Solution concepts and their computational methods in multiobjective two-level linear programming problems

We consider a multiobjective two-level linear programming problem in which the decision maker at each level has multiple objective functions conflicting with each other. The decision maker at the upper level must take account of multiple or infinite rational responses of the decision maker at the lower level in the problem. We examine three kinds of situations based on anticipation of the decision maker at the upper level; an optimistic anticipation, a pessimistic anticipation, and an anticipation arising from past behavior of the decision maker at the lower level. Mathematical programming problems for obtaining the Stackelberg solutions based on three kinds of anticipation are formulated and algorithms for solving the problems are presented