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A Double Band Control Policy of a Brownian Perishable Inventory System

Published online by Cambridge University Press:  27 July 2009

David Perry
David Perry
Affiliation:
Department of Statistics, The University of Haifa, Haifa, Israel, 31905
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Abstract

The blood bank system is a typical example of a perishable inventory system. The commodity arrival and customer demand processes are stochastic. However, the stored items have a constant lifetime. In this study, we introduce a diffusion approximation to this system. The stock level is represented by the amount of items arriving during the age of the oldest item; it is assumed to fluctuate as an alternating two-sided regulated Brownian motion between barriers 0 and 1. Hittings of level 0 are outdatings and hittings of level 1 are unsatisfied demands. Also, there are two predetermined switchover levels, a and b, with 0 ≤ a < b ≤ 1. Whenever the stock level process upcrosses level b, the controller generates a switch in the drift from γ = γ0 to γ = γ1, while downcrossings of level a generate switches from γ1 to γ0. A useful martingale is introduced for analyzing the stationary law of the controlled process as well as the total expected discounted cost.

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Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 11 , Issue 3 , July 1997 , pp. 361 - 373
Copyright
Copyright © Cambridge University Press 1997

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