Manfred W. Padberg

Minendra P. Rijal

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.

Location, Scheduling, Design and Integer Programming

Dimitris Alevras

Manfred Padberg

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.

Manfred W. Padberg

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