IDEAS home Printed from https://ideas.repec.org/a/eee/proeco/v118y2009i1p282-291.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0925-5273(08)00275-2
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Meyr, H., 2000. "Simultaneous Lotsizing and Scheduling by combining Local Search with Dual Reoptimization," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 39380, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    2. Kampf, M. & Kochel, P., 2006. "Simulation-based sequencing and lot size optimisation for a production-and-inventory system with multiple items," International Journal of Production Economics, Elsevier, vol. 104(1), pages 191-200, November.
    3. Meyr, Herbert, 2002. "Simultaneous lotsizing and scheduling on parallel machines," European Journal of Operational Research, Elsevier, vol. 139(2), pages 277-292, June.
    4. Drexl, A. & Kimms, A., 1997. "Lot sizing and scheduling -- Survey and extensions," European Journal of Operational Research, Elsevier, vol. 99(2), pages 221-235, June.
    5. MARCHAND, Hugues & MARTIN, Alexander & WEISMANTEL, Robert & WOLSEY, Laurence, 2002. "Cutting planes in integer and mixed integer programming," LIDAM Reprints CORE 1567, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. 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.
    7. Meyr, H., 2000. "Simultaneous lotsizing and scheduling by combining local search with dual reoptimization," European Journal of Operational Research, Elsevier, vol. 120(2), pages 311-326, January.
    8. BELVAUX, Gaetan & WOLSEY, Laurence A., 2001. "Modelling practical lot-sizing problems as mixed-integer programs," LIDAM Reprints CORE 1516, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Haase, Knut & Kimms, Alf, 2000. "Lot sizing and scheduling with sequence-dependent setup costs and times and efficient rescheduling opportunities," International Journal of Production Economics, Elsevier, vol. 66(2), pages 159-169, June.
    10. Meyr, H., 2002. "Simultaneous Lotsizing and Scheduling on Parallel Machines," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 36065, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    11. Karimi, B. & Fatemi Ghomi, S. M. T. & Wilson, J. M., 2003. "The capacitated lot sizing problem: a review of models and algorithms," Omega, Elsevier, vol. 31(5), pages 365-378, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tiacci, Lorenzo & Saetta, Stefano, 2012. "Demand forecasting, lot sizing and scheduling on a rolling horizon basis," International Journal of Production Economics, Elsevier, vol. 140(2), pages 803-814.
    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. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    4. Lee, Younsoo & Lee, Kyungsik, 2020. "Lot-sizing and scheduling in flat-panel display manufacturing process," Omega, Elsevier, vol. 93(C).
    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. 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.
    7. 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.
    8. Józefowska, J. & Zimniak, A., 2008. "Optimization tool for short-term production planning and scheduling," International Journal of Production Economics, Elsevier, vol. 112(1), pages 109-120, March.
    9. Andrea Raiconi & Julia Pahl & Monica Gentili & Stefan Voß & Raffaele Cerulli, 2017. "Tactical Production and Lot Size Planning with Lifetime Constraints: A Comparison of Model Formulations," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(05), pages 1-24, October.
    10. Camargo, Victor C.B. & Toledo, Franklina M.B. & Almada-Lobo, Bernardo, 2014. "HOPS – Hamming-Oriented Partition Search for production planning in the spinning industry," European Journal of Operational Research, Elsevier, vol. 234(1), pages 266-277.
    11. 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.
    12. Jans, Raf & Degraeve, Zeger, 2007. "Meta-heuristics for dynamic lot sizing: A review and comparison of solution approaches," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1855-1875, March.
    13. Masoumeh Mahdieh & Alistair Clark & Mehdi Bijari, 2018. "A novel flexible model for lot sizing and scheduling with non-triangular, period overlapping and carryover setups in different machine configurations," Flexible Services and Manufacturing Journal, Springer, vol. 30(4), pages 884-923, December.
    14. Wolosewicz, Cathy & Dauzère-Pérès, Stéphane & Aggoune, Riad, 2015. "A Lagrangian heuristic for an integrated lot-sizing and fixed scheduling problem," European Journal of Operational Research, Elsevier, vol. 244(1), pages 3-12.
    15. Tiacci, Lorenzo & Saetta, Stefano, 2012. "Demand forecasting, lot sizing and scheduling on a rolling horizon basis," International Journal of Production Economics, Elsevier, vol. 140(2), pages 803-814.
    16. Helber, Stefan & Sahling, Florian, 2010. "A fix-and-optimize approach for the multi-level capacitated lot sizing problem," International Journal of Production Economics, Elsevier, vol. 123(2), pages 247-256, February.
    17. 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.
    18. 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.
    19. Stadtler, Hartmut, 2011. "Multi-level single machine lot-sizing and scheduling with zero lead times," European Journal of Operational Research, Elsevier, vol. 209(3), pages 241-252, March.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:proeco:v:118:y:2009:i:1:p:282-291. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/ijpe .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.