Cooperative and Noncooperative Multi-Level Programming

Masatoshi Sakawa

• 06 december 2011
• 9781461417194

Samenvatting:

This monograph reviews the optimization concepts underlying fuzzy programming, multi-objective programming, stochastic programming, and genetic algorithms. The authors then apply these concepts to non-cooperative decision-making in hierarchical organizations.

This addition to the OPERATIONS RESEARCH/COMPUTER SCIENCE INTERFACES Series represents a sorely-needed advance in decision science and game theory literature. Drs. Sakawa and Nishizaki present their combined work in applying both cooperative and noncooperative game theory in the solving of real-world problems in fuzzy, multiobjective, and uncertain environments, and the potential applications of their approaches range from corporate environments to economics, applied mathematics, and policy decision making. Sakawa has gained recognition for his work on genetic algorithms, and shows in this book how they can be used when linear programming doesn’t suffice. Nishizaki has worked extensively in systems engineering, especially in game theory, multiobjective decision making and fuzzy mathematical programming, and is doing much to advance theory and practice in real-world decision science.

The monograph first provides a review of the optimization concepts that underlie the rest of the book: fuzzy programming; multiobjective programming; stochastic programming; and genetic algorithms. The authors then apply these concepts to noncooperative decision making in hierarchical organizations, using multiobjective and two-level linear programming, and then consider cooperative decision making in hierarchical organizations. They then present applications in a work force assignment problem; a transportation problem; and an inventory and production problem in supply chain management. After examining possible future directions in two-level programming, including use of metaheuristics and genetic algorithms to help manage large numbers of integer decision variables, they present conclusions.

To derive rational and convincible solutions to practical decision making problems in complex and hierarchical human organizations, the decision making problems are formulated as relevant mathematical programming problems which are solved by developing optimization techniques so as to exploit characteristics or structural features of the formulated problems. In particular, for resolving con?ict in decision making in hierarchical managerial or public organizations, the multi level formula tion of the mathematical programming problems has been often employed together with the solution concept of Stackelberg equilibrium. However,weconceivethatapairoftheconventionalformulationandthesolution concept is not always suf?cient to cope with a large variety of decision making situations in actual hierarchical organizations. The following issues should be taken into consideration in expression and formulation of decision making problems. Informulationofmathematicalprogrammingproblems,itistacitlysupposedthat decisions are made by a single person while game theory deals with economic be havior of multiple decision makers with fully rational judgment. Because two level mathematical programming problems are interpreted as static Stackelberg games, multi level mathematical programming is relevant to noncooperative game theory; in conventional multi level mathematical programming models employing the so lution concept of Stackelberg equilibrium, it is assumed that there is no communi cation among decision makers, or they do not make any binding agreement even if there exists such communication. However, for decision making problems in such as decentralized large ?rms with divisional independence, it is quite natural to sup pose that there exists communication and some cooperativerelationship among the decision makers.