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Optimal Replenishment Strategy for Inventory Mechanism with Step-Shaped Demand

Author

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  • Yiju Wang

    (Qufu Normal University)

  • Donglei Du

    (University of New Brunswick)

  • Jingfu Huang

    (Qufu Normal University)

Abstract

This paper extends the classical economic order quantity inventory model to that the planning horizon consists of two stages—a finite planning horizon and an infinite planning horizon, the demand in each stage is deterministic and stable but differs. The main goal is to find the optimal replenishment and stocking policy in each stage in order to keep the total relevant cost as low as possible, which is formulated as a mixed integer optimization problem. Using the alternating minimization method and the optimization theory, we develop a closed-form solution to the optimal inventory model and provide an optimal replenishment strategy to the retailer. Some numerical experiments are made to test the validity of the model and the effect of the involved parameters to the replenishment policy. A numerical example shows a counterintuitive fact that the economic ordering quantity may not necessarily be optimal for this inventory mechanism.

Suggested Citation

  • Yiju Wang & Donglei Du & Jingfu Huang, 2021. "Optimal Replenishment Strategy for Inventory Mechanism with Step-Shaped Demand," Journal of Optimization Theory and Applications, Springer, vol. 190(3), pages 841-860, September.
    • Handle: RePEc:spr:joptap:v:190:y:2021:i:3:d:10.1007_s10957-021-01909-9
    DOI: 10.1007/s10957-021-01909-9
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    References listed on IDEAS

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    1. Tiwari, Sunil & Cárdenas-Barrón, Leopoldo Eduardo & Goh, Mark & Shaikh, Ali Akbar, 2018. "Joint pricing and inventory model for deteriorating items with expiration dates and partial backlogging under two-level partial trade credits in supply chain," International Journal of Production Economics, Elsevier, vol. 200(C), pages 16-36.
    2. Wee, Hui-Ming, 1999. "Deteriorating inventory model with quantity discount, pricing and partial backordering," International Journal of Production Economics, Elsevier, vol. 59(1-3), pages 511-518, March.
    3. Arcelus, F. J. & Shah, Nita H. & Srinivasan, G., 2003. "Retailer's pricing, credit and inventory policies for deteriorating items in response to temporary price/credit incentives," International Journal of Production Economics, Elsevier, vol. 81(1), pages 153-162, January.
    4. Onur Kaya & Sajjad Rahimi Ghahroodi, 2018. "Inventory control and pricing for perishable products under age and price dependent stochastic demand," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(1), pages 1-35, August.
    5. Tiwari, Sunil & Jaggi, Chandra K. & Gupta, Mamta & Cárdenas-Barrón, Leopoldo Eduardo, 2018. "Optimal pricing and lot-sizing policy for supply chain system with deteriorating items under limited storage capacity," International Journal of Production Economics, Elsevier, vol. 200(C), pages 278-290.
    6. Xiaoming Li, 2015. "Optimal Policies and Bounds for Stochastic Inventory Systems with Lost Sales," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 359-375, January.
    7. Dobson, Gregory & Pinker, Edieal J. & Yildiz, Ozlem, 2017. "An EOQ model for perishable goods with age-dependent demand rate," European Journal of Operational Research, Elsevier, vol. 257(1), pages 84-88.
    8. 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.
    9. P. L. Abad, 1996. "Optimal Pricing and Lot-Sizing Under Conditions of Perishability and Partial Backordering," Management Science, INFORMS, vol. 42(8), pages 1093-1104, August.
    10. Bakker, Monique & Riezebos, Jan & Teunter, Ruud H., 2012. "Review of inventory systems with deterioration since 2001," European Journal of Operational Research, Elsevier, vol. 221(2), pages 275-284.
    11. Khanra, S. & Mandal, Buddhadev & Sarkar, Biswajit, 2013. "An inventory model with time dependent demand and shortages under trade credit policy," Economic Modelling, Elsevier, vol. 35(C), pages 349-355.
    12. Avinadav, Tal & Herbon, Avi & Spiegel, Uriel, 2013. "Optimal inventory policy for a perishable item with demand function sensitive to price and time," International Journal of Production Economics, Elsevier, vol. 144(2), pages 497-506.
    13. Yang, Hui-Ling & Teng, Jinn-Tsair & Chern, Maw-Sheng, 2002. "A forward recursive algorithm for inventory lot-size models with power-form demand and shortages," European Journal of Operational Research, Elsevier, vol. 137(2), pages 394-400, March.
    14. Dye, Chung-Yuan, 2007. "Joint pricing and ordering policy for a deteriorating inventory with partial backlogging," Omega, Elsevier, vol. 35(2), pages 184-189, April.
    15. 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.
    16. Lakdere Benkherouf & Konstantina Skouri & Ioannis Konstantaras, 2016. "Optimal Control of Production, Remanufacturing and Refurbishing Activities in a Finite Planning Horizon Inventory System," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 677-698, February.
    17. Maher A. N. Agi & Hardik N. Soni, 2020. "Joint pricing and inventory decisions for perishable products with age-, stock-, and price-dependent demand rate," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 71(1), pages 85-99, January.
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