
(b) Use marginal cost analysis to determine which activities should be crashed and by how much to minimize the overall cost of the project. Under this plan, what is the duration and cost of each activity? How much money is saved by doing this crashing?
(c) Now use the linear programming approach to do part (b) by shortening the deadline 1 week at a time from the project duration found in part (a).