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An Inventory With Constant Demand and Poisson Restocking

Published online by Cambridge University Press:  27 July 2009

Laurence A. Baxter  and
Eui Yong Lee
Laurence A. Baxter
Affiliation:
Department of Applied Mathematics and Statistics State University of New York at Stony Brook Stony Brook, New York 11794
Eui Yong Lee
Affiliation:
Department of Applied Mathematics and Statistics State University of New York at Stony Brook Stony Brook, New York 11794
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Abstract

An inventory whose stock decreases linearly with time is considered. The inventory may be replenished at the instants at which a deliveryman arrives provided that the level of the inventory does not exceed a certain threshold; deliveries are made according to a Poisson process. A partial differential equation for the distribution function of the level of the inventory is solved to yield a formula for the corresponding Laplace–Stieltjes transform. The evaluation of the transform is discussed and explicit results are obtained for the stationary case.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 1 , Issue 2 , April 1987 , pp. 203 - 210
Copyright
Copyright © Cambridge University Press 1987

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References

Brill, P. H. and Posner, M. J. M. (1977). Level crossings in point processes applied to queues: Single-server case. Operations Research 25: 662–674.CrossRefGoogle Scholar
Cox, D. R. (1962). Renewal Theory, Methuen, London.Google Scholar
Feller, W. (1936). Zur Theorie der stochastischen Prozesse (Existenz- und Eindeutigkeitssätze). Mathematische Annalen 113: 13–60.Google Scholar
Feller, W. (1971). An Introduction to Probability Theory and Its Applications, Volume II, Second Edition, John Wiley, New York.Google Scholar
McConalogue, D.J. (1978). Convolution integrals involving probability distribution functions (Algorithm 102). The Computer Journal 21: 270–272.Google Scholar
Royden, H. L. (1968). Real Analysis, Second Edition, Macmillan, New York.Google Scholar
Takács, L. (1955). Investigation of waiting time problems by reduction to Markov processes. Ada Mathematica Academiae Scientiarum Hungaricae 6: 101–129.Google Scholar