Analyzing changes in optimal variables in linear programming with uncertain parameters

Abstract

Linear problems often include many parameters that may be uncertain. Sensitivity analysis studies how these parameters impact optimal values. Instead of analyzing the objective function, we shift the focus to the optimal values of the variables. Three types of linear modifications are considered: on the cost vector, the right-hand side, and on the constraint matrix. Several theorems establish properties of these modifications, including conditions for continuity of optimal variable values, as well as local convexity and concavity properties.