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Stochastic inventory models with bulk demand and state-dependent leadtimes

Published online by Cambridge University Press:  14 July 2016

Donald Gross ,
Carl M. Harris  and
James A. Lechner
Donald Gross
Affiliation:
The George Washington University
Carl M. Harris*
Affiliation:
The George Washington University
James A. Lechner
Affiliation:
Research Analysis Corporation
*
* Formerly with the Research Analysis Corporation.
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Abstract

This paper describes two one-for-one ordering (S − 1, S) inventory models in which the time required for order replenishment is state-dependent. The demand is assumed to follow a compound Poisson distribution, and that portion of the leadtime corresponding to the actual filling of orders is assumed to depend on the number of outstanding orders. Since the orders placed are assumed to go into a single-server queue, queuing results are used to obtain the expected inventory cost as a function of S in order to obtain an optimal value of S.

Type
Research Papers
Information
Journal of Applied Probability , Volume 8 , Issue 3 , September 1971 , pp. 521 - 534
Copyright
Copyright © Applied Probability Trust 1971 

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Footnotes

An earlier version of this paper was presented by the authors to the 1969 Fall Meeting of the Operations Research Society of America, Miami Beach, Florida.

References

[1] Crabill, T. B. (1968) Sufficient conditions for positive recurrence and recurrence of specially structured Markov chains. Operat. Res. 16, 858–867.Google Scholar
[2] Fabens, A. J. (1961) The solution of queuing and inventory models by semi-Markov processes. J. R. Statist. Soc. B 23, 113–127.Google Scholar
[3] Gross, D. and Harris, C. M. (1971) On one-for-one ordering inventory policies with state-dependent leadtimes. To appear in Operat. Res. Google Scholar
[4] Gross, D., Harris, C. M., Lechner, J. A., Robers, P. D. and Miercort, F. A. (1969) Stochastic inventory models with bulk demand and state-dependent leadtimes. RAC-P-56. Research Analysis Corporation, Mchean, Virginia.Google Scholar
[5] Harris, C. M. (1970) Some results for bulk-arrival queues with state-dependent service times. Management Sci. 16, 313–326.Google Scholar