5.2 Consider a supply chain in which a number of distribution centers supply several markets. The goal is to identify distribution center locations as well as quantities shipped from distribution centers to markets that minimize the total costs. One distribution center can supply multiple markets. However, a market can only be supplied by a distribution center. Formulate this constrained optimization problem using the following notations:

a: number of markets (demand points)

b: number of potential distribution center locations Di: annual demand from market i, i = 1, 2, …, a Kj: potential annual capacity of distribution center at site j, j = 1, 2, …, b Fj: annual cost of locating a distribution center at site j cji: cost of shipping one unit from distribution center j to market i Hint: a constrained optimization problem is not necessarily a linear programming or mixed integer programming problem.