Upper and lower bounds for the optimal values of the interval bilevel linear programming problem

Abstract

In this paper, we will investigate the interval bilevel linear programming (IBLP) problem. Recently, Calvete et al. have proposed two algorithms to find the worst and the best (upper and lower bounds) optimal values of the leader objective function in the bilevel linear programming (BLP) problem when the coefficients of the leader and the follower objective functions are interval. Through some examples, we will first show that the algorithm to find the worst optimal value of the leader objective function does not always yield a correct solution. Then, after investigating its drawbacks, we will propose a revised algorithm with which the previous examples will yield correct solutions. Finally, it will be extended to the general BLP problem wherein all the coefficients are interval. It is, of course, possible to easily find the upper and the lower bounds for the lower level objective function too.