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Inventory allocation with full downward substitution and monotone cost differences

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  • Tseytlin, Yulia
  • Heese, H. Sebastian

Abstract

We study a single-period multi-product inventory allocation problem with full downward substitution and monotone cost differences. The cost structure with monotone differences is more general than the additive cost structure usually assumed in literature. Using the notion of Monge sequences, we identify conditions under which the problem can be solved efficiently using greedy allocation. For problems that do not meet these conditions, we develop an efficient algorithm that solves the problem to optimality. For this specific problem, our algorithm has substantially lower computational complexity than existing efficient algorithms for the more general transportation problem; we numerically confirm this superior computational efficiency and illustrate the importance of using efficient algorithms at the allocation stage of the inventory management problem.

Suggested Citation

  • Tseytlin, Yulia & Heese, H. Sebastian, 2023. "Inventory allocation with full downward substitution and monotone cost differences," European Journal of Operational Research, Elsevier, vol. 307(1), pages 130-139.
    • Handle: RePEc:eee:ejores:v:307:y:2023:i:1:p:130-139
    DOI: 10.1016/j.ejor.2022.08.027
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    References listed on IDEAS

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    1. Arthur Hsu & Yehuda Bassok, 1999. "Random Yield and Random Demand in a Production System with Downward Substitution," Operations Research, INFORMS, vol. 47(2), pages 277-290, April.
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    6. Freeman, Nickolas K. & Narayanan, Arunachalam & Keskin, Burcu B., 2021. "Optimal use of downward substitution in a manufacturing operation subject to uncertainty," Omega, Elsevier, vol. 103(C).
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