An automation project has the following activities and related data: Activity Time (Weeks) Activity Immediate Predecessor Most Optimistic (a) Most likely (m) Most Pessimistic (c) Crash Cost ($000) per week Maximum Crashable weeks A None 4 6 8 1 1 B None 4 5 6 5 1 C A 1 2 3 2 2 D A 1 4 7 4 2 E B 1 3 5 2 1 F B 4 5 12 3 1 G C, E 8 9 16 3 2 H D, F 2 6 16 2 1
13a. Compute the Expected Value E(t) and Variance V(t) for all activities. (5 points deducted for any error).
13b. There are three critical paths: ACG, BEG, and BFH, all with expected project completion time E(T)=18 weeks. Compute the variance of project completion time for each path. (5 points deducted for any error)
14. We will assume that the project completion time T is normally distributed with mean E(T)=18 weeks, and variance V(T) approximated by the maximum of the variances of the three individual critical paths.
14a. Compute the probability that the project can be completed in 19 weeks.
14b. Determine the time X in weeks for which there is a 90% probability that the project can be completed on or before X.
14c. List all alternatives and the respective costs for shortening the project by one week and identify the best alternative that has the minimum cost (5 points deducted for each missing or incorrect alternative).
15a. Formulate the linear program for minimizing the cost of shortening the project by one week. (5 points deducted for any missing part of the formulation
15b. Solve 15a with an LP software.