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(s, S) Inventory Systems with Random Lead Times: Harris Recurrence and Its Implications in Sensitivity Analysis

Published online by Cambridge University Press:  27 July 2009

Michael C. Fu  and
Jian-Qiang Hu
Michael C. Fu
Affiliation:
College of Business and Management, University of Maryland, College Park, Maryland 20742
Jian-Qiang Hu
Affiliation:
Manufacturing Engineering Department, Boston University, Boston, Massachusetts 02215
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Abstract

Most of the previous work on (s, S) inventory systems assumes that lead times for orders are such that orders never cross in time; i.e., the arrival of orders follows the same sequence as the placement of the orders. In this paper we consider more general mechanisms for random lead times. Because the introduction of a general random lead time mechanism makes the system essentially intractable for most performance measures of interest, simulation is a. natural candidate for estimating performance and/or optimizing the system. Two important issues in simulation are the stability and ergodicity of the system. Therefore, we first study some theoretical implications of the mechanism by providing conditions for which the system is stable and Harris ergodic, with the accompanying wide-sense regenerative properties. We then consider the problem of gradient estimation during simulation. Using the technique of perturbation analysis, we derive sample path-based gradient estimates for the finite-horizon average cost per period with respect to the parameters s and S and give a sample path proof of unbiasedness. We then show how stability and ergodicity can be used to simplify the estimators in the limiting infinite-horizon case and to establish strong consistency of the resulting estimators.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 8 , Issue 3 , July 1994 , pp. 355 - 376
Copyright
Copyright © Cambridge University Press 1994

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