Problem 1

The following network describes a transportation scenario in which there are four sources A, B, C, and D, and three destinations P, Q, and R. (The numbers next to each arrow represent the cost of transporting one unit from that particular source to the destination located at the other end of that arrow).

a) Write the mathematical formulation of the problem.

b) Use the Excel Solver to solve the problem. Generate the answer and sensitivity reports in Excel, and submit your Excel workbook as a separate attachment.

c) Provide the solution obtained in the space provided. What is the optimal cost of transportation?

Problem 2

By including intermediary distribution centers X and Y as shown in the figure and using the given network, will the company save money in its transportation costs compared to the results obtained in problem 1? (Note: For any two given nodes, a directed arrow represents an existing route between the two nodes.)

a) Write the mathematical formulation of the problem.

b) Use the Excel Solver to solve the problem. Generate the answer and sensitivity reports in Excel, and submit your Excel workbook as a separate attachment.

c) Provide the solution obtained in the space provided. What is the optimal cost of transportation? Will the transportation costs be reduced after the intermediate points have been included?