Reconsider the Electronic Toys Co. problem presented in Prob. 10.4-5. Sharon Lowe is concerned that there is a significant chance that the vitally important deadline of 57 days will not be met. Therefore, to make it virtually certain that the deadline will be met, she has decided to crash the project, using the CPM method of time-cost trade-offs to determine how to do this in the most economical way. Sharon now has gathered the data needed to apply this method, as given below.
The normal times are the estimates of the means obtained from the original data in Prob. 10.4-5. The mean critical path gives an estimate that the project will finish in 51 days. However, Sharon knows from the earlier analysis that some of the pessimistic estimates are far larger than the means, so the project duration might be considerably longer than 51 days. Therefore, to better ensure that the project will finish within 57 days, she has decided to require that the estimated project duration based on means (as used throughout the CPM analysis) must not exceed 47 days.
(a) Consider the lower path through the project network. Use marginal cost analysis to determine the most economical way of reducing the length of this path to 47 days.
(b) Repeat part (a) for the upper path through the project network. What is the total crashing cost for the optimal way of decreasing estimated project duration of 47 days?
(c) Use Excel to solve the problem.
(d) Use another software option to solve the problem.
Prob. 10.4-5
Sharon Lowe, vice president for marketing for the Electronic Toys Company, is about to begin a project to design an advertising campaign for a new line of toys. She wants the project completed within 57 days in time to launch the advertising campaign at the beginning of the Christmas season. Sharon has identified the six activities (labeled A, B, . . . , F) needed to execute this project. Considering the order in which these activities need to occur, she also has constructed the following project network.
Using the PERT three-estimate approach, Sharon has obtained the following estimates of the duration of each activity.
(a) Find the estimate of the mean and variance of the duration of each activity.
(b) Find the mean critical path.
(c) Use the mean critical path to find the approximate probability that the advertising campaign will be ready to launch within 57 days.
Using the PERT three-estimate approach, the usual three estimates of the duration of each activity have been obtained as given below.
(d) Now consider the other path through the project network. Find the approximate probability that this path will be completed within 57 days.
(e) Since these paths do not overlap, a better estimate of the probability that the project will finish within 57 days can be obtained as follows. The project will finish within 57 days if both paths are completed within 57 days. Therefore, the approximate probability that the project will finish within 57 days is the product of the probabilities found in parts (c) and (d). Perform this calculation. What does this answer say about the accuracy of the standard procedure used in part (c)?