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A Strong Cutting Plane Algorithm for Production Scheduling with Changeover Costs

Author

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  • T. L. Magnanti

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

  • R. Vachani

    (GTE Laboratories, Waltham, Massachusetts)

Abstract

Changeover costs (and times) are central to numerous manufacturing operations. These costs arise whenever work centers capable of processing only one product at a time switch from the manufacture of one product to another. Although many researchers have contributed to the solution of scheduling problems that include changeover costs, due to the problem's combinatorial explosiveness, optimization-based methods have met with limited success. In this paper, we develop and apply polyhedral methods from integer programming for a dynamic version of the problem. Computational tests with problems containing one to five products (and up to 225 integer variables) show that polyhedral methods based upon a set of facet inequalities developed in this paper can effectively reduce the gap between the value of an integer programming formulation of the problem and its linear programming relaxation (by a factor of 94 to 100%). These results suggest the use of a combined cutting plane/branch-and-bound procedure as a solution approach. In a test with a five product problem, this procedure, when compared with a standard linear programming-based branch-and-bound approach, reduced computation time by a factor of seven.

Suggested Citation

  • T. L. Magnanti & R. Vachani, 1990. "A Strong Cutting Plane Algorithm for Production Scheduling with Changeover Costs," Operations Research, INFORMS, vol. 38(3), pages 456-473, June.
    • Handle: RePEc:inm:oropre:v:38:y:1990:i:3:p:456-473
    DOI: 10.1287/opre.38.3.456
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    Citations

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    Cited by:

    1. François Vanderbeck, 1998. "Lot-Sizing with Start-Up Times," Management Science, INFORMS, vol. 44(10), pages 1409-1425, October.
    2. Manfred Padberg, 2005. "Classical Cuts for Mixed-Integer Programming and Branch-and-Cut," Annals of Operations Research, Springer, vol. 139(1), pages 321-352, October.
    3. Wolsey, Laurence A., 1997. "MIP modelling of changeovers in production planning and scheduling problems," European Journal of Operational Research, Elsevier, vol. 99(1), pages 154-165, May.
    4. van Eijl, C.A. & van Hoesel, C.P.M., 1995. "On the discrete lot-sizing and scheduling problem with Wagner-Whitin costs," Research Memorandum 018, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    5. 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.
    6. BELVAUX, Gaetan & WOLSEY, Laurence A., 1998. "Lot-sizing problems: modelling issues and a specialized branch-and-cut system BC-PROD," LIDAM Discussion Papers CORE 1998049, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Weidenhiller, Andreas & Jodlbauer, Herbert, 2009. "Equivalence classes of problem instances for a continuous-time lot sizing and scheduling problem," European Journal of Operational Research, Elsevier, vol. 199(1), pages 139-149, November.
    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. Drexl, Andreas & Haase, Knut, 1992. "A new type of model for multi-item capacitated dynamic lotsizing and scheduling," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 286, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    10. Francesco Gaglioppa & Lisa A. Miller & Saif Benjaafar, 2008. "Multitask and Multistage Production Planning and Scheduling for Process Industries," Operations Research, INFORMS, vol. 56(4), pages 1010-1025, August.
    11. Salomon, Marc & Solomon, Marius M. & Van Wassenhove, Luk N. & Dumas, Yvan & Dauzere-Peres, Stephane, 1997. "Solving the discrete lotsizing and scheduling problem with sequence dependent set-up costs and set-up times using the Travelling Salesman Problem with time windows," European Journal of Operational Research, Elsevier, vol. 100(3), pages 494-513, August.
    12. Milind Dawande & Srinagesh Gavirneni & Yinping Mu & Suresh Sethi & Chelliah Sriskandarajah, 2010. "On the Interaction Between Demand Substitution and Production Changeovers," Manufacturing & Service Operations Management, INFORMS, vol. 12(4), pages 682-691, September.
    13. Dror, M. & Haouari, M. & Chaouachi, J., 2000. "Generalized spanning trees," European Journal of Operational Research, Elsevier, vol. 120(3), pages 583-592, February.
    14. James D. Blocher & Suresh Chand & Kaushik Sengupta, 1999. "The Changeover Scheduling Problem with Time and Cost Considerations: Analytical Results and a Forward Algorithm," Operations Research, INFORMS, vol. 47(4), pages 559-569, August.
    15. Thomas L. Magnanti & Trilochan Sastry, 2002. "Facets and Reformulations for Solving Production Planning With Changeover Costs," Operations Research, INFORMS, vol. 50(4), pages 708-719, August.
    16. de Matta, Renato & Miller, Tan, 2004. "Production and inter-facility transportation scheduling for a process industry," European Journal of Operational Research, Elsevier, vol. 158(1), pages 72-88, October.
    17. 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.
    18. Zhou, Feng & Blocher, James D. & Hu, Xinxin & Sebastian Heese, H., 2014. "Optimal single machine scheduling of products with components and changeover cost," European Journal of Operational Research, Elsevier, vol. 233(1), pages 75-83.
    19. Jordan, Carsten & Drexl, Andreas, 1994. "Lotsizing and scheduling by batch sequencing," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 343, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.

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