LINEAR AND INTEGER OPTIMIZATION. THEORY AND PRACTICE, 3RD EDITION

Basic Concepts of Linear Optimization
• LINEAR OPTIMIZATION THEORY: BASIC TECHNIQUES
Geometry and Algebra of Feasible Regions
Dantzig’s Simplex Algorithm
Duality, Feasibility, and Optimality
Sensitivity Analysis
Large-Scale Linear Optimization
Integer Linear Optimization
Linear Network Models
Computational Complexity
• LINEAR OPTIMIZATION PRACTICE: ADVANCED TECHNIQUES
Designing a Reservoir for Irrigation
Classifying Documents by Language
Production Planning; A Single Product Case
Production of Coffee Machines
Conflicting Objectives: Producing Versus Importing
Coalition Formation and Profit Distribution
Minimizing Trimloss When Cutting Cardboard
Off-Shore Helicopter Routing
The Catering Service Problem

Appendix A Mathematical Proofs
Appendix B Linear Algebra
Appendix C Graph Theory
Appendix D Convexity
Appendix E Nonlinear Optimization
Appendix F Writing LO-Models in GNU MathProg (GMPL)

Presenting a strong and clear relationship between theory and practice, Linear and Integer Optimization: Theory and Practice is divided into two main parts. The first covers the theory of linear and integer optimization, including both basic and advanced topics. Dantzig’s simplex algorithm, duality, sensitivity analysis, integer optimization models, and network models are introduced.
More advanced topics also are presented including interior point algorithms, the branch-and-bound algorithm, cutting planes, complexity, standard combinatorial optimization models, the assignment problem, minimum cost flow, and the maximum flow/minimum cut theorem.
The second part applies theory through real-world case studies. The authors discuss advanced techniques such as column generation, multiobjective optimization, dynamic optimization, machine learning (support vector machines), combinatorial optimization, approximation algorithms, and game theory.
Besides the fresh new layout and completely redesigned figures, this new edition incorporates modern examples and applications of linear optimization. The book now includes computer code in the form of models in the GNU Mathematical Programming Language (GMPL). The models and corresponding data files are available for download and can be readily solved using the provided online solver.
This new edition also contains appendices covering mathematical proofs, linear algebra, graph theory, convexity, and nonlinear optimization. All chapters contain extensive examples and exercises. This textbook is ideal for courses for advanced undergraduate and graduate students in various fields including mathematics, computer science, industrial engineering, operations research, and management science.