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On the Optimal Policy for the Single-product Inventory Problem with Set-up Cost and a Restricted Production Capacity

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  • Wijngaard, J.
  • Foreest, N. D. van

    (Groningen University)

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    Abstract

    The single-product, stationary inventory problem with set-up cost is one of the classical problems in stochastic operations research. Theories have been developed to cope with finite production capacity in periodic review systems, and it has been proved that optimal policies for these cases are not of the (modified) (s, S)-type in general, but more complex. In this paper we consider a production system such that the production rate is constrained, rather than the amount as is common in periodic review models. Thus, in our case the production rate is positive and finite when the system is on and zero when off, while a cost is incurred to switching on or off. We prove that a long-run optimal stationary policy exists for this single-item continuous review inventory problem with non-zero switching cost and finite production rate, and that this optimal policy has an (s,S)-structure. We also provide an efficient numerical procedure to compute the parameters of the optimal policy.

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    File URL: http://irs.ub.rug.nl/ppn/327491353
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    Bibliographic Info

    Paper provided by University of Groningen, Research Institute SOM (Systems, Organisations and Management) in its series Research Report with number 10005.

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    Date of creation: 2010
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    Handle: RePEc:dgr:rugsom:10005

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    1. Lotfi Tadj & Gautam Choudhury, 2005. "Optimal design and control of queues," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 13(2), pages 359-412, December.
    2. Albert Y. Ha, 1997. "Inventory Rationing in a Make-to-Stock Production System with Several Demand Classes and Lost Sales," Management Science, INFORMS, vol. 43(8), pages 1093-1103, August.
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