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Technical Note—A One-Product Production/Inventory Problem under Continuous Review Policy

Author

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  • Bezalel Gavish

    (University of Rochester, Rochester, New York)

  • Stephen C. Graves

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

Abstract

A single production facility is dedicated to producing one type of product with completed units going directly into inventory. The demand for the product is governed by a Poisson process and is supplied directly to inventory when available, or is backordered until it is produced by the production facility. Relevant costs are a linear inventory holding cost, a linear backorder cost, a fixed setup cost for initiating a production run. The objective is to find a control policy to minimize the expected cost per time unit. It is shown that the problem may be modeled as an M / D /1 queueing system with the optimal policy being a two-critical-number policy. Cost expressions are derived as functions of the policy parameters, and based on a convexity property of these cost expressions, an efficient search procedure is proposed for finding the optimal policy. In computational tests that were performed on an IBM 360/65, optimal policies were computed in less than 1/8 second of CPU time.

Suggested Citation

  • Bezalel Gavish & Stephen C. Graves, 1980. "Technical Note—A One-Product Production/Inventory Problem under Continuous Review Policy," Operations Research, INFORMS, vol. 28(5), pages 1228-1236, October.
    • Handle: RePEc:inm:oropre:v:28:y:1980:i:5:p:1228-1236
    DOI: 10.1287/opre.28.5.1228
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    Cited by:

    1. Dimitris Bertsimas & Ioannis Ch. Paschalidis, 2001. "Probabilistic Service Level Guarantees in Make-to-Stock Manufacturing Systems," Operations Research, INFORMS, vol. 49(1), pages 119-133, February.
    2. Foreest, N. D. van & Wijngaard, J., 2010. "On the Optimal Policy for the Single-product Inventory Problem with Set-up Cost and a Restricted Production Capacity," Research Report 10005, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    3. Pablo Azcue & Esther Frostig & Nora Muler, 2023. "Optimal Strategies in a Production Inventory Control Model," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-43, March.
    4. Ioannis Ch. Paschalidis & Yong Liu, 2003. "Large Deviations-Based Asymptotics for Inventory Control in Supply Chains," Operations Research, INFORMS, vol. 51(3), pages 437-460, June.
    5. Tayfur Altiok & Goang An Shiue, 1995. "Single‐stage, multi‐product production/inventory systems with lost sales," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(6), pages 889-913, September.
    6. H. G. H. Tiemessen & M. Fleischmann & G. J. Houtum, 2017. "Dynamic control in multi-item production/inventory systems," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(1), pages 165-191, January.
    7. Jim (Junmin) Shi & Michael N. Katehakis & Benjamin Melamed & Yusen Xia, 2014. "Production-Inventory Systems with Lost Sales and Compound Poisson Demands," Operations Research, INFORMS, vol. 62(5), pages 1048-1063, October.

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