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Using Stochastic Approximation Methods to Compute Optimal Base-Stock Levels in Inventory Control Problems

Indian School of Business, Gachibowli, Hyderabad 500032, India
School of Operations Research and Information Engineering, Cornell University, Ithaca, New York 14853
sumit_kunnumkal{at}isb.edu
topaloglu{at}orie.cornell.edu

In this paper, we consider numerous inventory control problems for which the base-stock policies are known to be optimal, and we propose stochastic approximation methods to compute the optimal base-stock levels. The existing stochastic approximation methods in the literature guarantee that their iterates converge, but not necessarily to the optimal base-stock levels. In contrast, we prove that the iterates of our methods converge to the optimal base-stock levels. Moreover, our methods continue to enjoy the well-known advantages of the existing stochastic approximation methods. In particular, they only require the ability to obtain samples of the demand random variables, rather than to compute expectations explicitly, and they are applicable even when the demand information is censored by the amount of available inventory.

Subject classifications: inventory/production; uncertainty; stochastic; dynamic programming/optimal control; applications.
History: Received April 2006; revision received May 2007; accepted June 2007.