- Volume 25 Issue 4
The methods of sensitivity analysis for linear programming can be classified in two types: sensitivity analysis using an optimal solution, and sensitivity analysis using an approximate optimal solution. As the methods of sensitivity analysis using an optimal solution, there are three sensitivity analysis methods: sensitivity analysis using an optimal basis, positive sensitivity analysis, and optimal partition sensitivity analysis. Since they may provide different characteristic regions under degeneracy, it is not easy to understand and apply the results of the three methods. In this paper, we propose a generalized sensitivity analysis that can integrate the three existing methods of sensitivity analysis. When a right-hand side or a cost coefficient is perturbed, the generalized sensitivity analysis gives different characteristic regions according to the controlling index set that denotes the set of variables allowed to have positive values in optimal solutions to the perturbed problem. We show that the three existing sensitivity analysis methods are special cases of the generalized sensitivity analysis, and present some properties of the generalized sensitivity analysis.
- 선형계획법 박순달
- 내부점법에서 감도분석에 관한 연구 박찬규
- 한국경영과학회지 v.13 no.1 행렬게임에서의 감도분석 성기석;박순달
- 선형계획법에서 비정점최적해의 민감도분석에 관한 연구 양병학
- Algorithmica v.8 A geometric view of parametric linear programming Adler, I.;R. D. C. Monteiro
- Linear programming and extension Dantzig, G. B.
- Decision Sciences no.13 Degeneracy and the (mis)interpretation of sensitivity analysis in linear programming Evans, J. R.;N. R. Baker
- Postoptimal analysis, parametric programming, and related topics Gal, T.
- Inequalities and Related Systems(Annals of Mathematical Studies) no.38 Theory of linear programming Goldman, A. J.;A. W. Tucker;H. W. Kuhn(eds.);A. W. Tucker(eds.)
- European Journal of Operational Research no.101 Sensitivity analysis in linear programming : just be careful Jansen, B.;J. J. de Jong;C. Roos;T. Terlaky
- European Journal of Operational Research no.116 An ε -sensitivity analysis in the primal-dual interior point method Kim, W. J.;C. K. Park;S. D. Park
- ORSA Journal on Computing v.3 no.1 On finding primal- and dual-optimal bases Megiddo, N.
- Mathematical Programming no.92 A general parametric analysis approach and its implications to sensitivity analysis in interior point methods Monteiro, R. D.;S. Mehrotra
- Linear Programming Murty, K. G.
- Theory and Algorithms for Linear Optimization Roos, C.;T. Terlaky;J.-Ph. Vial
- Presented on APORS '94 Sensitivity analysis on the cost coefficients for the Karmarkar's algorithm in linear programming Yang, B. H.;Soondal Park