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Two-phase algorithm for the lot-sizing problem with backlogging for stepwise transportation cost without speculative motives

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  • Hwang, Hark-Chin
  • Kang, Jangha

Abstract

In this paper we consider the lot-sizing problem with backlogging under stepwise transportation costs. Inventory is carried over or backlogged in a trade-off with costs for production setup and transportation. Specifically, inventory is the main source for consolidating demand over periods to increase the chance of Full-Truck-Load (FTL) delivery. We assume that there are no speculative motives in production, which yields an important property for Less-Than-Load (LTL) delivery that the LTL cargo does not contain any unit carried over from the previous period or backlogged for the next period. We solve the problem in two phases. In phase one, we use a geometric technique to preprocess necessary functional values for FTL delivery. In phase two, we provide a residual zoning algorithm, involving not only FTL delivery but also LTL delivery, to obtain an optimal solution. The computational complexity is shown to be O(T2logT) where T is the length of the planning horizon.

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  • Hwang, Hark-Chin & Kang, Jangha, 2016. "Two-phase algorithm for the lot-sizing problem with backlogging for stepwise transportation cost without speculative motives," Omega, Elsevier, vol. 59(PB), pages 238-250.
    • Handle: RePEc:eee:jomega:v:59:y:2016:i:pb:p:238-250
    DOI: 10.1016/j.omega.2015.06.012
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    1. Xie, Fanrong & Butt, Muhammad Munir & Li, Zuoan & Zhu, Linzhi, 2017. "An upper bound on the minimal total cost of the transportation problem with varying demands and supplies," Omega, Elsevier, vol. 68(C), pages 105-118.
    2. Hwang, Hark-Chin & Kang, Jangha, 2021. "An improved algorithm for the lot-sizing problem with outbound shipment," Omega, Elsevier, vol. 100(C).
    3. Ou, Jinwen & Feng, Jiejian, 2019. "Production lot-sizing with dynamic capacity adjustment," European Journal of Operational Research, Elsevier, vol. 272(1), pages 261-269.
    4. Zhang, Guoqing & Nishi, Tatsushi & Turner, Sarina D.O. & Oga, Keisuke & Li, Xindan, 2017. "An integrated strategy for a production planning and warehouse layout problem: Modeling and solution approaches," Omega, Elsevier, vol. 68(C), pages 85-94.
    5. Hwang, Hark-Chin & Kang, Jangha, 2020. "The two-level lot-sizing problem with outbound shipment," Omega, Elsevier, vol. 90(C).

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