Manfred W. Padberg - Böcker
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3 produkter
3 produkter
Del 3 - International Series in Operations Research & Management Science
Location, Scheduling, Design and Integer Programming
Inbunden, Engelska, 1996
1 625 kr
Skickas inom 10-15 vardagar
This monograph focuses on a class of problems that in effect have yet to be solved. Location, scheduling and design problems are assignment type problems with quadratic cost functions and occur in many contexts. Applications of these problems abound in diverse disciplines, such as anthropology, archeology, architecture, chemistry, computer science, economics, electronics, ergonomics, marketing, operations management, political science, statistical physics, zoology, etc. The book classifies mathematical properties for ten classes of assignment problems: quadratic assignment problems, travelling salesman problems, triangulation problems, linear assignment problems, VLSI circuit layout design problems, multi-processor problems, scheduling problems with interaction costs, operation-scheduling problems, graph and clique partitioning problems, and Boolean quadratic problems. They note that before these problems can be solved computationally, one must know and understand their mathematical properties. After discussing these properties, an integer programming approach is offered for solving them. The computational approach has shown considerable algorithmic success.The heart of this monograph is the theoretical work on assignment problems and the computation results that were produced using algorithms developed at NYU.
Del 3 - International Series in Operations Research & Management Science
Location, Scheduling, Design and Integer Programming
Häftad, Engelska, 2011
1 578 kr
Skickas inom 10-15 vardagar
Location, scheduling and design problems are assignment type problems with quadratic cost functions and occur in many contexts stretching from spatial economics via plant and office layout planning to VLSI design and similar prob lems in high-technology production settings. The presence of nonlinear inter action terms in the objective function makes these, otherwise simple, problems NP hard. In the first two chapters of this monograph we provide a survey of models of this type and give a common framework for them as Boolean quadratic problems with special ordered sets (BQPSs). Special ordered sets associated with these BQPSs are of equal cardinality and either are disjoint as in clique partitioning problems, graph partitioning problems, class-room scheduling problems, operations-scheduling problems, multi-processor assign ment problems and VLSI circuit layout design problems or have intersections with well defined joins as in asymmetric and symmetric Koopmans-Beckmann problems and quadratic assignment problems. Applications of these problems abound in diverse disciplines, such as anthropology, archeology, architecture, chemistry, computer science, economics, electronics, ergonomics, marketing, operations management, political science, statistical physics, zoology, etc. We then give a survey of the traditional solution approaches to BQPSs. It is an unfortunate fact that even after years of investigation into these problems, the state of algorithmic development is nowhere close to solving large-scale real life problems exactly. In the main part of this book we follow the polyhedral approach to combinatorial problem solving because of the dramatic algorith mic successes of researchers who have pursued this approach.
800 kr
Skickas inom 10-15 vardagar
This book offers a comprehensive treatment of the exercises and case studies as well as summaries of the chapters of the book "Linear Optimization and Extensions" by Manfred Padberg. It covers the areas of linear programming and the optimization of linear functions over polyhedra in finite dimensional Euclidean vector spaces. Here are the main topics treated in the book: Simplex algorithms and their derivatives including the duality theory of linear programming. Polyhedral theory, pointwise and linear descriptions of polyhedra, double description algorithms, Gaussian elimination with and without division, the complexity of simplex steps. Projective algorithms, the geometry of projective algorithms, Newtonian barrier methods. Ellipsoids algorithms in perfect and in finite precision arithmetic, the equivalence of linear optimization and polyhedral separation. The foundations of mixed-integer programming and combinatorial optimization.