A Simple Class of Parametric Linear Programming Problems

S. Barnett
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S. Barnett: Loughborough University of Technology, Loughborough, Leicestershire, England

Operations Research, 1968, vol. 16, issue 6, 1160-1165

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.

Date: 1968
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