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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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References

[1] Çinlar, E. (1982) Introduction to Stochastic Processes. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
[2] Cohen, J. W. (1969) Single server queues with restricted accessibility. J. Engineering Math. 3, 265–285.CrossRefGoogle Scholar
[3] Cohen, J. W. (1976) On Regenerative Processes in Queueing Theory. Springer-Verlag, Berlin.Google Scholar
[4] Cohen, J. W. (1977) On up- and downcrossings. J. Appl. Prob. 14, 405–410.CrossRefGoogle Scholar
[5] Cohen, J. W. (1982) The Single-Server Queue, revised edn. North-Holland, Amsterdam.Google Scholar
[6] Daley, D. J. (1964) Single server queueing systems with uniformly limited queueing times. J. Austral. Math. Soc. 4, 489–505.CrossRefGoogle Scholar
[7] Harrison, J. M. and Resnick, S. I. (1976) The stationary distribution and first exit probabilities of a storage process with general release rule. Math. Operat. Res. 4, 347–358.Google Scholar
[8] Kaspi, H. and Perry, D. (1983) Inventory systems with perishable commodities. Adv. Appl. Prob. 15, 674–685.Google Scholar
[9] Nahmias, S. (1980) Perishable inventory theory: A review. Working paper, Department of Quantitative Methods, University of Santa Clara.Google Scholar
[10] Perry, D. (1983) Inventory Systems with Perishable Commodities. , Technion–Israel Institute of Technology, Haifa.Google Scholar