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Optimal Control Policy for Stochastic Inventory Systems with Markovian Discount Opportunities

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  • Yu-Shen Zheng

    (University of Pennsylvania, Philadelphia, Pennsylvania)

Abstract

In this paper, we study a single-item continuous-review inventory system with Poisson demand. In addition to the standard cost structure of a fixed setup cost and a quasiconvex expected inventory holding and shortage cost, special opportunities for placing orders at a discounted setup cost occur according to a Poisson process that is independent of the demand process. This model has been studied as a subproblem of multi-item/location inventory systems where there are economies-of-scale in joint replenishment. For the single-item model, the literature proposes the ( s , c , S ) policy, under which an order is placed to increase the inventory position to S either when the inventory position drops to s , or when the inventory position is at or below c and a discount opportunity occurs. We prove that the ( s , c , S ) policy is optimal for the model, develop an efficient algorithm for computing optimal control parameters s *, c *, S*, and carry out a parametric analysis showing the effects of changes in problem parameters on the optimal control parameters and the minimum cost.

Suggested Citation

  • Yu-Shen Zheng, 1994. "Optimal Control Policy for Stochastic Inventory Systems with Markovian Discount Opportunities," Operations Research, INFORMS, vol. 42(4), pages 721-738, August.
    • Handle: RePEc:inm:oropre:v:42:y:1994:i:4:p:721-738
    DOI: 10.1287/opre.42.4.721
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    Cited by:

    1. Hong-Qiao Chen & Xiao-Song Ding & Ji-Hong Zhang & Hua-Yi Li, 2020. "Optimal Production-Inventory Policy for a Periodic-Review Energy Buy-Back System over an Infinite Planning Horizon," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(02), pages 1-32, March.
    2. Xiuli Chao & Frank Y. Chen, 2005. "An Optimal Production and Shutdown Strategy when a Supplier Offers an Incentive Program," Manufacturing & Service Operations Management, INFORMS, vol. 7(2), pages 130-143, March.
    3. Schultz, Helle & Johansen, Soren Glud, 1999. "Can-order policies for coordinated inventory replenishment with Erlang distributed times between ordering," European Journal of Operational Research, Elsevier, vol. 113(1), pages 30-41, February.
    4. Eric Logan Huggins & Tava Lennon Olsen, 2010. "Inventory Control with Generalized Expediting," Operations Research, INFORMS, vol. 58(5), pages 1414-1426, October.
    5. Peter Berling & Victor Martínez-de-Albéniz, 2011. "Optimal Inventory Policies when Purchase Price and Demand Are Stochastic," Operations Research, INFORMS, vol. 59(1), pages 109-124, February.
    6. Y. Feng & J. Sun, 2001. "Computing the Optimal Replenishment Policy for Inventory Systems with Random Discount Opportunities," Operations Research, INFORMS, vol. 49(5), pages 790-795, October.
    7. Stefanny Ramirez & Laurence H. Brandenburg & Dario Bauso, 2023. "Coordinated Replenishment Game and Learning Under Time Dependency and Uncertainty of the Parameters," Dynamic Games and Applications, Springer, vol. 13(1), pages 326-352, March.
    8. Greenwood, Allen G. & Rees, Loren Paul & Siochi, Fernando C., 1998. "An investigation of the behavior of simulation response surfaces," European Journal of Operational Research, Elsevier, vol. 110(2), pages 282-313, October.
    9. Serguei Netessine & Sergei Savin & Wenqiang Xiao, 2006. "Revenue Management Through Dynamic Cross Selling in E-Commerce Retailing," Operations Research, INFORMS, vol. 54(5), pages 893-913, October.
    10. 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.
    11. S G Johansen & P Melchiors, 2003. "Can-order policy for the periodic-review joint replenishment problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(3), pages 283-290, March.
    12. Melchiors, Philip, 2002. "Calculating can-order policies for the joint replenishment problem by the compensation approach," European Journal of Operational Research, Elsevier, vol. 141(3), pages 587-595, September.
    13. Creemers, Stefan & Boute, Robert, 2022. "The joint replenishment problem: Optimal policy and exact evaluation method," European Journal of Operational Research, Elsevier, vol. 302(3), pages 1175-1188.
    14. Banu Yüksel Özkaya & Ülkü Gürler & Emre Berk, 2006. "The stochastic joint replenishment problem: A new policy, analysis, and insights," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(6), pages 525-546, September.
    15. Berling, Peter, 2008. "The capital cost of holding inventory with stochastically mean-reverting purchase price," European Journal of Operational Research, Elsevier, vol. 186(2), pages 620-636, April.
    16. Shaposhnik, Yaron & Herer, Yale T. & Naseraldin, Hussein, 2015. "Optimal ordering for a probabilistic one-time discount," European Journal of Operational Research, Elsevier, vol. 244(3), pages 803-814.
    17. De Moor, Bram J. & Creemers, Stefan & Boute, Robert N., 2023. "Breaking truck dominance in supply chains: Proactive freight consolidation and modal split transport," International Journal of Production Economics, Elsevier, vol. 257(C).
    18. Chakrabortty, Susovan & Pal, Madhumangal & Nayak, Prasun Kumar, 2013. "Intuitionistic fuzzy optimization technique for Pareto optimal solution of manufacturing inventory models with shortages," European Journal of Operational Research, Elsevier, vol. 228(2), pages 381-387.
    19. Youyi Feng & Zhan Pang, 2010. "Dynamic coordination of production planning and sales admission control in the presence of a spot market," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(4), pages 309-329, June.
    20. Perera, Sandun & Janakiraman, Ganesh & Niu, Shun-Chen, 2017. "Optimality of (s, S) policies in EOQ models with general cost structures," International Journal of Production Economics, Elsevier, vol. 187(C), pages 216-228.

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