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How to Analyze the Results of Linear Programs—Part 4: Forcing Substructures

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  • Harvey J. Greenberg

    (Mathematics Department, University of Colorado at Denver, PO Box 173364, Denver, Colorado 80217-3364)

Abstract

Often, solution values are forced by implication of some of the constraints. A forcing substructure is a portion of the linear program that forces some of the variables to have only one value in every feasible solution. In some cases, finding a forcing substructure reveals an error, and in other cases, it leads to a reduction of the linear program. Discovering and explaining forcing substructures are aspects of good model management. Besides its role when debugging a model, understanding forcing substructures deepens our understanding of the solution by revealing some activity levels that are determined by implications of the constraints, not by economic preference.

Suggested Citation

  • Harvey J. Greenberg, 1994. "How to Analyze the Results of Linear Programs—Part 4: Forcing Substructures," Interfaces, INFORMS, vol. 24(1), pages 121-130, February.
    • Handle: RePEc:inm:orinte:v:24:y:1994:i:1:p:121-130
    DOI: 10.1287/inte.24.1.121
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    Cited by:

    1. Pannell, David J. & Kingwell, Ross S. & Schilizzi, Steven, 1996. "Debugging Mathematical Programming Models: Principles and Practical Strategies," Review of Marketing and Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 64(01), pages 1-15, April.
    2. Murphy, Frederic H. & Mudrageda, Murthy & Soyster, Allen L. & Saric, Andrija T. & Stankovic, Aleksandar M., 2010. "The effect of contingency analysis on the nodal prices in the day-ahead market," Energy Policy, Elsevier, vol. 38(1), pages 141-150, January.
    3. Yilmaz, Hasan Ümitcan & Kimbrough, Steven O. & van Dinther, Clemens & Keles, Dogan, 2022. "Power-to-gas: Decarbonization of the European electricity system with synthetic methane," Applied Energy, Elsevier, vol. 323(C).
    4. Bruce A. McCarl, 1998. "Repairing Misbehaving Mathematical Programming Models: Concepts and a GAMS-Based Approach," Interfaces, INFORMS, vol. 28(5), pages 124-138, October.

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    Keywords

    programming: linear;

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