Reconsider Prob. 10.4-3, which involves trying to find the probability that a project will be completed by the deadline. Assume now that the duration of each activity has a triangular distribution that is based on the three estimates in the manner depicted in Fig. 22.10. Obtain a close estimate of the probability of meeting the deadline by performing 1,000 iterations of a simulation of the project on a spreadsheet. Generate the various available kinds of outputs similar to Fig. 22.12.

Prob. 10.4-3

Reconsider Prob. 10.4-2. For each of the 10 activities, here are the three estimates that led to the estimates of the mean and variance of the duration of the activity (rounded to the nearest integer) given in the table for Prob. 10.4-2.

(Note how the great uncertainty in the duration of these research activities causes each pessimistic estimate to be several times larger than either the optimistic estimate or the most likely estimate.) Now use the Excel template in your OR Courseware (as depicted in Fig. 10.10) to help you carry out the instructions for Prob. 10.4-2. In particular, enter the three estimates for each activity, and the template immediately will display the estimates of the means and variances of the activity durations. After indicating each path of interest, the template also will display the approximate probability that the path will be completed within 22 months

Prob. 10.4-2

Alfred Lowenstein is the president of the research division for Better Health, Inc., a major pharmaceutical company. His most important project coming up is the development of a new drug to combat AIDS. He has identified 10 groups in his division which will need to carry out different phases of this research and development project. Referring to the work to be done by the respective groups as activities A, B, . . . , J, the precedence relationships for when these groups need to do their work are shown in the following project network.

(a) Find the mean critical path for this project.

(b) Use this mean critical path to find the approximate probability that the project will be completed within 22 months.

(c) Now consider the other three paths through this project network. For each of these paths, find the approximate probability that the path will be completed within 22 months.

(d) What should Alfred tell his CEO about the likelihood that the drug will be ready within 22 months?

Fig. 22.12