Bilevel Biobjective Pseudo Boolean Programming Problems

In the present paper a kind of bilevel programming problem in 0–1 variables, based on the mathematical model attached by us to a concrete portfolio optimization problem, is analyzed. The upper level function is to be maximized, while the lower level function (which is a biobjective function) is to be maximized‐minimized in the lexicographic sense. The core idea of this paper is to present a way for solving the proposed bilevel problem by reducing it to a finite number of couples of linear pseudo boolean programming problems. One of these last types of problems is an assignment problem. Also, in this paper the notion of a max - p min - max point is introduced and several necessary and sufficient optimal conditions (useful for solving the problems gained after applying the splitting technique) are proved. Furthermore, an algorithm for solving the initial problem is proposed and an example is given.