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Inventory systems for perishable commodities with renewal input and Poisson output

Published online by Cambridge University Press:  01 July 2016

H. Kaspi  and
D. Perry
H. Kaspi*
Affiliation:
Technion—Israel Institute of Technology
D. Perry*
Affiliation:
Technion—Israel Institute of Technology
*
∗Postal address: Faculty of Industrial Engineering and Management, Technion—Israel Institute of Technology, Technion City, Haifa 32 000, Israel.
∗Postal address: Faculty of Industrial Engineering and Management, Technion—Israel Institute of Technology, Technion City, Haifa 32 000, Israel.
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Abstract

We consider an inventory system to which arrival of items stored is a renewal process, and the demand is a Poisson process. Items stored have finite and fixed lifetimes. The blood-bank model inspired this study. Three models are studied. In the first one, we assume that each demand is for one unit and unsatisfied demands leave the system immediately. Using results on this model one is able to study a model in which arrival of items is Poisson but demands are for several units, and a model in which demands are willing to wait. We compute ergodic limits for the lost demands and the lost items processes and the limiting distribution of the number of items stored. The main tool in this analysis is an analogy to M/G/1 queueing systems with impatient customers.

Keywords

M/G/1 QUEUEING SYSTEMSVIRTUAL WAITING TIMELEVEL CROSSINGSMARKOV PROCESSES
Type
Research Article
Information
Advances in Applied Probability , Volume 16 , Issue 2 , June 1984 , pp. 402 - 421
Copyright
Copyright © Applied Probability Trust 1984 

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