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Hint: Repla & (0, 1) for i = 1, 2, ..., 5. 5.10 (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: $110,000 tively. The retailer demands are 20,000 for the first four retailers and The capacities of the three sites are 100,000, 80,000, and 125,000 respec 25,000 for the remaining. The unit transportation costs ($) 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 mul- tiple sites. Solve using any optimization software. Write down the optimal solution. TABLE 5.17 Data for Exercise 5.10 R R R3 R R R6 R, R8 Site 1 4 5 5 4 4 4.2 3.3 Site 2 2.5 3.5 4.5 3 2.2 4 2.6 Site 3 2 4 2.6 3.8 2.9 LO 5 2.5 LO LO CO 5 5 3.5 loca assuming dedicated warehouses, that is, each retailer has to be sup- Reformulate the optimization problem as a linear integer program, one warehouse. Solve the integer programming plied by exactly model. What is the new optimal solution? Hint: Repla & (0, 1) for i = 1, 2, ..., 5. 5.10 (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: $110,000 tively. The retailer demands are 20,000 for the first four retailers and The capacities of the three sites are 100,000, 80,000, and 125,000 respec 25,000 for the remaining. The unit transportation costs ($) 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 mul- tiple sites. Solve using any optimization software. Write down the optimal solution. TABLE 5.17 Data for Exercise 5.10 R R R3 R R R6 R, R8 Site 1 4 5 5 4 4 4.2 3.3 Site 2 2.5 3.5 4.5 3 2.2 4 2.6 Site 3 2 4 2.6 3.8 2.9 LO 5 2.5 LO LO CO 5 5 3.5 loca assuming dedicated warehouses, that is, each retailer has to be sup- Reformulate the optimization problem as a linear integer program, one warehouse. Solve the integer programming plied by exactly model. What is the new optimal solution