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.