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Optimal Replenishment Strategy for Inventory Mechanism with Step-Shaped Demand

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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.

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Acknowledgements

We thank three anonymous referees for their careful reading of the paper and helpful comments and suggestions which greatly improved the presentation. This work is supported by the National Natural Science Foundation of China (Grant No.12071250).

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Authors and Affiliations

  1. School of Management Science, Qufu Normal University, Rizhao, Shandong, 276800, China

    Yiju Wang & Jingfu Huang

  2. Faculty of Business Administration Fredericton, University of New Brunswick, Fredericton, Canada

    Donglei Du

Authors
  1. Yiju Wang
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  2. Donglei Du
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  3. Jingfu Huang
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Correspondence to Yiju Wang.

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Communicated by Anita Schöbel.

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Wang, Y., Du, D. & Huang, J. Optimal Replenishment Strategy for Inventory Mechanism with Step-Shaped Demand. J Optim Theory Appl 190, 841–860 (2021). https://doi.org/10.1007/s10957-021-01909-9

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  • DOI: https://doi.org/10.1007/s10957-021-01909-9

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