Decomposition Techniques in Mathematical Programming: Engineering and Science Applications

Springer Science & Business Media
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Optimization plainly dominates the design, planning, operation, and c- trol of engineering systems. This is a book on optimization that considers particular cases of optimization problems, those with a decomposable str- ture that can be advantageously exploited. Those decomposable optimization problems are ubiquitous in engineering and science applications. The book considers problems with both complicating constraints and complicating va- ables, and analyzes linear and nonlinear problems, with and without in- ger variables. The decomposition techniques analyzed include Dantzig-Wolfe, Benders, Lagrangian relaxation, Augmented Lagrangian decomposition, and others. Heuristic techniques are also considered. Additionally, a comprehensive sensitivity analysis for characterizing the solution of optimization problems is carried out. This material is particularly novel and of high practical interest. This book is built based on many clarifying, illustrative, and compu- tional examples, which facilitate the learning procedure. For the sake of cl- ity, theoretical concepts and computational algorithms are assembled based on these examples. The results are simplicity, clarity, and easy-learning. We feel that this book is needed by the engineering community that has to tackle complex optimization problems, particularly by practitioners and researchersinEngineering,OperationsResearch,andAppliedEconomics.The descriptions of most decomposition techniques are available only in complex and specialized mathematical journals, di?cult to understand by engineers. A book describing a wide range of decomposition techniques, emphasizing problem-solving, and appropriately blending theory and application, was not previously available.
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About the author

Enrique Castillo is Professor of Applied Mathematics at the University of Cantabria in Santander (Spain). He is a Mathematician and a Civil engineer and Member of the Spanish Royal Academy of Engineering. He has taught at several other universities in the Europe and America. The author/coauthor of eleven other books in English and fourteen in Spanish, and more than 300 papers in journals and Congresses. More information can be found at his Web site: http: //

Juan R. Ruiz-Tolosa is an Industrial and Civil Engineer and has been Professor of Algebra, Tensors, Topology, Differential Geometry and Calculus at the Civil Engineering School, University of Cantabria for 30 years. His field of research includes Number Theory, Euclidean Geometry, Elliptic Integrals, Algebraic Roots of Equations, etc.

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Additional Information

Springer Science & Business Media
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Published on
Apr 28, 2006
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Best For
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Business & Economics / Operations Research
Mathematics / Applied
Technology & Engineering / General
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Today, time is the cutting edge. In fact, as a strategic weapon, contend George Stalk, Jr., and Thomas M. Hout, time is the equivalent of money, productivity, quality, even innovation. In this path-breaking book based upon ten years of research, the authors argue that the ways leading companies manage time—in production, in new product development, and in sales and distribution—represent the most powerful new sources of competitive advantage.
With many detailed examples from companies that have put time-based strategies in place, such as Federal Express, Ford, Milliken, Honda, Deere, Toyota, Sun Microsystems, Wal-Mart, Citicorp, Harley-Davidson, and Mitsubishi, the authors describe exactly how reducing elapsed time can make the critical difference between success and failure. Give customers what they want when they want it, or the competition will. Time-based companies are offering greater varieties of products and services, at lower costs, and with quicker delivery times than their more pedestrian competitors. Moreover, the authors show that by refocusing their organizations on responsiveness, companies are discovering that long-held assumptions about the behavior of costs and customers are not true: Costs do not increase when lead times are reduced; they decline. Costs do not increase with greater investment in quality; they decrease. Costs do not go up when product variety is increased and response time is decreased; they go down. And contrary to a commonly held belief that customer demand would be only marginally improved by expanded product choice and better responsiveness, the authors show that the actual results have been an explosion in the demand for the product or service of a time-sensitive competitor, in most cases catapulting it into the most profitable segments of its markets.
With persuasive evidence, Stalk and Hout document that time consumption, like cost, is quantifiable and therefore manageable. Today's new-generation companies recognize time as the fourth dimension of competitiveness and, as a result, operate with flexible manufacturing and rapid-response systems, and place extraordinary emphasis on R&D and innovation. Factories are close to the customers they serve. Organizations are structured to produce fast responses rather than low costs and control. Companies concentrate on reducing if not eliminating delays and using their response advantage to attract the most profitable customers.
Stalk and Hout conclude that virtually all businesses can use time as a competitive weapon. In industry after industry, they illustrate the processes involved in becoming a time-based competitor and the ways managers can open and sustain a significant advantage over the competition.
This book is an attempt to provide a uni?ed methodology to derive models for fatigue life. This includes S-N, ?-N and crack propagation models. This is not a conventional book aimed at describing the fatigue fundamentals, but rather a book in which the basic models of the three main fatigue approaches, the stress-based, the strain-based and the fracture mechanics approaches, are contemplated from a novel and integrated point of view. On the other hand, as an alternative to the preferential attention paid to deterministic models based on the physical, phenomenological and empirical description of fatigue, their probabilistic nature is emphasized in this book, in which stochastic fatigue and crack growth models are presented. This book is the result of a long period of close collaborationbetween its two authors who, although of di?erent backgrounds, mathematical and mechanical, both have a strong sense of engineering with respect to the fatigue problem. When the authors of this book ?rst approached the fatigue ?eld in 1982 (twenty six years ago), they found the following scenario: 1. Linear, bilinear or trilinear models were frequently proposed by relevant laboratoriesandacademiccenterstoreproducetheW ̈ ohler?eld. Thiswas the case of well known institutions, which justi?ed these models based on clientrequirementsorpreferences. Thisledtotheinclusionofsuchmodels and methods as, for example, the up-and-down, in standards and o?cial practical directives (ASTM, Euronorm, etc.), which have proved to be unfortunate.
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