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Techniques for Removing Nonbinding Constraints and Extraneous Variables from Linear Programming Problems

Author

Listed:
  • Gerald L. Thompson

    (Carnegie Institute of Technology)

  • Fred M. Tonge

    (University of California, Irvine)

  • Stanley Zionts

    (Carnegie Institute of Technology and the U.S. Steel Applied Research Laboratory, Monroeville, Pennsylvania)

Abstract

In formulating linear programming problems, analysts tend to include constraints that are not binding at the optimal solution for fear of excluding necessary constraints. The inclusion of such constraints does not alter the optimum solutions, but may require many additional iterations to be taken, as well as increase the computational difficulties encountered. Most of the methods proposed to date for identification of redundant and non-binding constraints are not warranted in practice because of the excessive computations required to implement them. These methods are reviewed in the present paper, and some of them are extended. A number of additional methods are also considered. Two of these new methods are not only practical, but have proven to be powerful in solving a number of problems. These methods may be incorporated in a variant of the simplex method. After each simplex iteration is made, constraints and variables are tested and, when identified as non-binding, are eliminated. The procedure is continued, with the problem size dwindling as the algorithm progresses, until the optimum is reached. Then the values of the eliminated variables are computed by substitution into the eliminated constraints. Early evidence shows that a size reduction for small problems (having 25-30 constraints) of 50 percent is not unusual. It is hoped that the results on larger problems will be even more significant.

Suggested Citation

  • Gerald L. Thompson & Fred M. Tonge & Stanley Zionts, 1966. "Techniques for Removing Nonbinding Constraints and Extraneous Variables from Linear Programming Problems," Management Science, INFORMS, vol. 12(7), pages 588-608, March.
    • Handle: RePEc:inm:ormnsc:v:12:y:1966:i:7:p:588-608
    DOI: 10.1287/mnsc.12.7.588
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    Cited by:

    1. Bernard M. S. van Praag & Nico L. van der Sar, 1988. "Household Cost Functions and Equivalence Scales," Journal of Human Resources, University of Wisconsin Press, vol. 23(2), pages 193-210.
    2. Löber, Gerrit & Staat, Matthias, 2010. "Integrating categorical variables in Data Envelopment Analysis models: A simple solution technique," European Journal of Operational Research, Elsevier, vol. 202(3), pages 810-818, May.
    3. Telgen, Jan, 1977. "Redundant And Non-Binding Constraints In Linear Programming Problems," Econometric Institute Archives 272156, Erasmus University Rotterdam.
    4. van der Hoek, Gerard & Telgen, Jan, 1976. "Projective Methods To Find A Feasible Solution To Systems Of Linear Constraints," Econometric Institute Archives 272134, Erasmus University Rotterdam.
    5. Telgen, J., 1977. "On R.W. Llewellyn'S Rules To Identify Redundant Constraints; A Detailed Critique And Some Generalizations," Econometric Institute Archives 272155, Erasmus University Rotterdam.
    6. Saito, G. & Corley, H.W. & Rosenberger, Jay M. & Sung, Tai-Kuan & Noroziroshan, Alireza, 2015. "Constraint Optimal Selection Techniques (COSTs) for nonnegative linear programming problems," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 586-598.
    7. James Folberth & Stephen Becker, 2020. "Safe Feature Elimination for Non-negativity Constrained Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 931-952, March.
    8. M.A. Goberna & V. Jornet & M. Molina, 2003. "Saturation in Linear Optimization," Journal of Optimization Theory and Applications, Springer, vol. 117(2), pages 327-348, May.
    9. Drynan, Ross G., 1987. "A Generalised Concept of Dominance in Linear Programming Models," Review of Marketing and Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 55(02), pages 1-7, August.

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