A company needs two parts, A and B, for its product. It can either buy them from another company, or can make them in its own plant, or do both. The costs of each alternative and the in-house production rates are given in Table 5.40.

The company must have at least 100 units of part A and 200 units of part B each week. There are 40 hours of production time per week and idle time on the machine costs $3.00/hour. Furthermore, no more than 60 units of A can be made each week, and no more than 120 units of B can be made each week. Also, no more than 150 units of B can be bought per week. The company wants to determine an optimal plan that will minimize the total costs per week. Formulate this as a linear programming problem and solve. What is the optimal make or buy plan for the company?

In this case study, you will be working on a supplier ranking problem. It is an actual application for a manufacturing company located in Tijuana, Mexico. Because of confidentiality issues, the data given here have been disguised. The supplier selection criteria and subcriteria have been defined by the Purchasing Manager as shown in Figure 5.12. Note that Flexibility, Process Capability (Cpk Index), and Service have to be maximized, while the other criteria have to be minimized. The company is considering 21 potential suppliers and the supplier data with respect to the criteria are given in Table 5.44.

Questions:

a. Scale the supplier criteria values using linear normalization (simple linearization).

b. Using the scaled values from part (a), apply the L2 metric method to rank the suppliers.

c. Determine the criteria/subcriteria weights using the following methods (use your own judgment):

i. Rating method.

ii. Pairwise comparison of criteria/subcriteria and Borda method.

iii. AHP. Test the consistency of all pairwise comparison matrices.

d. Using the weights obtained in part (c) and the scaled supplier data in part (a), determine the supplier rankings by all three methods.

[NOTE: For AHP, do not perform pairwise comparison of alternatives (suppliers) with each criterion/subcriterion. Instead, use directly the scaled supplier data from part (a) as the S matrix.

e. Compare the supplier rankings obtained by L2 metric, rating method, Borda method, and AHP. Discuss any rank reversals.