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The Optimality of Generalized (s, S) Policies under Uniform Demand Densities

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  • Evan L. Porteus

    (Stanford University)

Abstract

This note considers the single product, single echelon, periodic review, stochastic, dynamic inventory model discussed recently [Porteus, E. L. 1971. On the optimality of generalized (s, S) policies. Management Sci. 17 411-426.], where the ordering cost function is concave increasing, rather than simply linear with a setup cost. We show that a generalized (s, S) policy will be optimal in a finite horizon problem when the probability densities of demand are uniform or convolutions of a finite number of uniform and/or one-sided Pólya densities. Such densities are not necessarily one-sided Pólya densities, for which this result has already been established. To prove the result here we need only show, roughly, that a certain subclass of the quasi-K-convex functions is closed under convolution with uniform densities which describe nonnegative random variables.

Suggested Citation

  • Evan L. Porteus, 1972. "The Optimality of Generalized (s, S) Policies under Uniform Demand Densities," Management Science, INFORMS, vol. 18(11), pages 644-646, July.
    • Handle: RePEc:inm:ormnsc:v:18:y:1972:i:11:p:644-646
    DOI: 10.1287/mnsc.18.11.644
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    Cited by:

    1. Peng Hu & Ye Lu & Miao Song, 2019. "Joint Pricing and Inventory Control with Fixed and Convex/Concave Variable Production Costs," Production and Operations Management, Production and Operations Management Society, vol. 28(4), pages 847-877, April.
    2. Ozgun Caliskan-Demirag & Youhua Chen & Yi Yang, 2013. "Production-inventory control policy under warm/cold state-dependent fixed costs and stochastic demand: partial characterization and heuristics," Annals of Operations Research, Springer, vol. 208(1), pages 531-556, September.
    3. Liqing Zhang & Sıla Çetinkaya, 2017. "Stochastic Dynamic Inventory Problem Under Explicit Inbound Transportation Cost and Capacity," Operations Research, INFORMS, vol. 65(5), pages 1267-1274, October.
    4. Edward J. Fox & Richard Metters & John Semple, 2006. "Optimal Inventory Policy with Two Suppliers," Operations Research, INFORMS, vol. 54(2), pages 389-393, April.
    5. Gerchak, Yigal & Hassini, Elkafi & Ray, Saibal, 2002. "Capacity selection under uncertainty with ratio objectives," European Journal of Operational Research, Elsevier, vol. 143(1), pages 138-147, November.
    6. Hong Chen & Zhan Zhang, 2014. "Technical Note—Joint Inventory and Pricing Control with General Additive Demand," Operations Research, INFORMS, vol. 62(6), pages 1335-1343, December.
    7. Saif Benjaafar & David Chen & Yimin Yu, 2018. "Optimal policies for inventory systems with concave ordering costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(4), pages 291-302, June.
    8. Jianjun Xu & Mustafa Cagri Gürbüz & Youyi Feng & Shaoxiang Chen, 2020. "Optimal Spot Trading Integrated with Quantity Flexibility Contracts," Production and Operations Management, Production and Operations Management Society, vol. 29(6), pages 1532-1549, June.
    9. Shaolong Tang & Stella Cho & Jacqueline Wenjie Wang & Hong Yan, 2018. "The newsvendor model revisited: the impacts of high unit holding costs on the accuracy of the classic model," Frontiers of Business Research in China, Springer, vol. 12(1), pages 1-14, December.
    10. Shuangchi He & Dacheng Yao & Hanqin Zhang, 2017. "Optimal Ordering Policy for Inventory Systems with Quantity-Dependent Setup Costs," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 979-1006, November.

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