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A Simple Class of Parametric Linear Programming Problems

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  • S. Barnett

    (Loughborough University of Technology, Loughborough, Leicestershire, England)

Abstract

To find changes in coefficients that can occur without affecting the choice of optimal feasible basic variables is a well known problem in linear programming sensitivity theory. This paper shows that there is a very simple solution to this problem when the m × m matrix A of optimal basis vectors is varied parametrically, provided the matrix B of variations is chosen so that the inverse of A + λ B is linear in λ. It gives a general expression for such matrices B , which allows a considerable degree of arbitrariness; in particular, there exist B 's, that can have rank as high as m /2. Extensions to include variations in the nonbasic part of the coefficient matrix and in the objective function coefficients are briefly described.

Suggested Citation

  • S. Barnett, 1968. "A Simple Class of Parametric Linear Programming Problems," Operations Research, INFORMS, vol. 16(6), pages 1160-1165, December.
    • Handle: RePEc:inm:oropre:v:16:y:1968:i:6:p:1160-1165
    DOI: 10.1287/opre.16.6.1160
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