The “Modeling Issues” section described three alternative types of precedence relationships besides the usual finish-to-start relationship. The following questions ask you to explore the first of...

The “Modeling Issues” section described three alternative types of precedence relationships besides the usual finish-to-start relationship. The following questions ask you to explore the first of these alternatives for the LAN project.


a. Start-to-start relationships are sometimes useful for activities that can run parallel to one another. Suppose that there is a start-to-start relationship between activities J (developing training program) and M (training users). Specifically, activity M cannot start until activity J has started. In general, do the CPM formulas for earliest start times need to be changed when there are start-to-start relationships? What about the formulas for latest finish times? Redo the CPM calculations with this new relationship.

b. Repeat part a, but now generalize even a bit more. Assume that activity M cannot start until three weeks after activity J starts. This is a delayed startto-start relationship.


c. Getting the correct logic for earliest start and latest finish formulas for the relationships in parts a and b can be a bit tricky. As an alternative, modify the Solver model from Problem 7 for these relationships. This should be more straightforward. Do you get the same results as in parts a and b? (You should.)

Problem 7

We have illustrated the traditional CPM algorithm for finding the project length and the critical path. An alternative method is sometimes used. It sets up a Solver model for finding a feasible solution to a set of constraints, and there is no objective to maximize or minimize. Let d_j
be the duration of activity j, and let t_j
be the start time of activity j. Let the t_j
’s be the changing cells in the Solver model. There is a constraint for each arc in the AON network. Specifically, if there is an arc from activity i to activity j, then there is a constraint t_j
 t_i
+d_i
. This states that activity j cannot start until its predecessor, activity i, finishes. Develop this Solver model for the LAN project, making sure that there is no target cell in the Solver dialog box. (Just delete whatever is in the Target Cell box.) Then run Solver to find the project completion time. Can you tell from the solution which activities are critical?