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Multiple criteria optimization. Theory, computation, and application. (English) Zbl 0663.90085
Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics. New York: John Wiley & Sons, Inc. XXII, 546 p.; $ 39.95 (1986).
This book serves as a teaching text and as a comprehensive reference volume concerning the principles and practices of multicriteria optimization. Apart from calculus and computers, the book is self- contained because of the review material in Chapter 2 (Mathematical background, especially from linear algebra and set theory) and Chapter 3 (Single objective linear programming). Further preliminary chapters deal with methods for determining all alternative optima in linear optimization and linear programming problems with parameters in the objective function. Chapters 6-8 discuss the subtleties involved with the solution set notion of efficiency, and Chapter 9 presents the theory of linear vector-maximization for computing all efficient points. Chapter 10 addresses goal programming, Chapter 11, methods for filtering a representative subset of a larger set, and Chapter 12, multiple objective linear fractional programming. The discussion of interactive procedures in Chapters 13-15 is the climax of the book. Reports on some interactive applications, comments about the future and a bibliography are given in the last chapters. Many numerical examples, graphical illustrations and problem exercises support the understanding. For the present procedures references to available software are given, especially to those which are based on the MPSX-package.

MSC:
90C31 Sensitivity, stability, parametric optimization
90-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operations research and mathematical programming
90C32 Fractional programming
90C05 Linear programming
90B50 Management decision making, including multiple objectives