Approximating the stability region for binary mixed-integer programs

We consider optimization problems with some binary variables, where the objective function is linear in these variables. The stability region of a given solution is the polyhedral set of objective coefficients for which the solution is optimal. Knowledge of this set provides valuable information for sensitivity analysis and re-optimization. An exact description of the stability region may require an exponential number of inequalities. We develop polyhedral inner and outer approximations of linear size. Furthermore, when a new objective function is not in the stability region, we produce a list of high-quality solutions that can be used as a quick heuristic or as a warm start for future solves.