The Multiregion Dynamic Capacity Expansion Problem: An Improved Heuristic

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Abstract
We consider the problem of determining a schedule of capacity expansions for m producing regions and a schedule of shipments from the regions to n markets so as to meet market demands over a T-period planning horizon at minimum discounted capacity expansion and shipment costs. The proposed algorithm permits capacity expansion costs to be arbitrary nonnegative increasing functions of the expansion amounts, but the shipment (and production) costs are restricted to be proportional to the amounts shipped. The algorithm does not require market demands to be increasing over time. The cost functions are allowed to be nonstationary and the possibility of imports is considered. The proposed heuristic algorithm improves on feasible solutions by simultaneously reassigning several capacity expansions to different regions and/or time periods. A look-ahead feature prevents the algorithm from becoming myopic and a self-learning feature dynamically updates computational parameters. The heuristic algorithm was tested on both randomly generated and real-life based problems with m \le 15, and n \le 15 and T \le 25. The test problems had increasing market demands, capacity expansion costs specified in the form of a concave power function or a fixed charge plus linear function, stationary costs (aside from a constant discount factor), and no imports. Results indicate that for the class of problems tested, the heuristic algorithm is computationally efficient and provides solutions that are closer to optimum than those obtained by previous algorithms.facilities/equipment planning: capacity expansion, heuristics

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