This book describes the theory of linear and integer programming and surveys the algorithms for linear and integer programming problems, focusing on complexity analysis. It aims at complementing the more practically oriented books in this field. A special feature is the author’s coverage of important recent developments in linear and integer programming. Applications to combinatorial optimization are given, and the author also includes extensive historical surveys and bibliographies. The book is intended for graduate students and researchers in operations research, mathematics and computer science. It will also be of interest to mathematical historians.

Uniquely blends mathematical theory and algorithm design for understanding and modeling real-world problems

Optimization modeling and algorithms are key components to problem-solving across various fields of research, from operations research and mathematics to computer science and engineering. Addressing the importance of the algorithm design process. "Deterministic Operations Research" focuses on the design of solution methods for both continuous and discrete linear optimization problems. The result is a clear-cut resource for understanding three cornerstones of deterministic operations research: modeling real-world problems as linear optimization problem; designing the necessary algorithms to solve these problems; and using mathematical theory to justify algorithmic development.

Treating real-world examples as mathematical problems, the author begins with an introduction to operations research and optimization modeling that includes applications form sports scheduling an the airline industry. Subsequent chapters discuss algorithm design for continuous linear optimization problems, covering topics such as convexity. Farkas' Lemma, and the study of polyhedral before culminating in a discussion of the Simplex Method. The book also addresses linear programming duality theory and its use in algorithm design as well as the Dual Simplex Method. Dantzig-Wolfe decomposition, and a primal-dual interior point algorithm. The final chapters present network optimization and integer programming problems, highlighting various specialized topics including label-correcting algorithms for the shortest path problem, preprocessing and probing in integer programming, lifting of valid inequalities, and branch and cut algorithms.

Concepts and approaches are introduced by outlining examples that demonstrate and motivate theoretical concepts. The accessible presentation of advanced ideas makes core aspects easy to understand and encourages readers to understand how to think about the problem, not just what to think. Relevant historical summaries can be found throughout the book, and each chapter is designed as the continuation of the "story" of how to both model and solve optimization problems by using the specific problems-linear and integer programs-as guides. The book's various examples are accompanied by the appropriate models and calculations, and a related Web site features these models along with Maple(TM) and MATLAB(R) content for the discussed calculations.

Thoroughly class-tested to ensure a straightforward, hands-on approach, "Deterministic Operations Research" is an excellent book for operations research of linear optimization courses at the upper-undergraduate and graduate levels. It also serves as an insightful reference for individuals working in the fields of mathematics, engineering, computer science, and operations research who use and design algorithms to solve problem in their everyday work.

Linear optimisation is concerned with the solution of maximisation and minimisation problems that are described by linear functions and linear constraints. In particular, linear programming problems, assignment problems and transportation problems. Problems of this kind arise in areas such as engineering (e.g. optimising aggregate blends), economics (e.g. linear economic models), financial management (e.g. trend channels) and business (e.g. product mix, manpower allocation and transport management). This book is intended to introduce this highly applicable branch of applied mathematics to undergraduate and postgraduate students studying mathematics, engineering, operational research and business.

A thorough and highly accessible resource for analysts in a broad range of social sciences.

Optimization: Foundations and Applications presents a series of approaches to the challenges faced by analysts who must find the best way to accomplish particular objectives, usually with the added complication of constraints on the available choices. Award-winning educator Ronald E. Miller provides detailed coverage of both classical, calculus-based approaches and newer, computer-based iterative methods.

Dr. Miller lays a solid foundation for both linear and nonlinear models and quickly moves on to discuss applications, including iterative methods for root-finding and for unconstrained maximization, approaches to the inequality constrained linear programming problem, and the complexities of inequality constrained maximization and minimization in nonlinear problems. Other important features include:

• More than 200 geometric interpretations of algebraic results, emphasizing the intuitive appeal of mathematics
• Classic results mixed with modern numerical methods to aid users of computer programs
• Extensive appendices containing mathematical details important for a thorough understanding of the topic

With special emphasis on questions most frequently asked by those encountering this material for the first time, Optimization: Foundations and Applications is an extremely useful resource for professionals in such areas as mathematics, engineering, economics and business, regional science, geography, sociology, political science, management and decision sciences, public policy analysis, and numerous other social sciences.

The authoritative guide to modeling and solving complex problems with linear programming--extensively revised, expanded, and updated

The only book to treat both linear programming techniques and network flows under one cover, "Linear Programming and Network Flows, Fourth Edition" has been completely updated with the latest developments on the topic. This new edition continues to successfully emphasize modeling concepts, the design and analysis of algorithms, and implementation strategies for problems in a variety of fields, including industrial engineering, management science, operations research, computer science, and mathematics.

The book begins with basic results on linear algebra and convex analysis, and a geometrically motivated study of the structure of polyhedral sets is provided. Subsequent chapters include coverage of cycling in the simplex method, interior point methods, and sensitivity and parametric analysis. Newly added topics in the "Fourth Edition" include:

The cycling phenomenon in linear programming and the geometry of cycling

Duality relationships with cycling

Elaboration on stable factorizations and implementation strategies

Stabilized column generation and acceleration of Benders and Dantzig-Wolfe decomposition methods

Line search and dual ascent ideas for the out-of-kilter algorithm

Heap implementation comments, negative cost circuit insights, and additional convergence analyses for shortest path problems

The authors present concepts and techniques that are illustrated by numerical examples along with insights complete with detailed mathematical analysis and justification. An emphasis is placed on providing geometric viewpoints and economic interpretations as well as strengthening the understanding of the fundamental ideas. Each chapter is accompanied by "Notes" and "References" sections that provide historical developments in addition to current and future trends. Updated exercises allow readers to test their comprehension of the presented material, and extensive references provide resources for further study.

"Linear Programming and Network Flows, Fourth Edition" is an excellent book for linear programming and network flow courses at the upper-undergraduate and graduate levels. It is also a valuable resource for applied scientists who would like to refresh their understanding of linear programming and network flow techniques.