The only book to treat both linear programming techniques andnetwork flows under one cover, Linear Programming and NetworkFlows, Fourth Edition has been completely updated with thelatest developments on the topic. This new edition continues tosuccessfully emphasize modeling concepts, the design and analysisof algorithms, and implementation strategies for problems in avariety of fields, including industrial engineering, managementscience, operations research, computer science, andmathematics.
The book begins with basic results on linear algebra and convexanalysis, and a geometrically motivated study of the structure ofpolyhedral sets is provided. Subsequent chapters include coverageof cycling in the simplex method, interior point methods, andsensitivity and parametric analysis. Newly added topics in theFourth Edition include:
The cycling phenomenon in linear programming and the geometry ofcycling
Duality relationships with cycling
Elaboration on stable factorizations and implementationstrategies
Stabilized column generation and acceleration of Benders andDantzig-Wolfe decomposition methods
Line search and dual ascent ideas for the out-of-kilteralgorithm
Heap implementation comments, negative cost circuit insights,and additional convergence analyses for shortest path problems
The authors present concepts and techniques that are illustratedby numerical examples along with insights complete with detailedmathematical analysis and justification. An emphasis is placed onproviding geometric viewpoints and economic interpretations as wellas strengthening the understanding of the fundamental ideas. Eachchapter is accompanied by Notes and Referencessections that provide historical developments in addition tocurrent and future trends. Updated exercises allow readers to testtheir comprehension of the presented material, and extensivereferences provide resources for further study.
Linear Programming and Network Flows, Fourth Edition isan excellent book for linear programming and network flow coursesat the upper-undergraduate and graduate levels. It is also avaluable resource for applied scientists who would like to refreshtheir understanding of linear programming and network flowtechniques.