| Title:
|
On Rohn's relative sensitivity coefficient of the optimal value for a linear-fractional program (English) |
| Author:
|
Tigan, Stefan |
| Author:
|
Stancu-Minasian, I. M. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
125 |
| Issue:
|
2 |
| Year:
|
2000 |
| Pages:
|
227-234 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
linear-fractional programming |
| Keyword:
|
generalized relative sensitivity coefficient |
| MSC:
|
90C05 |
| MSC:
|
90C31 |
| MSC:
|
90C32 |
| idZBL:
|
Zbl 1030.90125 |
| idMR:
|
MR1768810 |
| DOI:
|
10.21136/MB.2000.125953 |
| . |
| Date available:
|
2009-09-24T21:42:46Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125953 |
| . |
| Reference:
|
[1] A. Charnes W. W. Cooper: Programming with linear fractional programming.Naval Res. Logist. Quart. 9 (1962), 3-4, 181-186. MR 0152370 |
| Reference:
|
[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. Zbl 0072.37702, MR 0081803 |
| Reference:
|
[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 |
| Reference:
|
[4] A. Prékopa: On the probability distribution of the optimum of a random linear program.J. SIAM Control 4 (1966), 1, 211-222. MR 0191638, 10.1137/0304020 |
| Reference:
|
[5] J. Rohn: On sensitivity of the optimal value of a linear program.Ekonom. -Mat. Obzor 25 (1989), 1, 105-107. Zbl 0663.90089, MR 0996949 |
| Reference:
|
[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 |
| Reference:
|
[7] I. M. Stancu-Minasian: Fractional Programming: Theory, Methods and Applications.Kluwer Academic Publishers, Dordrecht, 1997. Zbl 0899.90155, MR 1472981 |
| Reference:
|
[8] I. M. Stancu-Minasian: Stochastic Programming with Multiple Objective Functions.Editura Academiei Române, Bucuresti and D. Reidel Publishing Company, Dordrecht, Boston, Laucester, 1984. Zbl 0554.90069, MR 0459619 |
| Reference:
|
[9] A. C. Williams: Marginal values in linear programming.Journal of Society of Industrial and Applied Mathematics 11 (1963), 1, 82-94. Zbl 0115.38102, MR 0184725, 10.1137/0111006 |
| . |
