PROBLEM 8: (Project Management)

Refer again to the Imagination Toy Corporation marketing problem from Case 15.3. It was shown that the minimum project duration could be found through an LP formulation. Now, suppose that each task may be crashed as indicated in the table below:

For example, activity A may be crashed by three days at a daily cost of $333. However, activity K may not be crashed at all.

Question 1:

Provide an LP formulation that minimises the total crash cost while restricting the completion time. Clearly indicate the decision variables, objective function, and all of the necessary constraints.

Question 2:

The graph below captures the trade-off between the total crash cost and the completion time:

For example, completing the project in a maximum of 21 days incurs a total crash cost of $7,750, whereas completing the project in a maximum of 36 days incurs no crash cost. Create the trade-off chart by solving successive LP implementations in Excel. Clearly indicate the Solver settings and the total crash cost associated with each completion time between 21 and 36 days.