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Control Policies for Two Classes of Inventory Systems via a Duality-Equivalence Relationship

Published online by Cambridge University Press:  27 July 2009

D. Perry  and
M. J. M. Posner
D. Perry
Affiliation:
Department of StatisticsUniversity of Haifa Haifa, 3000 Israel and Department of Management ScienceUniversity of Toronto Tronto, Ontario, M5S 1A4, Canada
M. J. M. Posner
Affiliation:
Department of StatisticsUniversity of Haifa Haifa, 3000 Israel and Department of Management ScienceUniversity of Toronto Tronto, Ontario, M5S 1A4, Canada
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Abstract

Two classes of inventory systems are considered, and modeled under a control policy of the bang-bang type. For the first, items and demands for those items arrive independently and singly at a system. Unsatisfied demands are lost, and items staying on the shelf too long are considered unsuitable for use and are rejected. For the second, items are produced continuously over time with fixed rate in a storage/production system with capacity k, in which demands of exponential size arrive according to a Poisson process, and no backorders are allowed. The problem of controlling the demand rate in the first model is shown to be equivalent to the problem of controlling the production rate in the second model. Optimization methods are then considered for both models employing discounted cost and averaged cost rate criteria for the optimal selection of switchover levels for arrival and demand rates.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 3 , Issue 4 , October 1989 , pp. 561 - 579
Copyright
Copyright © Cambridge University Press 1989

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References

Harrison, M. (1985). Brownian motion and stochastic flow systems. New York: J. Wiley.Google Scholar
Kaspi, H. & Perry, D. (1983). Inventory systems of perishable commodities. Advances in Applied Probability 15: 674–685.CrossRefGoogle Scholar
Perry, D. & Levikson, B. (1989). Continuous production/inventory models with analogy to certain queueing and dam models. Advances in Applied Probability (to appear).CrossRefGoogle Scholar
Perry, D. & Posner, M.J.M. (1987). Demand control in inventory systems of perishable commodities. Working Paper 87−02, Department of Industrial Engineering, University of Toronto, Ontario, Canada.Google Scholar
Ross, S.M. (1983). Stochastic processes. New York: J. Wiley.Google Scholar