A Novel Technique for Solving Integer Linear Bilevel Programming Problems

A novel technique that addresses the solution of the general integer linear bilevel programming problem to global optimality is presented i.e. the general case of bilevel linear programming problems where each decision maker has objective functions conflicting with each other. We introduce linear programming problem of which resolution can permit to generate the whole feasible set of the upper level decisions. The approach is based on the relaxation of the feasible region by convex underestimation. Finally, we illustrate our approach with a numerical example.