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Cutting Big M Down to Size

Author

Listed:
  • Jeffrey D. Camm

    (Department of Quantitative Analysis and Information Systems, University of Cincinnati, Cincinnati, Ohio 45221-0130)

  • Amitabh S. Raturi

    (Department of Quantitative Analysis and Information Systems, University of Cincinnati, Cincinnati, Ohio 45221-0130)

  • Shigeru Tsubakitani

    (Department of Quantitative Analysis and Information Systems, University of Cincinnati, Cincinnati, Ohio 45221-0130)

Abstract

Some texts and applied research papers continue to advocate the use of “M,” an “extremely large number,” in modeling a fixed charge in binary integer programs. This choice of M can be very detrimental to solving even reasonably sized problems. Previous research provides straightforward techniques which should be implemented by any person intelligent enough to develop an MIP model.

Suggested Citation

  • Jeffrey D. Camm & Amitabh S. Raturi & Shigeru Tsubakitani, 1990. "Cutting Big M Down to Size," Interfaces, INFORMS, vol. 20(5), pages 61-66, October.
    • Handle: RePEc:inm:orinte:v:20:y:1990:i:5:p:61-66
    DOI: 10.1287/inte.20.5.61
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    Cited by:

    1. Emily M. Craparo & Mumtaz Karatas & Tobias U. Kuhn, 2017. "Sensor placement in active multistatic sonar networks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(4), pages 287-304, June.
    2. David Huber & Felix Birkelbach & René Hofmann, 2023. "HENS Unchained: MILP Implementation of Multi-Stage Utilities with Stream Splits, Variable Temperatures and Flow Capacities," Energies, MDPI, vol. 16(12), pages 1-22, June.
    3. Kuthambalayan, Thyagaraj S. & Mehta, Peeyush & Shanker, Kripa, 2014. "Integrating operations and marketing decisions using delayed differentiation of products and guaranteed delivery time under stochastic demand," European Journal of Operational Research, Elsevier, vol. 237(2), pages 617-627.
    4. Sandra Benítez-Peña & Rafael Blanquero & Emilio Carrizosa & Pepa Ramírez-Cobo, 2019. "On support vector machines under a multiple-cost scenario," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(3), pages 663-682, September.
    5. Meissner, Joern & Strauss, Arne, 2012. "Network revenue management with inventory-sensitive bid prices and customer choice," European Journal of Operational Research, Elsevier, vol. 216(2), pages 459-468.
    6. Alexandra M. Newman & Martin Weiss, 2013. "A Survey of Linear and Mixed-Integer Optimization Tutorials," INFORMS Transactions on Education, INFORMS, vol. 14(1), pages 26-38, September.
    7. Daeho Kim & Hyungkyu Cheon & Dong Gu Choi & Seongbin Im, 2022. "Operations Research Helps the Optimal Bidding of Virtual Power Plants," Interfaces, INFORMS, vol. 52(4), pages 344-362, July.
    8. Schulz, Arne & Pfeiffer, Christian, 2024. "Using fixed paths to improve branch-and-cut algorithms for precedence-constrained routing problems," European Journal of Operational Research, Elsevier, vol. 312(2), pages 456-472.
    9. Coelho, Vitor N. & Coelho, Igor M. & Coelho, Bruno N. & de Oliveira, Glauber C. & Barbosa, Alexandre C. & Pereira, Leo & de Freitas, Alan & Santos, Haroldo G. & Ochi, Luis S. & Guimarães, Frederico G., 2017. "A communitarian microgrid storage planning system inside the scope of a smart city," Applied Energy, Elsevier, vol. 201(C), pages 371-381.
    10. Qi, Yingxiu & Harrod, Steven & Psaraftis, Harilaos N. & Lang, Maoxiang, 2022. "Transport service selection and routing with carbon emissions and inventory costs consideration in the context of the Belt and Road Initiative," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 159(C).
    11. Mehdi Zeynivand & Mehdi Najafi & Mohammad Modarres Yazdi, 2023. "A Recourse Policy to Improve Number of Successful Transplants in Uncertain Kidney Exchange Programs," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 476-507, May.
    12. Jesse Pietz & Johannes O. Royset, 2013. "Generalized orienteering problem with resource dependent rewards," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(4), pages 294-312, June.
    13. Scott P. Stevens & Susan W. Palocsay, 2017. "Teaching Use of Binary Variables in Integer Linear Programs: Formulating Logical Conditions," INFORMS Transactions on Education, INFORMS, vol. 18(1), pages 28-36, September.

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    Keywords

    programming: integer applications;

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