Generalized Sensitivity Analysis at a Degenerate Optimal Solution

퇴화최적해에서 일반감도분석

  • 박찬규 (한국전산원 정보화평가분석단) ;
  • 김우제 (대진대학교 산업공학과) ;
  • 박순달 (서울대학교 산업공학과)
  • Published : 2000.12.01


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.



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