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Algorithms for the two-stage production-capacitated lot-sizing problem

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  • Hark-Chin Hwang

    (Kyung Hee University)

  • Hyun-Soo Ahn

    (University of Michigan)

  • Philip Kaminsky

    (University of California)

Abstract

We model the two-stage production-capacitated lot-sizing problem as a concave minimum cost network flow problem and characterize the possible patterns of flow between successive periods in which transportation occurs. We demonstrate that production and transportation decisions can be made based only on the local state of transportation patterns between successive transportation periods. Utilizing this observation together with the insight that it is not necessary to consider transportation decisions between transportation periods, we provide a novel improved $$O(T^6)$$ O ( T 6 ) algorithm (where T is the length of the planning horizon). We extend this approach to special cases, and develop an $$O(T^5)$$ O ( T 5 ) algorithm for the case with non-speculative costs, and an $$O(T^4)$$ O ( T 4 ) algorithm for the case with linear costs.

Suggested Citation

  • Hark-Chin Hwang & Hyun-Soo Ahn & Philip Kaminsky, 2016. "Algorithms for the two-stage production-capacitated lot-sizing problem," Journal of Global Optimization, Springer, vol. 65(4), pages 777-799, August.
    • Handle: RePEc:spr:jglopt:v:65:y:2016:i:4:d:10.1007_s10898-015-0392-2
    DOI: 10.1007/s10898-015-0392-2
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    References listed on IDEAS

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    1. Michael Florian & Morton Klein, 1971. "Deterministic Production Planning with Concave Costs and Capacity Constraints," Management Science, INFORMS, vol. 18(1), pages 12-20, September.
    2. 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.
    3. Hark-Chin Hwang & Hyun-Soo Ahn & Philip Kaminsky, 2013. "Basis Paths and a Polynomial Algorithm for the Multistage Production-Capacitated Lot-Sizing Problem," Operations Research, INFORMS, vol. 61(2), pages 469-482, April.
    4. VAN VYVE, Mathieu & WOLSEY, Laurence A & YAMAN, Hande, 2014. "Relaxations for two-level multi-item lot-sizing problems," LIDAM Reprints CORE 2611, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Stan van Hoesel & H. Edwin Romeijn & Dolores Romero Morales & Albert P. M. Wagelmans, 2005. "Integrated Lot Sizing in Serial Supply Chains with Production Capacities," Management Science, INFORMS, vol. 51(11), pages 1706-1719, November.
    6. MELO, Rafael A. & WOLSEY, Laurence A., 2010. "Uncapacitated two-level lot-sizing," LIDAM Reprints CORE 2235, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Rowshannahad, Mehdi & Absi, Nabil & Dauzère-Pérès, Stéphane & Cassini, Bernard, 2018. "Multi-item bi-level supply chain planning with multiple remanufacturing of reusable by-products," International Journal of Production Economics, Elsevier, vol. 198(C), pages 25-37.
    2. Jing, Fuying & Chao, Xiangrui, 2022. "Forecast horizons for a two-echelon dynamic lot-sizing problem," Omega, Elsevier, vol. 110(C).
    3. Hwang, Hark-Chin & Kang, Jangha, 2020. "The two-level lot-sizing problem with outbound shipment," Omega, Elsevier, vol. 90(C).

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