Reconsider the Lockhead Aircraft Co. problem presented in Prob. 10.4-6 regarding a project to develop a new fighter airplane for the U.S. Air Force. Management is extremely concerned that current plans for this project have a substantial likelihood (roughly a probability of 0.5) of missing the deadline imposed in the Department of Defense contract to finish within 100 weeks. The company has a bad record of missing deadlines, and management is worried that doing so again would jeopardize obtaining future contracts for defense work. Furthermore, management would like to avoid the hefty penalties for missing the deadline in the current contract. Therefore, the decision has been made to crash the project, using the CPM method of time-cost trade-offs to determine how to do this in the most economical way. The data needed to apply this method are given next.

These normal times are the rounded estimates of the means obtained from the original data in Prob. 10.4-6. The corresponding mean critical path provides an estimate that the project will finish in 100 weeks. However, management understands well that the high variability of activity durations means that the actual duration of the project may be much longer. Therefore, the decision is made to require that the estimated project duration based on means (as used throughout the CPM analysis) must not exceed 92 weeks.

(a) Formulate a linear programming model for this problem.

(b) Use Excel to solve the problem.

(c) Use another software option to solve the problem.

Problem 10.4-6

The Lockhead Aircraft Co. is ready to begin a project to develop a new fighter airplane for the U.S. Air Force. The company's contract with the Department of Defense calls for project completion within 100 weeks, with penalties imposed for late delivery. The project involves 10 activities (labeled A, B, . . . , J), where their precedence relationships are shown in the following project network.

(a) Find the estimate of the mean and variance of the duration of each activity.

(b) Find the mean critical path.

(c) Find the approximate probability that the project will finish within 100 weeks.

(d) Is the approximate probability obtained in part (c) likely to be higher or lower than the true value?