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On dynamic lot sizing with bounded inventory for a perishable product

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  • Fan, Jie
  • Ou, Jinwen

Abstract

It is well-known in the single-item dynamic lot-sizing (DLS) literature that the DLS problem for a perishable product (DLS-P) can be solved in polynomial time (see, e.g., Hsu [1]), and that the DLS problem with bounded inventory (DLS-BI) is also polynomially solvable (see, e.g., Love [2]). However, the computational complexity of the DLS problem with bounded inventory for a perishable product (DLS-BI-P) remains to be open. In this note, we answer this open problem and show that DLS-BI-P is NP-hard. Recently, Jing and Mu [20] presented an exact algorithm for an important extension of DLS-BI-P and claimed that the proposed algorithm is polynomial, while Jing and Chao [19] also developed an exact algorithm for another important extension of DLS-BI-P. In this note, we also point out that both of these two exact algorithms are exponential, and that the algorithm by Jing and Chao [19] may not generate an optimal solution in general.

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  • Fan, Jie & Ou, Jinwen, 2023. "On dynamic lot sizing with bounded inventory for a perishable product," Omega, Elsevier, vol. 119(C).
    • Handle: RePEc:eee:jomega:v:119:y:2023:i:c:s0305048323000592
    DOI: 10.1016/j.omega.2023.102895
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    References listed on IDEAS

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    1. Harvey M. Wagner & Thomson M. Whitin, 1958. "Dynamic Version of the Economic Lot Size Model," Management Science, INFORMS, vol. 5(1), pages 89-96, October.
    2. Liu, X. & Tu, Yl., 2008. "Production planning with limited inventory capacity and allowed stockout," International Journal of Production Economics, Elsevier, vol. 111(1), pages 180-191, January.
    3. Hark-Chin Hwang & Wilco van den Heuvel & Albert Wagelmans, 2013. "The economic lot-sizing problem with lost sales and bounded inventory," IISE Transactions, Taylor & Francis Journals, vol. 45(8), pages 912-924.
    4. Gökçe Palak & Sandra Duni Ekşioğlu & Joseph Geunes, 2018. "Heuristic algorithms for inventory replenishment with perishable products and multiple transportation modes," IISE Transactions, Taylor & Francis Journals, vol. 50(4), pages 345-365, April.
    5. Alvarez, Aldair & Miranda, Pedro & Rohmer, S.U.K., 2022. "Production routing for perishable products," Omega, Elsevier, vol. 111(C).
    6. Jing, Fuying & Chao, Xiangrui, 2021. "A dynamic lot size model with perishable inventory and stockout," Omega, Elsevier, vol. 103(C).
    7. Mahmutoğulları, Özlem & Yaman, Hande, 2023. "A Branch-and-Cut Algorithm for the Inventory Routing Problem with Product Substitution," Omega, Elsevier, vol. 115(C).
    8. Stephen F. Love, 1973. "Bounded Production and Inventory Models with Piecewise Concave Costs," Management Science, INFORMS, vol. 20(3), pages 313-318, November.
    9. Vernon Ning Hsu, 2000. "Dynamic Economic Lot Size Model with Perishable Inventory," Management Science, INFORMS, vol. 46(8), pages 1159-1169, August.
    10. Jing, Fuying & Chao, Xiangrui, 2022. "Forecast horizons for a two-echelon dynamic lot-sizing problem," Omega, Elsevier, vol. 110(C).
    11. M. Florian & J. K. Lenstra & A. H. G. Rinnooy Kan, 1980. "Deterministic Production Planning: Algorithms and Complexity," Management Science, INFORMS, vol. 26(7), pages 669-679, July.
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    Cited by:

    1. Ding, Jingying & Peng, Zhenkang, 2024. "Heuristics for perishable inventory systems under mixture issuance policies," Omega, Elsevier, vol. 126(C).
    2. Li, Yuchen & Liu, Ming & Saldanha-da-Gama, Francisco & Yang, Zaoli, 2024. "Risk-averse two-stage stochastic programming for assembly line reconfiguration with dynamic lot sizes," Omega, Elsevier, vol. 127(C).

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