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Joint Pricing and Inventory Control with Fixed and Convex/Concave Variable Production Costs

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  • Peng Hu
  • Ye Lu
  • Miao Song

Abstract

This study considers a periodic‐review joint pricing and inventory control problem for a single product, where production incurs a fixed cost plus a convex or concave variable cost. Our objective is to maximize the expected discounted profit over the entire planning horizon. We fully characterize the optimal policy for the single‐period problem. As the optimal policy for the multi‐period problem is too complicated to be implemented in practice, we develop well‐structured heuristic policies, and establish worst‐case performance bounds on the profit gap between the heuristic policies and the optimal policies. Numerical studies show that our heuristic policies perform extremely well. To further reveal the structural properties of the optimal policies, we also introduce two new concepts named κ‐convexity and sym‐κ‐convexity, provide the associated preservation results, and then characterize the optimal policies.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:popmgt:v:28:y:2019:i:4:p:847-877
    DOI: 10.1111/poms.12950
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    References listed on IDEAS

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    Cited by:

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    2. Hao Yuan & Qi Luo & Cong Shi, 2021. "Marrying Stochastic Gradient Descent with Bandits: Learning Algorithms for Inventory Systems with Fixed Costs," Management Science, INFORMS, vol. 67(10), pages 6089-6115, October.
    3. Ling Zhao & Jun Liu & Minghua Xiong & Anquan Zou, 2022. "Dual-Channel Retailer’s Multi-Period Inventory and Pricing Policy with the Quantity-Sales Mode," Sustainability, MDPI, vol. 14(18), pages 1-18, September.
    4. Boxiao Chen & David Simchi-Levi & Yining Wang & Yuan Zhou, 2022. "Dynamic Pricing and Inventory Control with Fixed Ordering Cost and Incomplete Demand Information," Management Science, INFORMS, vol. 68(8), pages 5684-5703, August.
    5. Ling Zhao & Anquan Zou & Pin Zhou, 2023. "E‐retailer's dynamic inventory and pricing policy with price‐protection services," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 44(1), pages 490-501, January.
    6. Gurkan, M. Edib & Tunc, Huseyin & Tarim, S. Armagan, 2022. "The joint stochastic lot sizing and pricing problem," Omega, Elsevier, vol. 108(C).
    7. Li, Mengmeng & Mizuno, Shinji, 2022. "Dynamic pricing and inventory management of a dual-channel supply chain under different power structures," European Journal of Operational Research, Elsevier, vol. 303(1), pages 273-285.
    8. Xiting Gong & Youhua (Frank) Chen & Quan Yuan, 2022. "Coordinating Inventory and Pricing Decisions Under Total Minimum Commitment Contracts," Production and Operations Management, Production and Operations Management Society, vol. 31(2), pages 511-528, February.
    9. Bai, Tian & Wu, Meng & Zhu, Stuart X., 2019. "Pricing and ordering by a loss averse newsvendor with reference dependence," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 131(C), pages 343-365.
    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.

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