Optimization in Operations Research, 2nd edition

For courses in Operations Research, Optimization, and Nonlinear Programming.

Developing skills and intuitions through accessible optimization models and analysis.

Rardin’s Optimization in Operations Research, Second Edition builds on the critically acclaimed first edition published nearly two decades ago and named Book of the Year in 1999 by the Institute of Industrial Engineers. The goal of the Second Edition is to make the tools of optimization modeling and analysis even more widely accessible to advanced undergraduate and beginning graduate students, as well as to researchers and working practitioners who use it as a reference for self-study. The emphasis lies in developing skills and intuitions that students can apply in real settings or later coursework.

Like the first, the Second Edition covers the full scope of optimization (mathematical programming), spanning linear, integer, nonlinear, network, and dynamic programming models and algorithms, in both single and multiobjective contexts. New material adds large-scale, stochastic and complexity topics, while broadly deepening mathematical rigor without sacrificing the original’s intuitive style. This edition also continues the author’s belief that making optimization materials accessible and exciting to readers of diverse backgrounds requires a continuing discourse on optimization modeling. Every algorithm and analytic principle is developed in the context of a brief story, and computational exercises often begin with a formulation step.

Optimization in Operations Research offers the following features to facilitate learning:

NEW! Practical coursework with a strong emphasis on skills that can be applied in real-life settings

• Coverage of linear programming techniques is expanded to encompass dual and primal-dual methods.
• Mathematical rigor is added to justifications of methods throughout the book, including tracking computational orders.
• Assignments on the Hungarian Algorithm along with minimum and maximum spanning tree methods make these crucial topics more accessible than ever.
• The nonlinear now includes coverage of the popular Sequential Quadratic programming method.
• Chapter 13 is entirely devoted to large-scale optimisation techniques including Delayed Column Generations, Lagrangian Relaxation, Dantzig-Wolfe Decomposition, and Benders’ Partitioning.
• Stochastic optimisation is covered for the first time with Stochastic Programming and Markov Decision Processes.
• Added sections rigorously formalise optimality conditions for linear programming, and cutting plane theory.
• Chapter 14 treats the theory of computational complexity to provide a rigorous foundation for comparing problems and algorithms.
• Bridges the gaps in comprehension by focusing on the strategies behind methods, and on their relative tractability, while offering only limited arguments for their correctness.

Integrates treatment of network flows, integer and combinatorial optimisation, and nonlinear programming with coverage of standard linear programming topics

• Prepares students for the variety of model forms needed in practice and provides instructors with flexibility in depth of coverage.
• Develops algorithms around a unified search theme, providing students with a paradigm that will extend into more advanced cases.
• Allows instructors to efficiently treat both simplex and interior-point methods for linear programming.
• Integrates modeling and formulation with coverage of optimisation algorithms to develop an understanding of formulation skills, algorithms and principles simultaneously.
• Highlights all main definitions, principles and algorithms in special-interest boxes.
• Features one- to two-page primers reviewing prerequisite material where necessary.
• Sample exercises recap constructions and computations of longer developments.
• Includes a wealth of charts, tables and figures.
• Exercises at the ends of chapters provide practice with calculations, concepts, and formulation of small problems, in addition to developing modeling skills. .

NEW! Practical coursework with a strong emphasis on skills that can be applied in real-life settings

• NEW! Coverage of linear programming techniques is expanded to encompass dual and primal-dual methods.
• NEW! Mathematical rigor is added to justifications of methods throughout the book, including tracking computational orders.
• NEW! Assignments on the Hungarian Algorithm along with minimum and maximum spanning tree methods make these crucial topics more accessible than ever.
• NEW! The nonlinear now includes coverage of the popular Sequential Quadratic programming method.
• NEW! Chapter 13 is entirely devoted to large-scale optimization techniques including Delayed Column Generations, Lagrangian Relaxation, Dantzig-Wolfe Decomposition, and Benders’ Partitioning.
• NEW! Stochastic optimization is covered for the first time with Stochastic Programming and Markov Decision Processes.
• NEW! Added sections rigorously formalize optimality conditions for linear programming, and cutting plane theory.
• NEW! Chapter 14 treats the theory of computational complexity to provide a rigorous foundation for comparing problems and algorithms.
• NEW! Bridges the gaps in comprehension by focusing on the strategies behind methods, and on their relative tractability, while offering only limited arguments for their correctness.