{"product_id":"linear-programming-and-network-flows-isbn-9780470462720","title":"Linear Programming and Network Flows","description":"\u003cb\u003eThe authoritative guide to modeling and solving complex problems with linear programming—extensively revised, expanded, and updated\u003c\/b\u003e  \u003cp\u003eThe only book to treat both linear programming techniques and network flows under one cover, \u003ci\u003eLinear Programming and Network Flows, Fourth Edition\u003c\/i\u003e 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.\u003c\/p\u003e \u003cp\u003eThe 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 \u003ci\u003eFourth Edition\u003c\/i\u003e include:\u003c\/p\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eThe cycling phenomenon in linear programming and the geometry of cycling\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eDuality relationships with cycling\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eElaboration on stable factorizations and implementation strategies\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eStabilized column generation and acceleration of Benders and Dantzig-Wolfe decomposition methods\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eLine search and dual ascent ideas for the out-of-kilter algorithm\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eHeap implementation comments, negative cost circuit insights, and additional convergence analyses for shortest path problems\u003c\/p\u003e \u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eThe 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 \u003ci\u003eNotes\u003c\/i\u003e and \u003ci\u003eReferences\u003c\/i\u003e 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.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eLinear Programming and Network Flows, Fourth Edition\u003c\/i\u003e 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.\u003c\/p\u003e  \u003cb\u003ePreface.\u003c\/b\u003e  \u003cp\u003e\u003cb\u003eONE: INTRODUCTION\u003c\/b\u003e.\u003c\/p\u003e \u003cp\u003e1.1 The Linear Programming Problem.\u003c\/p\u003e \u003cp\u003e1.2 Linear Programming Modeling and Examples.\u003c\/p\u003e \u003cp\u003e1.3 Geometric Solution.\u003c\/p\u003e \u003cp\u003e1.4 The Requirement Space.\u003c\/p\u003e \u003cp\u003e1.5 Notation.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003eNotes and References.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eTWO: LINEAR ALGEBRA, CONVEX ANALYSIS, AND POLYHEDRAL SETS.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Vectors.\u003c\/p\u003e \u003cp\u003e2.2 Matrices.\u003c\/p\u003e \u003cp\u003e2.3 Simultaneous Linear Equations.\u003c\/p\u003e \u003cp\u003e2.4 Convex Sets and Convex Functions.\u003c\/p\u003e \u003cp\u003e2.5 Polyhedral Sets and Polyhedral Cones.\u003c\/p\u003e \u003cp\u003e2.6 Extreme Points, Faces, Directions, and Extreme Directions of Polyhedral Sets: Geometric Insights.\u003c\/p\u003e \u003cp\u003e2.7 Representation of Polyhedral Sets.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003eNotes and References.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eTHREE: THE SIMPLEX METHOD\u003c\/b\u003e.\u003c\/p\u003e \u003cp\u003e3.1 Extreme Points and Optimality.\u003c\/p\u003e \u003cp\u003e3.2 Basic Feasible Solutions.\u003c\/p\u003e \u003cp\u003e3.3 Key to the Simplex Method.\u003c\/p\u003e \u003cp\u003e3.4 Geometric Motivation of the Simplex Method.\u003c\/p\u003e \u003cp\u003e3.5 Algebra of the Simplex Method.\u003c\/p\u003e \u003cp\u003e3.6 Termination: Optimality and Unboundedness.\u003c\/p\u003e \u003cp\u003e3.7 The Simplex Method.\u003c\/p\u003e \u003cp\u003e3.8 The Simplex Method in Tableau Format.\u003c\/p\u003e \u003cp\u003e3.9 Block Pivoting.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003eNotes and References.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eFOUR: STARTING SOLUTION AND CONVERGENCE.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 The Initial Basic Feasible Solution.\u003c\/p\u003e \u003cp\u003e4.2 The Two-Phase Method.\u003c\/p\u003e \u003cp\u003e4.3 The Big-M Method.\u003c\/p\u003e \u003cp\u003e4.4 How Big Should Big-M Be?\u003c\/p\u003e \u003cp\u003e4.5 The Single Artificial Variable Technique.\u003c\/p\u003e \u003cp\u003e4.6 Degeneracy, Cycling, and Stalling.\u003c\/p\u003e \u003cp\u003e4.7 Validation of Cycling Prevention Rules.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003eNotes and References.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eFIVE: SPECIAL SIMPLEX IMPLEMENTATIONS AND OPTIMALITY CONDITIONS.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 The Revised Simplex Method.\u003c\/p\u003e \u003cp\u003e5.2 The Simplex Method for Bounded Variables.\u003c\/p\u003e \u003cp\u003e5.3 Farkas’ Lemma via the Simplex Method.\u003c\/p\u003e \u003cp\u003e5.4 The Karush-Kuhn-Tucker Optimality Conditions.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003eNotes and References.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eSIX: DUALITY AND SENSITIVITY ANALYSIS.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Formulation of the Dual Problem.\u003c\/p\u003e \u003cp\u003e6.2 Primal-Dual Relationships.\u003c\/p\u003e \u003cp\u003e6.3 Economic Interpretation of the Dual.\u003c\/p\u003e \u003cp\u003e6.4 The Dual Simplex Method.\u003c\/p\u003e \u003cp\u003e6.5 The Primal-Dual Method.\u003c\/p\u003e \u003cp\u003e6.6 Finding an Initial Dual Feasible Solution: The Artificial Constraint Technique.\u003c\/p\u003e \u003cp\u003e6.7 Sensitivity Analysis.\u003c\/p\u003e \u003cp\u003e6.8 Parametric Analysis.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003eNotes and References.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eSEVEN: THE DECOMPOSITION PRINCIPLE.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 The Decomposition Algorithm.\u003c\/p\u003e \u003cp\u003e7.2 Numerical Example.\u003c\/p\u003e \u003cp\u003e7.3 Getting Started.\u003c\/p\u003e \u003cp\u003e7.4 The Case of Unbounded Region X.\u003c\/p\u003e \u003cp\u003e7.5 Block Diagonal or Angular Structure.\u003c\/p\u003e \u003cp\u003e7.6 Duality and Relationships with other Decomposition Procedures.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003eNotes and References.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eEIGHT: COMPLEXITY OF THE SIMPLEX ALGORITHM AND POLYNOMIAL-TIME ALGORITHMS.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Polynomial Complexity Issues.\u003c\/p\u003e \u003cp\u003e8.2 Computational Complexity of the Simplex Algorithm.\u003c\/p\u003e \u003cp\u003e8.3 Khachian’s Ellipsoid Algorithm.\u003c\/p\u003e \u003cp\u003e8.4 Karmarkar’s Projective Algorithm.\u003c\/p\u003e \u003cp\u003e8.5 Analysis of Karmarkar’s Algorithm: Convergence, Complexity, Sliding Objective Method, and Basic Optimal Solutions.\u003c\/p\u003e \u003cp\u003e8.6 Affine Scaling, Primal-Dual Path-Following, and Predictor-Corrector Variants of Interior Point Methods.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003eNotes and References.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eNINE: MINIMAL-COST NETWORK FLOWS.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 The Minimal-Cost Network Flow Problem.\u003c\/p\u003e \u003cp\u003e9.2 Some Basic Definitions and Terminology from Graph Theory.\u003c\/p\u003e \u003cp\u003e9.3 Properties of the \u003cb\u003eA\u003c\/b\u003e Matrix.\u003c\/p\u003e \u003cp\u003e9.4 Representation of a Nonbasic Vector in Terms of the Basic Vectors.\u003c\/p\u003e \u003cp\u003e9.5 The Simplex Method for Network Flow Problems.\u003c\/p\u003e \u003cp\u003e9.6 An Example of the Network Simplex Method.\u003c\/p\u003e \u003cp\u003e9.7 Finding an Initial Basic Feasible Solution.\u003c\/p\u003e \u003cp\u003e9.8 Network Flows with Lower and Upper Bounds.\u003c\/p\u003e \u003cp\u003e9.9 The Simplex Tableau Associated with a Network Flow Problem.\u003c\/p\u003e \u003cp\u003e9.10 List Structures for Implementing the Network Simplex Algorithm.\u003c\/p\u003e \u003cp\u003e9.11 Degeneracy, Cycling, and Stalling.\u003c\/p\u003e \u003cp\u003e9.12 Generalized Network Problems.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003eNotes and References.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eTEN: THE TRANSPORTATION AND ASSIGNMENT PROBLEMS.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Definition of the Transportation Problem.\u003c\/p\u003e \u003cp\u003e10.2 Properties of the \u003cb\u003eA\u003c\/b\u003e Matrix.\u003c\/p\u003e \u003cp\u003e10.3 Representation of a Nonbasic Vector in Terms of the Basic Vectors.\u003c\/p\u003e \u003cp\u003e10.4 The Simplex Method for Transportation Problems.\u003c\/p\u003e \u003cp\u003e10.5 Illustrative Examples and a Note on Degeneracy.\u003c\/p\u003e \u003cp\u003e10.6 The Simplex Tableau Associated with a Transportation Tableau.\u003c\/p\u003e \u003cp\u003e10.7 The Assignment Problem: (Kuhn’s) Hungarian Algorithm.\u003c\/p\u003e \u003cp\u003e10.8 Alternating Path Basis Algorithm for Assignment Problems.\u003c\/p\u003e \u003cp\u003e10.9 A Polynomial-Time Successive Shortest Path Approach for Assignment Problems.\u003c\/p\u003e \u003cp\u003e10.10 The Transshipment Problem.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003eNotes and References.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eELEVEN: THE OUT-OF-KILTER ALGORITHM\u003c\/b\u003e.\u003c\/p\u003e \u003cp\u003e11.1 The Out-of-Kilter Formulation of a Minimal Cost Network Flow Problem.\u003c\/p\u003e \u003cp\u003e11.2 Strategy of the Out-of-Kilter Algorithm.\u003c\/p\u003e \u003cp\u003e11.3 Summary of the Out-of-Kilter Algorithm.\u003c\/p\u003e \u003cp\u003e11.4 An Example of the Out-of-Kilter Algorithm.\u003c\/p\u003e \u003cp\u003e11.5 A Labeling Procedure for the Out-of-Kilter Algorithm.\u003c\/p\u003e \u003cp\u003e11.6 Insight into Changes in Primal and Dual Function Values.\u003c\/p\u003e \u003cp\u003e11.7 Relaxation Algorithms.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003eNotes and References.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eTWELVE: MAXIMAL FLOW, SHORTEST PATH, MULTICOMMODITY FLOW, AND NETWORK SYNTHESIS PROBLEMS.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 The Maximal Flow Problem.\u003c\/p\u003e \u003cp\u003e12.2 The Shortest Path Problem.\u003c\/p\u003e \u003cp\u003e12.3 Polynomial-Time Shortest Path Algorithms for Networks Having Arbitrary Costs.\u003c\/p\u003e \u003cp\u003e12.4 Multicommodity Flows.\u003c\/p\u003e \u003cp\u003e12.5 Characterization of a Basis for the Multicommodity Minimal-Cost Flow Problem.\u003c\/p\u003e \u003cp\u003e12.6 Synthesis of Multiterminal Flow Networks.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003eNotes and References.\u003c\/p\u003e \u003cp\u003eBIBLIOGRAPHY.\u003c\/p\u003e \u003cp\u003eINDEX.\u003c\/p\u003e  \"The book can be used both as reference and as textbook for advanced undergraduate students and first-year graduate students in the fields of industrial engineering, management, operation research, computer science, mathematics and other engineering disciplines that deal with the subjects of linear programming and network flows.\" (Zentralblatt MATH, 2011)  \u003cp\u003e \u003c\/p\u003e  \u003cb\u003eMokhtar S. Bazaraa, PhD\u003c\/b\u003e, is Emeritus Professor at the H. Milton Stewart School of Industrial and Systems Engineering at Georgia Institute of Technology. He is the coauthor of \u003ci\u003eNonlinear Programming: Theory and Algorithms, Third Edition\u003c\/i\u003e and \u003ci\u003eLinear Programming and Network Flows, Third Edition,\u003c\/i\u003e both published by Wiley.  \u003cp\u003e\u003cb\u003eJohn J. Jarvis, PhD,\u003c\/b\u003e is Emeritus Professor at the H. Milton Stewart School of Industrial and Systems Engineering at Georgia Institute of Technology. A Fellow of the Institute of Industrial Engineers (IIE) and the Institute for Operations Research and the Management Sciences (INFORMS), Dr. Jarvis is the coauthor of \u003ci\u003eLinear Programming and Network Flows, Third Edition\u003c\/i\u003e (Wiley).\u003c\/p\u003e \u003cp\u003e\u003cb\u003eHanif D. Sherali, PhD,\u003c\/b\u003e is University Distinguished Professor and the W. Thomas Rice Chaired Professor of Engineering at the Virginia Polytechnic and State University. A Fellow of INFORMS and IIE, he is the coauthor of \u003ci\u003eNonlinear Programming: Theory and Algorithms, Third Edition\u003c\/i\u003e and \u003ci\u003eLinear Programming and Network Flows, Third Edition,\u003c\/i\u003e both published by Wiley.\u003c\/p\u003e  \u003cb\u003eThe authoritative guide to modeling and solving complex problems with linear programming—extensively revised, expanded, and updated\u003c\/b\u003e  \u003cp\u003eThe only book to treat both linear programming techniques and network flows under one cover, \u003ci\u003eLinear Programming and Network Flows, Fourth Edition\u003c\/i\u003e 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.\u003c\/p\u003e \u003cp\u003eThe 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 \u003ci\u003eFourth Edition\u003c\/i\u003e include:\u003c\/p\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eThe cycling phenomenon in linear programming and the geometry of cycling\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eDuality relationships with cycling\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eElaboration on stable factorizations and implementation strategies\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eStabilized column generation and acceleration of Benders and Dantzig-Wolfe decomposition methods\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eLine search and dual ascent ideas for the out-of-kilter algorithm\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eHeap implementation comments, negative cost circuit insights, and additional convergence analyses for shortest path problems\u003c\/p\u003e \u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eThe 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 \u003ci\u003eNotes\u003c\/i\u003e and \u003ci\u003eReferences\u003c\/i\u003e 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.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eLinear Programming and Network Flows, Fourth Edition\u003c\/i\u003e 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.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989532164325,"sku":"NP9780470462720","price":159.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780470462720.jpg?v=1761784487","url":"https:\/\/k12savings.com\/es\/products\/linear-programming-and-network-flows-isbn-9780470462720","provider":"K12savings","version":"1.0","type":"link"}