Cooperative and Noncooperative Multi-Level Programming

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.

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.

Presents the latest advances in the new field of multi-level mathematical programming problems in fuzzy, multi-objective, and uncertain environments Provides mathematical models that can be used to solve real-world problems in large organization settings, including corporate, political, economic, and social situations Cutting-edge research that combines for the first time cooperative and non-cooperative game theory Includes supplementary material: sn.pub/extras

Auteur

Masatoshi Sakawa was born in Matsuyama, Japan on 11 August 1947. He received B.E., M.E., and D.E. degrees in applied mathematics and physics at Kyoto University in 1970, 1972, and 1975, respectively. From 1975 he was with Kobe University where, since 1981, he was an Associate Professor in the Department of Systems Engineering. From 1987 to 1990 he was a Professor in the Department of Computer Science at Iwate University. At present he is a Professor at Hiroshima University and is working with the Department of Artificial Complex Systems Engineering in the Graduate School of Engineering. He was an Honorary Visiting Professor at University of Manchester Institute of Science and Technology (UMIST), Computation Department, sponsored by the Japan Society for the Promotion of Science (JSPS) from March to December 1991. He was also a Visiting Professor at the Kyoto Institute of Economic Research, Kyoto University from April 1991 to March 1992.

His research and teaching activities are in the area of systems engineering, especially mathematical optimization, multiobjective decision making, fuzzy mathematical programming and game theory. In addition to over 300 articles in National and International Journals, he is an author and coauthor of 5 books in English and 14 books in Japanese, including the Springer titles Genetic Algorithms and Fuzzy Multiobjective Optimization; Fuzzy Sets and Interactive Multiobject Optimization; Large-Scale Interactive Fuzzy Multiobjective Programming: Decomposition Approaches; and, with Nishizaki, Fuzzy and Multiobjective Games for Conflict Resolution.

Ichiro Nishizaki was born in Osaka, Japan, in January, 1959. He received B.E. and M.E. degrees in systems engineering at Kobe University in 1982 and 1984, respectively, and he received the D.E. degree from Hiroshima University in 1993. From 1984 to 1990, he worked for Nippon Steel Corporation. From 1990 to 1993, he was a Research Associateat the Kyoto Institute of Economic Research, Kyoto University. From 1993 to 1996, he was an Associate Professor in the Faculty of Business Administration and Informatics at Setsunan University. From 1997 to 2001, he was an Associate Professor at Hiroshima University, and was working with the Department of Artificial Complex Systems Engineering in the Graduate School of Engineering. At present, he is a Professor in that department. His research and teaching activities are in the area of systems engineering, especially game theory, multiobjective decision making, and fuzzy mathematical programming. He is an author or coauthor of about eighty papers, one book in English (Springer: Fuzzy and Multiobjective Games for Conflict Resolution), and two books in Japanese.

Texte du rabat

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.

Contenu
Optimization Concepts and Computational Methods.- Noncooperative Decision Making in Hierarchical Organizations.- Cooperative Decision Making in Hierarchical Organizations.- Some applications.