Consider an order allocation problem under multiple sourcing, where it is required to buy 2000 units of a certain product from three different suppliers. The fixed setup cost (independent of the order quantity), variable cost (unit price), and the maximum capacity of each supplier are given in Table 5.43 (two suppliers offer quantity discounts).

The objective is to minimize the total cost of purchasing (fixed plus variable cost). Formulate this as a linear integer programming problem. You must define all your variables clearly, write out the constraints to be satisfied with a brief explanation of each, and develop the objective function.

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TABLE 5.43 Supplier Data for Exercise 5.18 Supplier 1 2 3 Fixed Cost $100 $500 $300 Capacity 600 units 800 units 1200 units Unit Price $10/unit for the first 300 units $7/unit for the remaining 300 units $2/unit for all 800 units $6/unit for the first 500 units $4/unit for the remaining 700 units