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Supply and Demand Functions in Inventory Models

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  • Qi Feng

    (Krannert School of Management, Purdue University, West Lafayette, Indiana 47907)

  • J. George Shanthikumar

    (Krannert School of Management, Purdue University, West Lafayette, Indiana 47907)

Abstract

The central issue in supply chain management is to match supply with demand, and the heart of a planning model is the modeling of supply and demand functions. To allow for analytical tractability, the existing literature often assumes almost surely linear supply and demand functions, which greatly limits the applicability of the models. The goal of this paper is to provide a unified approach to analyze general random supply and demand functions. By transforming the problem into one defined on a higher dimension, we show that many of the seemingly highly nonlinear supply and demand functions (in the almost sure sense) are linear in the stochastic sense. With this new notion of linearity, called stochastic linearity in midpoint , our ability to analyze supply chain problems is much enhanced. We are able to prove the concavity of the profit function in the transformed supply and demand decisions for a general class of supply and demand functions that include, but are not restricted to, the ones studied in the existing literature. Thus, many of the challenging problems now become tractable. Moreover, we characterize a set of easy-to-verify conditions for stochastic linearity in midpoint. The online appendix is available at https://doi.org/10.1287/opre.2017.1648 .

Suggested Citation

  • Qi Feng & J. George Shanthikumar, 2018. "Supply and Demand Functions in Inventory Models," Operations Research, INFORMS, vol. 66(1), pages 77-91, 1-2.
    • Handle: RePEc:inm:oropre:v:66:y:2018:i:1:p:77-91
    DOI: 10.1287/opre.2017.1648
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    References listed on IDEAS

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    2. Qi Feng & Zhongjie Ma & Zhaofang Mao & J. George Shanthikumar, 2021. "Multi‐Stage Supply Chain with Production Uncertainty," Production and Operations Management, Production and Operations Management Society, vol. 30(4), pages 921-940, April.
    3. Li, Yanhai & Ou, Jinwen, 2022. "Replenishment decisions for complementary components with supply capacity uncertainty under the CVaR criterion," European Journal of Operational Research, Elsevier, vol. 297(3), pages 904-916.
    4. Weidong Chen & Cong Shi & Izak Duenyas, 2020. "Optimal Learning Algorithms for Stochastic Inventory Systems with Random Capacities," Production and Operations Management, Production and Operations Management Society, vol. 29(7), pages 1624-1649, July.
    5. Qi Feng & Sirong Luo & J. George Shanthikumar, 2020. "Integrating Dynamic Pricing with Inventory Decisions Under Lost Sales," Management Science, INFORMS, vol. 66(5), pages 2232-2247, May.
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    8. Hanzhang Qin & David Simchi-Levi & Li Wang, 2022. "Data-Driven Approximation Schemes for Joint Pricing and Inventory Control Models," Management Science, INFORMS, vol. 68(9), pages 6591-6609, September.
    9. Gurkan, M. Edib & Tunc, Huseyin & Tarim, S. Armagan, 2022. "The joint stochastic lot sizing and pricing problem," Omega, Elsevier, vol. 108(C).
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    11. Qi Feng & J. George Shanthikumar, 2022. "Applications of Stochastic Orders and Stochastic Functions in Inventory and Pricing Problems," Production and Operations Management, Production and Operations Management Society, vol. 31(4), pages 1433-1453, April.

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