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Inventory Policies for Systems with Stochastic and Deterministic Demand

Author

Listed:
  • Matthew J. Sobel

    (Weatherhead School of Management, Case Western Reserve University, Cleveland, Ohio 44106)

  • Rachel Q. Zhang

    (Johnson Graduate School of Management, Cornell University, Ithaca, New York 14853)

Abstract

We consider a periodic review inventory system with demand arriving simultaneously from a deterministic source and a random source. The deterministic demand has to be satisfied immediately and the stochastic demand can be backordered. Assuming that the stochastic demand is never backlogged if there is stock in the system, we prove that a modified ( s, S ) policy is optimal under general conditions if there is a setup cost. If there is a smoothing cost instead of the setup cost, we observe that the problem corresponds to a standard model with one source of demand.

Suggested Citation

  • Matthew J. Sobel & Rachel Q. Zhang, 2001. "Inventory Policies for Systems with Stochastic and Deterministic Demand," Operations Research, INFORMS, vol. 49(1), pages 157-162, February.
    • Handle: RePEc:inm:oropre:v:49:y:2001:i:1:p:157-162
    DOI: 10.1287/opre.49.1.157.11197
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    References listed on IDEAS

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    Cited by:

    1. Quan-Lin Li & Yi-Meng Li & Jing-Yu Ma & Heng-Li Liu, 2023. "A complete algebraic solution to the optimal dynamic rationing policy in the stock-rationing queue with two demand classes," Journal of Combinatorial Optimization, Springer, vol. 45(3), pages 1-54, April.
    2. Roni, Mohammad S. & Eksioglu, Sandra D. & Jin, Mingzhou & Mamun, Saleh, 2016. "A hybrid inventory policy with split delivery under regular and surge demand," International Journal of Production Economics, Elsevier, vol. 172(C), pages 126-136.
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    6. Z Shen & M Dessouky & F Ordonez, 2011. "Perishable inventory management system with a minimum volume constraint," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(12), pages 2063-2082, December.
    7. Siawsolit, Chokdee & Gaukler, Gary M., 2021. "Offsetting omnichannel grocery fulfillment cost through advance ordering of perishables," International Journal of Production Economics, Elsevier, vol. 239(C).
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    9. Katia C. Frank & Rachel Q. Zhang & Izak Duenyas, 2003. "Optimal Policies for Inventory Systems with Priority Demand Classes," Operations Research, INFORMS, vol. 51(6), pages 993-1002, December.
    10. Qing Li & Xiaoli Wu & Ki Ling Cheung, 2009. "Optimal Policies for Inventory Systems with Separate Delivery-Request and Order-Quantity Decisions," Operations Research, INFORMS, vol. 57(3), pages 626-636, June.
    11. Diwakar Gupta & Lei Wang, 2007. "Capacity Management for Contract Manufacturing," Operations Research, INFORMS, vol. 55(2), pages 367-377, April.
    12. Sandun C. Perera & Suresh P. Sethi, 2023. "A survey of stochastic inventory models with fixed costs: Optimality of (s, S) and (s, S)‐type policies—Continuous‐time case," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 154-169, January.
    13. Guillermo Gallego & Özalp Özer, 2001. "Integrating Replenishment Decisions with Advance Demand Information," Management Science, INFORMS, vol. 47(10), pages 1344-1360, October.
    14. Perla, Abhinav & Nikolaev, Alexander & Pasiliao, Eduardo, 2018. "Workforce management under social Link Based Corruption," Omega, Elsevier, vol. 78(C), pages 222-236.
    15. Ayanso, Anteneh & Diaby, Moustapha & Nair, Suresh K., 2006. "Inventory rationing via drop-shipping in Internet retailing: A sensitivity analysis," European Journal of Operational Research, Elsevier, vol. 171(1), pages 135-152, May.
    16. Roni, Mohammad S. & Jin, Mingzhou & Eksioglu, Sandra D., 2015. "A hybrid inventory management system responding to regular demand and surge demand," Omega, Elsevier, vol. 52(C), pages 190-200.
    17. 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.
    18. Xiaobo, Zhao & Xu, Deju & Zhang, Hanqin & He, Qi-Ming, 2007. "Modeling and analysis of a supply-assembly-store chain," European Journal of Operational Research, Elsevier, vol. 176(1), pages 275-294, January.
    19. Alfieri, Arianna & Pastore, Erica & Zotteri, Giulio, 2017. "Dynamic inventory rationing: How to allocate stock according to managerial priorities. An empirical study," International Journal of Production Economics, Elsevier, vol. 189(C), pages 14-29.
    20. Tan, Tarkan & Güllü, Refik & Erkip, Nesim, 2009. "Using imperfect advance demand information in ordering and rationing decisions," International Journal of Production Economics, Elsevier, vol. 121(2), pages 665-677, October.
    21. Basten, Rob J.I. & Ryan, Jennifer K., 2019. "The value of maintenance delay flexibility for improved spare parts inventory management," European Journal of Operational Research, Elsevier, vol. 278(2), pages 646-657.
    22. Jain, Apurva, 2007. "Value of capacity pooling in supply chains with heterogeneous customers," European Journal of Operational Research, Elsevier, vol. 177(1), pages 239-260, February.
    23. Tarim, S. Armagan & Kingsman, Brian G., 2004. "The stochastic dynamic production/inventory lot-sizing problem with service-level constraints," International Journal of Production Economics, Elsevier, vol. 88(1), pages 105-119, March.
    24. Vinayak Deshpande & Ananth V. Iyer & Richard Cho, 2006. "Efficient Supply Chain Management at the U.S. Coast Guard Using Part-Age Dependent Supply Replenishment Policies," Operations Research, INFORMS, vol. 54(6), pages 1028-1040, December.
    25. Barron, Yonit, 2023. "A stochastic card balance management problem with continuous and batch-type bilateral transactions," Operations Research Perspectives, Elsevier, vol. 10(C).

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