Spring 2005 Seminar Series

DATE: Thursday, April 14, 2005
LOCATION: E40-298
TIME: 4:15pm
Reception immediately following in the Philip M. Morse Reading Room, E40-106

SPEAKER:
Robert A. Shumsky
Associate Professor of Operations Management
Simon School of Business
University of Rochester

TITLE
Dynamic Capacity Management with Substitution

ABSTRACT
Many manufacturing and service firms use flexible inventory to meet uncertain demand from multiple classes of customers. When inventory for a product has been exhausted, demand for that product may be met by a substitute (e.g., a car rental agency that runs out of economy-class cars may upgrade economy-class customers to full-sized cars). Here we examine a multiperiod capacity allocation model with upgrading. There are multiple product types, corresponding to classes of demand, and the firm purchases capacity of each product before the first period and thereafter replenishment is not possible. Customers who arrive to find that their product has been depleted can be upgraded by at most one level. We characterize the optimal policy as a rationing policy using state-dependent protection limits. We show that the protection limits are monotonic in current inventory and in time, and the monotonicity results lead to simple bounds for the optimal protection limits. The bounds can be used to find rationing strategies that are nearly optimal for large problems. Finally, we compare the optimal initial capacities under our dynamic model with the optimal capacities under a single-period 'static' model.