A method for solving bilevel linear programming problems

This paper presents an approach for solving bilevel linear programming problems (BLPP). It is based on the result that an optimal solution to the BLPP is reachable at an extreme point of the underlying region. Consequently, we develop a pivot technique to find the global optimal solution on an expanded tableau that represents the data of the BLPP. The pivot technique allows to rank in increasing order the outer level objective function value until a value is reached with a corresponding extreme point feasible for the BLPP. This solution is then the required global solution. Numerical examples are provided. Solutions obtained through our algorithm to some problems available in the literature show that these problems were until now wrongly solved.