Abstract
Decision making problems in decentralized organizations are often modeled as Stackelberg games, and they are formulated as two-level mathematical programming problems. There are two decision makers in the problems. If they do not have any motivation to cooperate mutually and behave rationally, the outcomes of the problems can be explained by Stackelberg equilibrium which is not always Pareto optimal. From the computational aspect, it is known that solving the problem is NP-hard even if the objective functions and the constraint are linear. In contrast, if decision makers can select strategies cooperatively, the most important aspect is to derive Pareto optimal solutions favorable to the decision makers, and as a method of this line of approach interactive fuzzy programming has been developed, taking into account fuzziness of human judgments. In this paper, after reviewing the development of solution methods for two- and multi-level programming problems, we focus on cooperative decision making in decentralized organizations and present interactive fuzzy programming for two-level linear programming problems, which provide satisfactory solutions in accordance with preference of the decision makers. Moreover, we describe extensions of interactive fuzzy programming for two-level linear programming problems under multiobjective environments and under uncertainty.
