Consider a supplier order allocation problem under multiple sourcing, where it is required to buy 2000 units of a certain product from three different suppliers. The fixed set-up cost (independent of the order quantity), variable cost (unit price), and the maximum capacity of each supplier are given in Table 5.15 (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.
