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Dynamic Capacity Management with Substitution

Tuck School of Business, Dartmouth College, Hanover, New Hampshire 03755
Olin Business School, Washington University in St. Louis, St. Louis, Missouri 63130
robert.shumsky{at}dartmouth.edu
fzhang22{at}wustl.edu

We examine a multiperiod capacity allocation model with upgrading. There are multiple product types, corresponding to multiple classes of demand, and the firm purchases capacity of each product before the first period. Within each period, after demand arrives, products are allocated to customers. Customers who arrive to find that their product has been depleted can be upgraded by at most one level. We show that the optimal allocation policy is a simple two-step algorithm: First, use any available capacity to satisfy same-class demand, and then upgrade customers until capacity reaches a protection limit, so that in the second step the higher-level capacity is rationed. We show that these results hold both when all capacity is salvaged at the end of the last demand period as well as when capacity can be replenished (in the latter case, an order-up-to policy is optimal for replenishment). Although finding the optimal protection limits is computationally intensive, we describe bounds for the optimal protection limits that take little effort to compute and can be used to effectively solve large problems. Using these heuristics, we examine numerically the relative value of strictly optimal capacity and dynamic rationing, the value of perfect demand information, and the impact of demand and economic parameters on the value of optimal substitution.

Subject classifications: inventory/production; uncertainty; stochastic; multi-item; approximations/heuristics.
History: Received February 2007; revision received November 2007; accepted January 2008.