Geodesic
On Rohn's relative sensitivity coefficient of the optimal value for a linear-fractional program
Mathematica Bohemica, Tome 125 (2000) no. 2, pp. 227-234

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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.
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.
DOI : 10.21136/MB.2000.125953
Classification : 90C05, 90C31, 90C32
Keywords: linear-fractional programming; generalized relative sensitivity coefficient 
Tigan, Stefan; Stancu-Minasian, I. M. On Rohn's relative sensitivity coefficient of the optimal value for a linear-fractional program. Mathematica Bohemica, Tome 125 (2000) no. 2, pp. 227-234. doi: 10.21136/MB.2000.125953
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