Stackelberg solutions to multiobjective two-level linear programming problems

In this paper, we consider a multiobjective two-level linear programming pr oblem in which the decision maker at each level has multiple-objective func tions conflicting with each other. The decision maker at the upper level mu st take account of multiple or infinite rational responses of the decision maker at the lower level in the problem. We examine three kinds of situatio ns based on anticipation of the decision maker at the upper level: optimist ic anticipation, pessimistic anticipation, and anticipation arising from th e past behavior of the decision maker at the lower level. Mathematical prog ramming problems for obtaining the Stackelberg solutions based on the three kinds of anticipation are formulated and algorithms for solving the proble ms are presented. Illustrative numerical examples are provided to understan d the geometrical properties of the solutions and demonstrate the feasibili ty of the proposed methods.