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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.

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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