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An efficient MIP model for the capacitated lot-sizing and scheduling problem with sequence-dependent setups

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  • Kovcs, Andrs
  • Brown, Kenneth N.
  • Tarim, S. Armagan

Abstract

This paper presents a novel mathematical programming approach to the single-machine capacitated lot-sizing and scheduling problem with sequence-dependent setup times and setup costs. The approach is partly based on the earlier work of Haase and Kimms [2000. Lot sizing and scheduling with sequence-dependent setup costs and times and efficient rescheduling opportunities. International Journal of Production Economics 66(2), 159-169] which determines during pre-processing all item sequences that can appear in given time periods in optimal solutions. We introduce a new mixed-integer programming model in which binary variables indicate whether individual items are produced in a period, and parameters for this program are generated by a heuristic procedure in order to establish a tight formulation. Our model allows us to solve in reasonable time instances where the product of the number of items and number of time periods is at most 60-70. Compared to known optimal solution methods, it solves significantly larger problems, often with orders of magnitude speedup.

Suggested Citation

  • Kovcs, Andrs & Brown, Kenneth N. & Tarim, S. Armagan, 2009. "An efficient MIP model for the capacitated lot-sizing and scheduling problem with sequence-dependent setups," International Journal of Production Economics, Elsevier, vol. 118(1), pages 282-291, March.
    • Handle: RePEc:eee:proeco:v:118:y:2009:i:1:p:282-291
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    References listed on IDEAS

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    Cited by:

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    2. Bruno, Giuseppe & Genovese, Andrea & Piccolo, Carmela, 2014. "The capacitated Lot Sizing model: A powerful tool for logistics decision making," International Journal of Production Economics, Elsevier, vol. 155(C), pages 380-390.
    3. Mac Cawley, Alejandro & Maturana, Sergio & Pascual, Rodrigo & Tortorella, Guilherme Luz, 2022. "Scheduling wine bottling operations with multiple lines and sequence-dependent set-up times: Robust formulation and a decomposition solution approach," European Journal of Operational Research, Elsevier, vol. 303(2), pages 819-839.
    4. Sun, Lin-Hui & Sun, Lin-Yan & Wang, Ming-Zheng & Wang, Ji-Bo, 2012. "Flow shop makespan minimization scheduling with deteriorating jobs under dominating machines," International Journal of Production Economics, Elsevier, vol. 138(1), pages 195-200.
    5. Guimarães, Luis & Klabjan, Diego & Almada-Lobo, Bernardo, 2013. "Pricing, relaxing and fixing under lot sizing and scheduling," European Journal of Operational Research, Elsevier, vol. 230(2), pages 399-411.
    6. Koulamas, Christos & Kyparisis, George J., 2010. "Single-machine scheduling problems with past-sequence-dependent delivery times," International Journal of Production Economics, Elsevier, vol. 126(2), pages 264-266, August.
    7. Karina Copil & Martin Wörbelauer & Herbert Meyr & Horst Tempelmeier, 2017. "Simultaneous lotsizing and scheduling problems: a classification and review of models," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(1), pages 1-64, January.
    8. Ferreira, Deisemara & Clark, Alistair R. & Almada-Lobo, Bernardo & Morabito, Reinaldo, 2012. "Single-stage formulations for synchronised two-stage lot sizing and scheduling in soft drink production," International Journal of Production Economics, Elsevier, vol. 136(2), pages 255-265.

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