MATHEMATICA BOHEMICA, Vol. 125, No. 2, pp. 227-234 (2000)

On Rohn's relative sensitivity coefficient of the optimal value for a linear-fractional program

Stefan Tigan, I.M. Stancu-Minasian

S. Tigan, Univ. of Medicine and Pharmacy, Cluj-Napoca, Str. Pasteur no. 6, RO-3400 Cluj-Napoca, Romania; I. M. Stancu-Minasian, Centre for Mathematical Statistics "Gheorghe Mihoc" of the Romanian Academy, Casa Academiei, Calea 13 Septembrie no. 13, RO-76100 Bucharest 5, Romania

Abstract: In this note we consider a linear-fractional programming problem with equality linear constraints. Following Rohn, we define a generalized relative sensitivity coefficient measuring the sensitivity of the optimal value for a linear program and a linear-fractional minimization problem with respect to the perturbations in the problem data.
By using an extension of Rohn's result for the linear programming case, we obtain, via Charnes-Cooper variable change, the relative sensitivity coefficient for the linear-fractional problem. This coefficient involves only the measure of data perturbation, the optimal solution for the initial linear-fractional problem and the optimal solution of the dual problem of linear programming equivalent to the initial fractional problem.

Keywords: linear-fractional programming, generalized relative sensitivity coefficient

Classification (MSC2000): 90C31, 90C32

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