Solving Fixed Charge Location-Allocation Problems with Capacity and Configuration Constraints

Location-allocation problems involve the selection of locations that will be used as sources to satisfy a demand at various destinations. Associated with each potential source is a capacity limitation on output and a cost function which is broken down into a fixed charge plus an output dependent variable cost. Linear distribution costs comprise the remaining part of the total system cost. Configuration constraints which rule that specific source combinations are infeasible may be included for consideration. A solution procedure is presented that finds the minimal cost solution. The procedure utilizes a new enumerative search scheme in conjunction with adaptive bounds on the fixed costs, and constraints based on the dual variables to reduce the feasible solution set to a manageable size. For each of the small number of enumerated source configurations that pass all fixed cost and duality tests, a transportation problem is optimized to determine the minimum cost allocation. An experimental computer code was developed and numerical results are presented.