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Optimal Control of Production-Inventory Systems with Constant and Compound Poisson Demand

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  • Germs, Remco
  • Foreest, Nicky D. van

    (Groningen University)

Abstract

In this paper, we study a production-inventory systems with finite production capacity and fixed setup costs. The demand process is modeled as a mixture of a compound Poisson process and a constant demand rate. For the backlog model we establish conditions on the holding and backlogging costs such that the average-cost optimal policy is of (s, S)-type. The method of proof is based on the reduction of the production-inventory problem to an appropriate optimal stopping problem and the analysis of the associated free-boundary problem. We show that our approach can also be applied to lost-sales models and that inventory models with un onstrained order capacity can be obtained as a limiting case of our model. This allows us to analyze a large class of single-item inventory models, including many of the classical cases, and compute in a numerical efficient way optimal policies for these models, whether these optimal policies are of (s, S)-type or not.

Suggested Citation

  • Germs, Remco & Foreest, Nicky D. van, 2014. "Optimal Control of Production-Inventory Systems with Constant and Compound Poisson Demand," Research Report 14001-OPERA, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    • Handle: RePEc:gro:rugsom:14001-opera
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    File URL: http://hdl.handle.net/11370/03552d54-f811-4b72-93b5-538ef4446840
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    References listed on IDEAS

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    1. R. G. Vickson, 1986. "A Single Product Cycling Problem Under Brownian Motion Demand," Management Science, INFORMS, vol. 32(10), pages 1336-1345, October.
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    Cited by:

    1. Yonit Barron, 2016. "Performance analysis of a reflected fluid production/inventory model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(1), pages 1-31, February.
    2. Yonit Barron, 2016. "Performance analysis of a reflected fluid production/inventory model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(1), pages 1-31, February.
    3. Germs, Remco & Van Foreest, Nicky D. & Kilic, Onur A., 2016. "Optimal policies for production-clearing systems under continuous-review," European Journal of Operational Research, Elsevier, vol. 255(3), pages 747-757.
    4. Azoury, Katy S. & Miyaoka, Julia, 2020. "Optimal and simple approximate solutions to a production-inventory system with stochastic and deterministic demand," European Journal of Operational Research, Elsevier, vol. 286(1), pages 178-189.

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