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Basis Paths and a Polynomial Algorithm for the Multistage Production-Capacitated Lot-Sizing Problem

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  • Hark-Chin Hwang

    (School of Management, Kyung Hee University, Seoul 130-701, Republic of Korea)

  • Hyun-Soo Ahn

    (Ross School of Business, University of Michigan, Ann Arbor, Michigan 48109)

  • Philip Kaminsky

    (Department of Industrial Engineering and Operations Research, University of California, Berkeley, Berkeley, California 94720)

Abstract

We consider the multilevel lot-sizing problem with production capacities (MLSP-PC), in which production and transportation decisions are made for a serial supply chain with capacitated production and concave cost functions. Existing approaches to the multistage version of this problem are limited to nonspeculative cost functions---up to now, no algorithm for the multistage version of this model with general concave cost functions has been developed. In this paper, we develop the first polynomial algorithm for the MLSP-PC with general concave costs at all of the stages, and we introduce a novel approach to overcome the limitations of previous approaches. In contrast to traditional approaches to lot-sizing problems, in which the problem is decomposed by time periods and is analyzed unidirectionally in time, we solve the problem by introducing the concept of a basis path, which is characterized by time and stage. Our dynamic programming algorithm proceeds both forward and backward in time along this basis path, enabling us to solve the problem in polynomial time.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:61:y:2013:i:2:p:469-482
    DOI: 10.1287/opre.1120.1141
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Radha Mookerjee & Subodha Kumar & Vijay S. Mookerjee, 2017. "Optimizing Performance-Based Internet Advertisement Campaigns," Operations Research, INFORMS, vol. 65(1), pages 38-54, February.
    3. Giri, B.C. & Bardhan, Sudarshan, 2017. "Sub-supply chain coordination in a three-layer chain under demand uncertainty and random yield in production," International Journal of Production Economics, Elsevier, vol. 191(C), pages 66-73.
    4. Hadi Farhangi, 2021. "Multi-Echelon Supply Chains with Lead Times and Uncertain Demands," SN Operations Research Forum, Springer, vol. 2(3), pages 1-25, September.
    5. Ming Zhao & Minjiao Zhang, 2020. "Multiechelon Lot Sizing: New Complexities and Inequalities," Operations Research, INFORMS, vol. 68(2), pages 534-551, March.
    6. Radha Mookerjee & Subodha Kumar & Vijay S. Mookerjee, 2017. "Optimizing Performance-Based Internet Advertisement Campaigns," Operations Research, INFORMS, vol. 65(1), pages 38-54, February.
    7. Jing, Fuying & Chao, Xiangrui, 2022. "Forecast horizons for a two-echelon dynamic lot-sizing problem," Omega, Elsevier, vol. 110(C).
    8. Goisque, Guillaume & Rapine, Christophe, 2017. "An efficient algorithm for the 2-level capacitated lot-sizing problem with identical capacities at both levels," European Journal of Operational Research, Elsevier, vol. 261(3), pages 918-928.
    9. Bunn, Kevin A. & Ventura, José A., 2023. "A dynamic programming approach for the two-product capacitated lot-sizing problem with concave costs," European Journal of Operational Research, Elsevier, vol. 307(1), pages 116-129.
    10. Wu, Kan & Yuan, Xue-Ming, 2016. "Optimal production-inventory policy for an integrated multi-stage supply chain with time-varying demandAuthor-Name: Zhao, Shi Tao," European Journal of Operational Research, Elsevier, vol. 255(2), pages 364-379.
    11. Zhen Sun & Milind Dawande & Ganesh Janakiraman & Vijay Mookerjee, 2017. "Not Just a Fad: Optimal Sequencing in Mobile In-App Advertising," Information Systems Research, INFORMS, vol. 28(3), pages 511-528, September.
    12. Feng Xue & Qiumin Li, 2024. "Forecast Horizon of Dynamic Lot Sizing Problem with Perishable Inventory and Multiple Chain Stores: Shipping and Stockout Cost," Mathematics, MDPI, vol. 12(13), pages 1-17, July.

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