Previous |  Up |  Next


linear-fractional programming; generalized relative sensitivity coefficient
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.
[1] A. Charnes W. W. Cooper: Programming with linear fractional programming. Naval Res. Logist. Quart. 9 (1962), 3-4, 181-186. MR 0152370
[2] H. D. Mills: Marginal values of matrix: games and linear programs. Linear inequalities and related systems (H.W.Kuhn, A.W.Tucker, eds.). Princeton University Press, Princeton, 1956, pp. 183-193. MR 0081803 | Zbl 0072.37702
[3] L. Podkaminer: The dual price and other parameters in the fractional programming problem. Przeglad Statyst. 18 (1971), 3-4, 333-338. (In Polish.) MR 0299223
[4] A. Prékopa: On the probability distribution of the optimum of a random linear program. J. SIAM Control 4 (1966), 1, 211-222. DOI 10.1137/0304020 | MR 0191638
[5] J. Rohn: On sensitivity of the optimal value of a linear program. Ekonom. -Mat. Obzor 25 (1989), 1, 105-107. MR 0996949 | Zbl 0663.90089
[6] J. K. Sengupta, K. A. Fox: Economic Analysis and Operations Research: Optimization Techniques in Quantitative Economic Models. Studies in Mathematical and Managerial Economics, vol. 10, North-Holland Publishing Co., Amsterdam-London, American Elsevier Publishing Co., Inc., New York, 1969. MR 0270726
[7] I. M. Stancu-Minasian: Fractional Programming: Theory, Methods and Applications. Kluwer Academic Publishers, Dordrecht, 1997. MR 1472981 | Zbl 0899.90155
[8] I. M. Stancu-Minasian: Stochastic Programming with Multiple Objective Functions. Editura Academiei Române, Bucuresti and D. Reidel Publishing Company, Dordrecht, Boston, Laucester, 1984. MR 0459619 | Zbl 0554.90069
[9] A. C. Williams: Marginal values in linear programming. Journal of Society of Industrial and Applied Mathematics 11 (1963), 1, 82-94. DOI 10.1137/0111006 | MR 0184725 | Zbl 0115.38102
Partner of
EuDML logo