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On the decomposition property for a dynamic inventory rationing problem with multiple demand classes and backorder

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  • Bao, Lina
  • Liu, Zhiying
  • Yu, Yimin
  • Zhang, Wei

Abstract

In this paper, we study a dynamic inventory rationing problem of a single item with multiple demand classes and backorder. Demand classes are differentiated by their unit backlogging costs. The corresponding dynamic programming problem is multidimensional and computationally challenging. With a novel state transformation, we find that the optimal policy can be described by a nested base stock policy. In particular, we can decompose the value function as the sum of single-variable convex functions. This property breaks the curse of dimensionality and significantly reduces computational effort in computing optimal policies. Our approach allows us to extend the results to systems with ordering, exogenous supply, priority upgrading.

Suggested Citation

  • Bao, Lina & Liu, Zhiying & Yu, Yimin & Zhang, Wei, 2018. "On the decomposition property for a dynamic inventory rationing problem with multiple demand classes and backorder," European Journal of Operational Research, Elsevier, vol. 265(1), pages 99-106.
    • Handle: RePEc:eee:ejores:v:265:y:2018:i:1:p:99-106
    DOI: 10.1016/j.ejor.2017.07.021
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    Cited by:

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    4. Baishakhi Ganguly & Bikash Koli Dey & Sarla Pareek & Biswajit Sarkar, 2023. "Cost-Effective Imperfect Production-Inventory System under Variable Production Rate and Remanufacturing," Mathematics, MDPI, vol. 11(15), pages 1-24, August.
    5. Wang, Yi & Zhang, Sheng Hao, 2021. "Optimal production and inventory rationing policies with selective-information sharing and two demand classes," European Journal of Operational Research, Elsevier, vol. 288(2), pages 394-407.
    6. Saha, Kushal & Bhattacharya, Subir, 2021. "‘Buy online and pick up in-store’: Implications for the store inventory," European Journal of Operational Research, Elsevier, vol. 294(3), pages 906-921.
    7. ElHafsi, Mohsen & Fang, Jianxin & Hamouda, Essia, 2021. "Optimal production and inventory control of multi-class mixed backorder and lost sales demand class models," European Journal of Operational Research, Elsevier, vol. 291(1), pages 147-161.

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