Linear Programming and Network Flows

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John Wiley & Sons, Sep 28, 2011 - Mathematics - 768 pages
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The authoritative guide to modeling and solving complex problemswith linear programming—extensively revised, expanded, andupdated

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.

 

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Contents

PREFACE
LINEAR ALGEBRA CONVEX ANALYSIS
POLYHEDRAL SETS 2 1 VECTORS
STARTING SOLUTION AND CONVERGENCE
THE SIMPLEX METHOD 3 1 EXTREME POINTSAND OPTIMALITY
CONDITIONS
DUALITY AND SENSITIVITY ANALYSIS
THE DECOMPOSITION PRINCIPLE
KUHNS
EXERCISES
AND REFERENCES
ALGORITHM
MAXIMAL FLOW SHORTEST PATH MULTICOMMODITY FLOWAND
SYNTHESIS PROBLEMS 12 1 THEMAXIMAL FLOWPROBLEM
PROBLEM
NETWORKS

COMPLEXITY OF THESIMPLEX ALGORITHM
NOTES AND REFERENCES
THE TRANSPORTATION AND ASSIGNMENT

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About the author (2011)

Mokhtar S. Bazaraa, PhD, is Emeritus Professor at the H.Milton Stewart School of Industrial and Systems Engineering atGeorgia Institute of Technology. He is the coauthor of NonlinearProgramming: Theory and Algorithms, Third Edition and LinearProgramming and Network Flows, Third Edition, both published byWiley.

John J. Jarvis, PhD, is Emeritus Professor at the H.Milton Stewart School of Industrial and Systems Engineering atGeorgia Institute of Technology. A Fellow of the Institute ofIndustrial Engineers (IIE) and the Institute for OperationsResearch and the Management Sciences (INFORMS), Dr. Jarvis is thecoauthor of Linear Programming and Network Flows, ThirdEdition (Wiley).

Hanif D. Sherali, PhD, is University DistinguishedProfessor and the W. Thomas Rice Chaired Professor of Engineeringat the Virginia Polytechnic and State University. A Fellow ofINFORMS and IIE, he is the coauthor of Nonlinear Programming:Theory and Algorithms, Third Edition and Linear Programmingand Network Flows, Third Edition, both published by Wiley.

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