Stability in linear programming models: An index set approach

Arbitrary perturbations of arbitrary coefficients in linear programming models on the canonical form are studied. Perturbations that preserve stability (lower semi-continuity of the feasible set mapping) are characterized in terms of subsets of the index set of the decision variable. A necessary condition for stability is used to formulate a method for identification of unstable perturbations. Instability is illustrated in various situations including multi-level decision making, descriptions of locally and globally optimal parameters in linear parametric programming, and a marginal value formula for models with a convex objective and linear canonical constraints.