Sensitivity analysis in linear optimization: Invariant support set intervals

Sensitivity analysis is one of the most interesting and preoccupying areas in optimization. Many attempts are made to investigate the problem’s behavior when the input data changes. Usually variation occurs in the right hand side of the constraints and/or the objective function coefficients. Degeneracy of optimal solutions causes considerable difficulties in sensitivity analysis. In this paper we briefly review three types of sensitivity analysis and consider the question: what is the range of the parameter, where for each parameter value, an optimal solution exists with exactly the same set of positive variables that the current optimal solution has. This problem is coming from managerial requirements. Managers want to know in what range of variation of sources or prices in the market can they keep the installed production lines active, and only production’s levels would change.