“Combines the theoretical and practical aspects of linear and integer programming. Provides practical case studies and techniques, including rounding-off, column-generation, game theory, multiobjective optimization, and goal programming, as well as real-world solutions to the transportation and transshipment problem, project scheduling, and decentralization.”

Available at amazon.com, amazon.co.uk, crcpress.com, Google Play and bol.com.

A preview is available on Google Books.

Features

  • Reflects modern approaches and new applications.
  • Extends prototype examples to more realistic settings.
  • Introduces the elementary theory of linear and integer optimization.
  • Uses real-world case studies to illustrate application of the theory.

Summary

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.

Online resources

  • Table of contents.
  • A solution manual (with solutions to selected exercises) is available upon request via email.

Online optimizer

To assist teaching students hands-on optimization and modeling skills, we provide an online linear optimization solver app. This web application:

  • Solves linear and integer optimization models through an in-browser version of the GNU GLPK optimizer.
  • Has several built-in example models.
  • Performs sensitivity analysis.
  • Graphs the feasible region (for two-dimensional models).
  • Integrates with Google Drive.

Source code and data files

All source code in this book and on this website is licensed under the MIT License.

Chapter 1: Basic concepts of linear optimization

Chapter 6: Large-scale linear optimization

Chapter 7: Integer linear optimization

Chapter 8: Linear network models

Chapter 10: Designing a reservoir for irrigation

Chapter 11: Classifying documents by language

Chapter 12: Production planning: a single product case

Chapter 13: Production of coffee machines

Chapter 14: Conflicting objectives: producing versus importing

Chapter 15: Coalition formation and profit distribution

Chapter 16: Minimizing trimloss when cutting cardboard

Chapter 17: Off-shore helicopter routing

Chapter 18: The catering service problem

Appendix E: Writing LP-models in GNU MathProg