A project has the following activities and related data: Activity. Time (Weeks) Immediate Activity Predecessor Crash Most Most Most Cost Maximum Optimistic likely Pessimistic ($000) Crashable (a) (m) (C) per weeks week A None 1 3 11 3 1 00 None 4 5 6 4 1 С А 5 6 7 1 2 D А 4 5 12 1 2 1 E B 6 11 2 1 B 1 2 15 F 1 3 2 4 6 6 G CD 2 3 4 2 1 2 H EF G CD 2 4 6 6 N H EF 2 3 3 4 4 2 1 34a. (20 points) a. Compute the expected value E(t) and variance V(t) for all activities
Activity A B C D E F G H
E(t) weeks
V(t) weeks^2
b. there are three critical paths ACG, ADG, and BEH, all with expected project completion time time E(t) = 14 weeks. Compute the variance of project completion time for each path
V(ACG)=
V(ADG)=
V(BEH)
c. Assume that the project completion time T is normally distributed with mean E(T)=14 weeks and variance V(T) approximately by the maximum of the variances of the three individual critical paths. Determine the time X in weeks for which there is a 40% probability that the project can be completed on or before x.
d. List all alternatives and the respective costs for shortening the project by one week and identify the best alternative that has the minimum costs. Hint there are 8 alternatives
Alternative cost
the best alternative is..
e. For activity i, let Xi be the earliest finishing time and Yi be the number of weeks shortened. Formulate the linear program for minimizing the cost for shortening the project by one week