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Approximations for a Lost-Sales Production/Inventory Control Model with Service Level Constraints

Author

Listed:
  • A. G. de Kok

    (Vrije Universiteit, Department of Actuarial Sciences and Econometrics, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands)

Abstract

This paper deals with a one-product production/inventory model, where the production rate can be dynamically adjusted in order to cope with random fluctuations in demand. The inventory level is controlled by using one of two possible production rates where under each production rate the production is continually added to the inventory. The demand process for the product is described by a compound Poisson process. Also, excess demand is lost. In accordance with common practice we consider service measures as the average number of lost-sales occurrences per unit time and the fraction of demand that is lost. For a two-critical-number control rule we derive practically useful approximations for the switch-over level in order to achieve a prespecified service level. Numerical experiments reveal that the approximations are quite accurate.

Suggested Citation

  • A. G. de Kok, 1985. "Approximations for a Lost-Sales Production/Inventory Control Model with Service Level Constraints," Management Science, INFORMS, vol. 31(6), pages 729-737, June.
    • Handle: RePEc:inm:ormnsc:v:31:y:1985:i:6:p:729-737
    DOI: 10.1287/mnsc.31.6.729
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    Cited by:

    1. Chiu, Singa Wang & Chou, Chung-Li & Wu, Wen-Kuei, 2013. "Optimizing replenishment policy in an EPQ-based inventory model with nonconforming items and breakdown," Economic Modelling, Elsevier, vol. 35(C), pages 330-337.
    2. Opher Baron, 2008. "Regulated Random Walks and the LCFS Backlog Probability: Analysis and Application," Operations Research, INFORMS, vol. 56(2), pages 471-486, April.
    3. (Ai-Chih) Chang, Jasmine & Lu, Haibing & (Junmin) Shi, Jim, 2019. "Stockout risk of production-inventory systems with compound Poisson demands," Omega, Elsevier, vol. 83(C), pages 181-198.
    4. Chiu, Singa Wang & Liang, Gang-Ming & Chiu, Yuan-Shyi Peter & Chiu, Tiffany, 2019. "Production planning incorporating issues of reliability and backlogging with service level constraint," Operations Research Perspectives, Elsevier, vol. 6(C).
    5. 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.
    6. Sajadieh, Mohsen S. & Larsen, Christian, 2015. "A coordinated manufacturer-retailer model under stochastic demand and production rate," International Journal of Production Economics, Elsevier, vol. 168(C), pages 64-70.
    7. Bijvank, Marco & Vis, Iris F.A., 2011. "Lost-sales inventory theory: A review," European Journal of Operational Research, Elsevier, vol. 215(1), pages 1-13, November.
    8. Klosterhalfen, Steffen T. & Holzhauer, Falk & Fleischmann, Moritz, 2018. "Control of a continuous production inventory system with production quantity restrictions," European Journal of Operational Research, Elsevier, vol. 268(2), pages 569-581.
    9. Jim Shi, 2022. "Optimal continuous production-inventory systems subject to stockout risk," Annals of Operations Research, Springer, vol. 317(2), pages 777-804, October.
    10. Tseng, Chao-Tang & Wu, Mei-Fang & Lin, Hong-Dar & Chiu, Yuan-Shyi Peter, 2014. "Solving a vendor–buyer integrated problem with rework and a specific multi-delivery policy by a two-phase algebraic approach," Economic Modelling, Elsevier, vol. 36(C), pages 30-36.
    11. 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.
    12. 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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