(Adapted from Srinivasan, 2010) Consider a supply chain network with three potential sites for warehouses and eight retailer regions. The fixed costs of locating warehouses at the three sites are given as follows:

Site 1: $100,000
Site 2: $80,000
Site 3: $110,000

The capacities of the three sites are 100,000, 80,000, and 125,000 respectively. The retailer demands are 20,000 for the first four retailers and 25,000 for the remaining. The unit transportation costs ($) are given in Table 5.17:

(a) Formulate a mixed integer linear program to determine the optimal location and distribution plan that will minimize the total cost. You must define your variables clearly, write out the constraints, explaining briefly the significance of each and write the objective function. Assume that the retailers can receive supply from multiple sites. Solve using any optimization software. Write down the optimal solution.

(b) Reformulate the optimization problem as a linear integer program, assuming dedicated warehouses, that is, each retailer has to be supplied by exactly one warehouse. Solve the integer programming model. What is the new optimal solution?

(c) Compare the two optimal solutions and comment on their distribution plans.