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CONTROL POLICIES FOR INVENTORY SYSTEMS WITH PERISHABLE ITEMS: OUTSOURCING AND URGENCY CLASSES

Published online by Cambridge University Press:  22 June 2005

Shaul K. Bar-Lev ,
David Perry  and
Wolfgang Stadje
Shaul K. Bar-Lev
Affiliation:
Department of Statistics, University of Haifa, 31905 Haifa, Israel
David Perry
Affiliation:
Department of Statistics, University of Haifa, 31905 Haifa, Israel
Wolfgang Stadje
Affiliation:
Department of Mathematics and Computer Science, University of Osnabrück, 49069 Osnabrück, Germany, E-mail: [email protected]
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Abstract

We consider control policies for perishable inventory systems with random input whose purpose is to mitigate the effects of unavailability. In the basic uncontrolled system, the arrival times of the items to be stored and the ones of the demands for those items form independent Poisson processes. The shelf lifetime of every item is finite and deterministic. Every demand is for a single item and is satisfied by the oldest item on the shelf, if available. The first controlled model excludes the possibility of unsatisfied demands by introducing a second source of fresh items that is completely reliable and delivers without delay whenever the system becomes empty. In the second model, there is no additional ordering option by outsourcing. However, to avoid the most adverse effects of unavailability, the demands are classified into different categories of urgency. An incoming demand is satisfied or not according to its category and the current state of the system. For both models, we determine the steady-state distribution of the virtual outdating process, which is then used to derive the relevant cost functionals: the steady-state distribution and expected value of the number of items in the system, the rate of outdatings, as well as, for model 1, the rate of special orders from the external source and, for model 2, the rate of unsatisfied demands.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 19 , Issue 3 , July 2005 , pp. 309 - 326
Copyright
© 2005 Cambridge University Press

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