Control policies for two classes of inventory systems via a duality-equivalence relationship

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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.

Original languageEnglish
Pages (from-to)561-579
Number of pages19
JournalProbability in the Engineering and Informational Sciences
Issue number4
StatePublished - Oct 1989

Bibliographical note

Funding Information:
The authors appreciate the financial support of the National Sciences and Engineering Research Council of Canada under Grant A4374. They are also grateful to the referee for the helpful comments on the presentation of this paper.

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering


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