Capacity Acquisition and Disposal with Discrete Facility Sizes

We consider some key features of capacity acquisition, disposal, and replacement decisions in this paper that are seldom captured in capacity expansion models in the literature. First, capacity is often purchased in the form of equipment which comes only in a few discrete sizes. Second, some or all of the capacity may be replaced periodically due to the availability of better and cheaper equipment, or due to deterioration and increased operating costs of older equipment. Finally, some capacity may be disposed due to declining demand. We present integer programming formulations that model all of these aspects. We identify special structures in these formulations that are then exploited to develop efficient procedures for solving the linear relaxation optimally. The solution to the linear relaxation together with a heuristic interchange procedure are used in a branch-and-bound procedure to obtain optimal solutions. Computational results are presented that establish the effectiveness of the procedures in solving realistic problems to optimality.