Reconsider the Tinker Construction Co. problem presented in Prob. 10.5-1. While in college, Sean Murphy took an OR course that devoted a month to linear programming, so Sean has decided to use linear programming to analyze this problem
(a) Consider the upper path through the project network. Formulate a two-variable linear programming model for the problem of how to minimize the cost of performing this sequence of activities within 12 months. Use the graphical method to solve this model.
(b) Repeat part (a) for the lower path through the project network.
(c) Combine the models in parts (a) and (b) into a single complete linear programming model for the problem of how to minimize the cost of completing the project within 12 months. What must an optimal solution for this model be?
(d) Use the CPM linear programming formulation presented in Sec. 10.5 to formulate a complete model for this problem. [This model is a little larger than the one in part (c) because this method of formulation is applicable to more complicated project networks as well.]
(e) Use Excel to solve this problem. The project manager, Sean Murphy, has concluded that he cannot meet the deadline by performing all these activities in the normal way. Therefore, Sean has decided to use the CPM method of time-
(f) Use another software option to solve this problem.
(g) Check the effect of changing the deadline by repeating part (e) or (
) with the deadline of 11 months and then with a deadline of 13 months.
Prob. 10.5-1
The Tinker Construction Company is ready to begin a project that must be completed in 12 months. This project has four activities (A, B, C, D) with the project network shown below.
cost trade-offs to determine the most economical way of crashing the project to meet the deadline. He has gathered the following data for the four activities.
