SOLVING THE BILEVEL LINEAR PROGRAMMING PROBLEM USING THE MONTE CARLO METHOD

Abstract

In this paper we propose to use the "Monte Carlo" method for solving bilevel linear programming (the bilevel linear programming problem – BLP problem). In the BLP problem, each decision maker tries to optimize their own objective function without considering the objective of the other party, but the decision of each party affects the objective value of the other party as the decision space. The existing methods for solving the BLP problem can be grouped into four categories: a) methods based on vertices enumeration; b) methods based on Kuhn-Tuck conditions; c) the fuzzy approach; d) metaheuristics methods. Starting from Gnedenko's theorem, this paper uses the "Monte Carlo" method to determine an approximate solution for the BLP problem. The numerical example presents the performance of the proposed approach.