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Lotsizing and Scheduling on Parallel Machines with Sequence-Dependent Setup Costs

Author

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  • Sungmin Kang

    (Department of Business Administration, The Catholic University of Korea, Seoul 420-743, Korea)

  • Kavindra Malik

    (i2 Technologies, 909 E. Las Colinas Boulevard, Irving, TX 75039)

  • L. Joseph Thomas

    (Johnson Graduate School of Management, Cornell University, Ithaca, New York 14850)

Abstract

Industrial lotsizing and scheduling pose very difficult analytical problems. We propose an unconventional model that deals with sequence-dependent setup costs in a multiple-machine environment. The sequence-splitting model splits an entire schedule into subsequences, leading to tractable subproblems. An optimization approach based on a column generation/branch and bound methodology is developed, and heuristically adapted to test problems including five real-world problem instances gathered from industry.

Suggested Citation

  • Sungmin Kang & Kavindra Malik & L. Joseph Thomas, 1999. "Lotsizing and Scheduling on Parallel Machines with Sequence-Dependent Setup Costs," Management Science, INFORMS, vol. 45(2), pages 273-289, February.
    • Handle: RePEc:inm:ormnsc:v:45:y:1999:i:2:p:273-289
    DOI: 10.1287/mnsc.45.2.273
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. BELVAUX, Gaetan & WOLSEY, Laurence A., 2000. "Modelling practical lot-sizing problems as mixed integer programs," LIDAM Discussion Papers CORE 2000009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Daniel Quadt & Heinrich Kuhn, 2009. "Capacitated lot‐sizing and scheduling with parallel machines, back‐orders, and setup carry‐over," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(4), pages 366-384, June.
    3. Raf Jans, 2009. "Solving Lot-Sizing Problems on Parallel Identical Machines Using Symmetry-Breaking Constraints," INFORMS Journal on Computing, INFORMS, vol. 21(1), pages 123-136, February.
    4. Zhi‐Long Chen & Warren B. Powell, 2003. "Exact algorithms for scheduling multiple families of jobs on parallel machines," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(7), pages 823-840, October.
    5. Guimarães, Luis & Klabjan, Diego & Almada-Lobo, Bernardo, 2014. "Modeling lotsizing and scheduling problems with sequence dependent setups," European Journal of Operational Research, Elsevier, vol. 239(3), pages 644-662.
    6. Haugen, Kjetil K. & Olstad, Asmund & Pettersen, Bard I., 2007. "The profit maximizing capacitated lot-size (PCLSP) problem," European Journal of Operational Research, Elsevier, vol. 176(1), pages 165-176, January.
    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. Fabrizio Marinelli & Maria Nenni & Antonio Sforza, 2007. "Capacitated lot sizing and scheduling with parallel machines and shared buffers: A case study in a packaging company," Annals of Operations Research, Springer, vol. 150(1), pages 177-192, March.
    9. Gaetan Belvaux & Laurence A. Wolsey, 2001. "Modelling Practical Lot-Sizing Problems as Mixed-Integer Programs," Management Science, INFORMS, vol. 47(7), pages 993-1007, July.
    10. Philip Doganis & Haralambos Sarimveis, 2008. "Optimal production scheduling for the dairy industry," Annals of Operations Research, Springer, vol. 159(1), pages 315-331, March.
    11. Meyr, Herbert, 2002. "Simultaneous lotsizing and scheduling on parallel machines," European Journal of Operational Research, Elsevier, vol. 139(2), pages 277-292, June.
    12. Weng, Michael X. & Lu, John & Ren, Haiying, 2001. "Unrelated parallel machine scheduling with setup consideration and a total weighted completion time objective," International Journal of Production Economics, Elsevier, vol. 70(3), pages 215-226, April.
    13. Meyr, Herbert & Mann, Matthias, 2013. "A decomposition approach for the General Lotsizing and Scheduling Problem for Parallel production Lines," European Journal of Operational Research, Elsevier, vol. 229(3), pages 718-731.
    14. Carvalho, Desiree M. & Nascimento, Mariá C.V., 2022. "Hybrid matheuristics to solve the integrated lot sizing and scheduling problem on parallel machines with sequence-dependent and non-triangular setup," European Journal of Operational Research, Elsevier, vol. 296(1), pages 158-173.
    15. Mili Mehrotra & Milind Dawande & Srinagesh Gavirneni & Mehmet Demirci & Sridhar Tayur, 2011. "OR PRACTICE---Production Planning with Patterns: A Problem from Processed Food Manufacturing," Operations Research, INFORMS, vol. 59(2), pages 267-282, April.
    16. 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.
    17. Diego Fiorotto & Silvio Araujo, 2014. "Reformulation and a Lagrangian heuristic for lot sizing problem on parallel machines," Annals of Operations Research, Springer, vol. 217(1), pages 213-231, June.
    18. Gerald G. Brown & Robert F. Dell & Ray L. Davis & Richard H. Duff, 2002. "Optimizing Plant-Line Schedules and an Application at Hidden Valley Manufacturing Company," Interfaces, INFORMS, vol. 32(3), pages 1-14, June.
    19. Jans, R.F., 2006. "Solving Lotsizing Problems on Parallel Identical Machines Using Symmetry Breaking Constraints," ERIM Report Series Research in Management ERS-2006-051-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    20. 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.
    21. Hop, Nguyen Van & Tabucanon, Mario T., 2005. "Adaptive genetic algorithm for lot-sizing problem with self-adjustment operation rate," International Journal of Production Economics, Elsevier, vol. 98(2), pages 129-135, November.
    22. K. A. G. Araujo & E. G. Birgin & M. S. Kawamura & D. P. Ronconi, 2023. "Relax-and-Fix Heuristics Applied to a Real-World Lot Sizing and Scheduling Problem in the Personal Care Consumer Goods Industry," SN Operations Research Forum, Springer, vol. 4(2), pages 1-30, June.

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