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.

本书为华章数学译丛中的一本。线性规划是运筹学的一个分支，它是最优化问题领域中最简单、最基本和使用最广泛的方法，广泛应用于工农业、军事、交通运输、决策管理与规划、科学实验等领域。 　　这本教材是从一门高级的本科生数学课程演变而来的。覆盖了线性规划的基本主题，同时包含许多高级主题。通过不同难易程度的习题，为学生提供逐步提高的机会，并使优秀的学生完成更具挑战性的任务。 　　本书特点： 　　强调逻辑和应用建模，使得管理、经济和运筹学等非数学专业的学生能在各自的领域中学习使用线性规划。 　　应用数学工具，但不依赖严密的数学研究进展，为数学专业的高年级学生提供进一步研究所需的理论。 　　难易不同的习题为不同程度的学生提供具有挑战性的任务。 　　附录介绍有关数学规划更深入的材料，为数学专业学生提供高级主题，为面向应用的学生提供已知方法的参考。 　　论述建模问题的系统方法论，为学生指明如何将建模发展为一种技能，而不是依赖他们的直觉解决问题。 　　利用计算机软件解决线性规划问题，指导学生利用各种计算机软件包以及在线软件解决线性规划问题。

"The true merit of this book, however, lies in its pedagogical qualities which are so impressive..." "Throughout the book, the authors make serious efforts to give geometric and intuitive explanations of various algebraic concepts, and they are widely successful in this effort." "In conclusion, this is an outstanding textbook that presents linear optimization in a truly modern and up-to-date light. One reading of this book is sufficient to appreciate the tremendous amount of quality effort that the authors have put into the writing, and I strongly recommend it to all teachers, researchers and practitioners of mathematical programming." --Motakuri Ramana in Optima, Issue 54 Bertsimas and Tsitsiklis have written a comprehensive treatise, offering an easy-to-understand presentation of linear programming and related topics, including network-flow programming and discrete optimization. --Jonathan Bard in Interfaces, Issue 30(4), July 2000