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Goal programming is one of the most widely used methodologies in operations research and management science, and encompasses most classes of multiple objective programming models. Ignizio provides a concise and lucid overview of (a) the linear goal programming model, (b) a computationally efficient algorithm for solution, (c) duality and sensitivity analysis and (d) extensions of the methodology to integer as well as non-linear models.
The generalized area of multiple criteria decision making (MCDM) can be defined as the body of methods and procedures by which the concern for multiple conflicting criteria can be formally incorporated into the analytical process. MCDM consists mostly of two branches, multiple criteria optimization and multi-criteria decision analysis (MCDA). While MCDA is typically concerned with multiple criteria problems that have a small number of alternatives often in an environment of uncertainty (location of an airport, type of drug rehabilitation program), multiple criteria optimization is typically directed at problems formulated within a mathematical programming framework, but with a stack of objectives instead of just one (river basin management, engineering component design, product distribution). It is about the most modern treatment of multiple criteria optimization that this book is concerned. I look at this book as a nicely organized and well-rounded presentation of what I view as ”new wave” topics in multiple criteria optimization. Looking back to the origins of MCDM, most people agree that it was not until about the early 1970s that multiple criteria optimization c- gealed as a field. At this time, and for about the following fifteen years, the focus was on theories of multiple objective linear programming that subsume conventional (single criterion) linear programming, algorithms for characterizing the efficient set, theoretical vector-maximum dev- opments, and interactive procedures.
During the week of September 20-23, 1983, an International Workshop on Interactive Decision Analysis and Interpretative Computer Intelligence was held at the International Institute for Applied Systems Analysis (IIASA) in Laxenburg, Austria. More than fifty scientists representing seventeen coun tries participated. The aim of the Workshop was to review existing approaches to problems involving multiple conflicting objectives, to look at methods and techniques for interactive decision analysis, and to demonstrate theuse of existing interactive decision-support systems. The Workshop was motivated, firstly, by the realization that the rapid development of computers, especially microcomputers, will greatly increase the scope and capabilities of computerized decision-support systems. It is important to explore the potential of these systems for use in handling the complex technological, environmental, economic and social problems thatface the world today. Research in decision-support systems also has another, less tangible but possibly more important, motivation. The development of efficient sys tems for decision support requires a thorough understanding of the dif ferences between the decision-making processes in different nations and cultures. An understanding of the different rationales underlying decision making is not only necessary for the development of efficient decision support systems, but is also an important factor in encouraging inter national understanding and cooperation.
Although several books or monographs on multiobjective optimization under uncertainty have been published, there seems to be no book which starts with an introductory chapter of linear programming and is designed to incorporate both fuzziness and randomness into multiobjective programming in a unified way. In this book, five major topics, linear programming, multiobjective programming, fuzzy programming, stochastic programming, and fuzzy stochastic programming, are presented in a comprehensive manner. Especially, the last four topics together comprise the main characteristics of this book, and special stress is placed on interactive decision making aspects of multiobjective programming for human-centered systems in most realistic situations under fuzziness and/or randomness. Organization of each chapter is briefly summarized as follows: Chapter 2 is a concise and condensed description of the theory of linear programming and its algorithms. Chapter 3 discusses fundamental notions and methods of multiobjective linear programming and concludes with interactive multiobjective linear programming. In Chapter 4, starting with clear explanations of fuzzy linear programming and fuzzy multiobjective linear programming, interactive fuzzy multiobjective linear programming is presented. Chapter 5 gives detailed explanations of fundamental notions and methods of stochastic programming including two-stage programming and chance constrained programming. Chapter 6 develops several interactive fuzzy programming approaches to multiobjective stochastic programming problems. Applications to purchase and transportation planning for food retailing are considered in Chapter 7. The book is self-contained because of the three appendices and answers to problems. Appendix A contains a brief summary of the topics from linear algebra. Pertinent results from nonlinear programming are summarized in Appendix B. Appendix C is a clear explanation of the Excel Solver, one of the easiest ways to solve optimization problems, through the use of simple examples of linear and nonlinear programming.
This textbook presents methodologies and applications associated with multiple criteria decision analysis (MCDA), especially for those students with an interest in industrial engineering. With respect to methodology, the book covers (1) problem structuring methods; (2) methods for ranking multi-dimensional deterministic outcomes including multiattribute value theory, the analytic hierarchy process, the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), and outranking techniques; (3) goal programming,; (4) methods for describing preference structures over single and multi-dimensional probabilistic outcomes (e.g., utility functions); (5) decision trees and influence diagrams; (6) methods for determining input probability distributions for decision trees, influence diagrams, and general simulation models; and (7) the use of simulation modeling for decision analysis. This textbook also offers: · Easy to follow descriptions of how to apply a wide variety of MCDA techniques · Specific examples involving multiple objectives and/or uncertainty/risk of interest to industrial engineers · A section on outranking techniques ; this group of techniques, which is popular in Europe, is very rarely mentioned as a methodology for MCDA in the United States · A chapter on simulation as a useful tool for MCDA, including ranking & selection procedures. Such material is rarely covered in courses in decision analysis · Both material review questions and problems at the end of each chapter . Solutions to the exercises are found in the Solutions Manual which will be provided along with PowerPoint slides for each chapter. The methodologies are demonstrated through the use of applications of interest to industrial engineers, including those involving product mix optimization, supplier selection, distribution center location and transportation planning, resource allocation and scheduling of a medical clinic, staffing of a call center, quality control, project management, production and inventory control,and so on. Specifically, industrial engineering problems are structured as classical problems in multiple criteria decision analysis, and the relevant methodologies are demonstrated.
This book covers the fundamentals of linear programming, extension of linear programming to discrete optimization methods, multi-objective functions, quadratic programming, geometric programming, and classical calculus methods for solving nonlinear programming problems.
Both the 'First International Summer School on Multiple Criteria Decision Making Methods, Applications and Software' and the present volume of readings could only be realised with assistance and support from many sides. We would like to express our gratitude to all those who have contributed to making a success of the first of a hopefully long series of summer schools in this field and to all those who have contribut. ed to the present volume. First of all we are grateful for the financial means supplied by a long list of sponsors, the most important of which are mentioned on the copyright page. Next, we are grateful to the members of the organising committee, Anna Ostanello and Giovanni Zambruno. Since this is the first of what will become a series of summer schools, the chairman of the organising committee, Benedetto Matarazzo, will start this volume with a brief account of the school held in Acireale. The programme committee consisted of Jean Fichefet, Anna Ostanello, Bernard Roy, Jaap Spronk (chairman) and Stanley Zionts. Their valuable contribu tion is gratefully acknowledged, as is the contribution of all the lecturers at the school. Of course, a school is not only made by its teachers, but just as much by its students. The primary aim of a school is to teach and to stimulate the students.
As its title implies, Advances in Multicriteria Analysis presents the most recent developments in multicriteria analysis and in some of its principal areas of application, including marketing, research and development evaluation, financial planning, and medicine. Special attention is paid to the interaction between multicriteria analysis, decision support systems and preference modeling. The five sections of the book cover: methodology; problem structuring; utility assessment; multi-objective optimisation; real world applications. Audience: Researchers and professionals who are operations researchers, management scientists, computer scientists, statisticians, decision analysts, marketing managers and financial analysts.