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A Single-Product Inventory Model for Multiple Demand Classes

Sawyer Business School, Suffolk University, Boston, Massachusetts 02108
Leaders for Manufacturing Program and A. P. Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
The Rady School of Management, University of California, San Diego, La Jolla, California 92093
harslan{at}suffolk.edu
sgraves{at}mit.edu
troemer{at}ucsd.edu

We consider a single-product inventory system that serves multiple demand classes, which differ in their shortage costs or service-level requirements. We assume a critical-level control policy, and a backorder clearing mechanism in which we treat a backorder for a lower-priority class equivalent to a reserve-stock shortfall for the higher-priority class. We show the equivalence between this inventory system and a serial inventory system. Based on this equivalence, we develop a model for cost evaluation and optimization under the assumptions of Poisson demand, deterministic replenishment lead time, and a continuous-review (Q, R) policy with rationing. We propose a computationally efficient heuristic and develop a bound on its performance. We provide a numerical experiment to show the effectiveness of the heuristic and the value from a rationing policy. Finally, we describe how to extend the model to permit service times, and how to extend the model to a multi-echelon setting.

Key Words: inventory rationing; service differentiation; serial inventory system; priority demand classes
History: Received: March 12, 2005;

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