Linear Programming and Network Flows (eBook)

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.