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Optimal dynamic pricing and replenishment policy for perishable items with inventory-level-dependent demand

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  • Lihao Lu
  • Jianxiong Zhang
  • Wansheng Tang

Abstract

An inventory system for perishable items with limited replenishment capacity is introduced in this paper. The demand rate depends on the stock quantity displayed in the store as well as the sales price. With the goal to realise profit maximisation, an optimisation problem is addressed to seek for the optimal joint dynamic pricing and replenishment policy which is obtained by solving the optimisation problem with Pontryagin’s maximum principle. A joint mixed policy, in which the sales price is a static decision variable and the replenishment rate remains to be a dynamic decision variable, is presented to compare with the joint dynamic policy. Numerical results demonstrate the advantages of the joint dynamic one, and further show the effects of different system parameters on the optimal joint dynamic policy and the maximal total profit.

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  • Lihao Lu & Jianxiong Zhang & Wansheng Tang, 2016. "Optimal dynamic pricing and replenishment policy for perishable items with inventory-level-dependent demand," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(6), pages 1480-1494, April.
    • Handle: RePEc:taf:tsysxx:v:47:y:2016:i:6:p:1480-1494
    DOI: 10.1080/00207721.2014.938784
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    2. Chenavaz, Régis & Paraschiv, Corina, 2018. "Dynamic pricing for inventories with reference price effects," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 12, pages 1-16.
    3. Hongliang Li & Jun Liu & Jiangjie Qiu & Yunsen Zhou & Xu Zhang & Yuming Wang & Wei Guo, 2024. "ARIMA-Driven Vegetable Pricing and Restocking Strategy for Dual Optimization of Freshness and Profitability in Supermarket Perishables," Sustainability, MDPI, vol. 16(10), pages 1-26, May.
    4. Umakanta Mishra & Leopoldo Eduardo Cárdenas-Barrón & Sunil Tiwari & Ali Akbar Shaikh & Gerardo Treviño-Garza, 2017. "An inventory model under price and stock dependent demand for controllable deterioration rate with shortages and preservation technology investment," Annals of Operations Research, Springer, vol. 254(1), pages 165-190, July.
    5. Yongming Zhu & Lanxiao Niu & Zheyun Zhao & Jing Li, 2022. "The Tripartite Evolution Game of Environmental Governance under the Intervention of Central Government," Sustainability, MDPI, vol. 14(10), pages 1-19, May.
    6. Jing Lu & Jianxiong Zhang & Fuxiao Lu & Wansheng Tang, 2020. "Optimal pricing on an age-specific inventory system for perishable items," Operational Research, Springer, vol. 20(2), pages 605-625, June.
    7. Anton, Ramona & Chenavaz, Régis Y. & Paraschiv, Corina, 2023. "Dynamic pricing, reference price, and price-quality relationship," Journal of Economic Dynamics and Control, Elsevier, vol. 146(C).
    8. Chen, Jing & Dong, Ming & Rong, Ying & Yang, Liang, 2018. "Dynamic pricing for deteriorating products with menu cost," Omega, Elsevier, vol. 75(C), pages 13-26.
    9. R. Schlosser, 2021. "Scalable relaxation techniques to solve stochastic dynamic multi-product pricing problems with substitution effects," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 20(1), pages 54-65, February.
    10. Rabbani, Masoud & Pourmohammad Zia, Nadia & Rafiei, Hamed, 2016. "Joint optimal dynamic pricing and replenishment policies for items with simultaneous quality and physical quantity deterioration," Applied Mathematics and Computation, Elsevier, vol. 287, pages 149-160.
    11. Sun, Zhongmiao & Xu, Qi & Liu, Jinrong, 2021. "Pricing and replenishment decisions for seasonal and nonseasonal products in a shared supply chain," International Journal of Production Economics, Elsevier, vol. 233(C).
    12. Yan-Kwang Chen & Fei-Rung Chiu & Yu-Cheng Chang, 2019. "Implementing Green Supply Chain Management for Online Pharmacies through a VADD Inventory Model," IJERPH, MDPI, vol. 16(22), pages 1-18, November.

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