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Deterministic Operations Research Models and Methods in Linear Optimization

ISBN-10: 0470484519
ISBN-13: 9780470484517
Edition: 2010
Authors: David J. Rader
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Description: Thoroughly classroom-tested over the past eight years, this book focuses on the study of linear optimization (both continuous and discrete), and it also emphasizes the modeling of real problems as linear optimization problems and designs algorithms  More...

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Book details

Copyright year: 2010
Publisher: John Wiley & Sons, Limited
Publication date: 8/6/2010
Binding: Hardcover
Pages: 632
Size: 6.00" wide x 9.25" long x 1.50" tall
Weight: 2.398
Language: English

Thoroughly classroom-tested over the past eight years, this book focuses on the study of linear optimization (both continuous and discrete), and it also emphasizes the modeling of real problems as linear optimization problems and designs algorithms to solve them.Topics in linear programming, network optimization, and integer programming are discussed, and three aspects of deterministic operations research are emphasized: modeling real-world problems as linear optimization problems; designing algorithms (both heuristic and exact methods) to solve these problems; and using mathematical theory to improve the understanding of the problem, to improve existing algorithms, and to design new algorithms. These three aspects are important for both researchers and practitioners of operations research. Such topics are not always in the forefront of operations research textbooks, and while it is true that many books highlight optimization modeling and algorithms to solve these problems, very few, if any, explicitly discuss the algorithm design process used to solve problems.This book successfully fills this gap in the literature and incorporates these components into the study of linear and integer programming, currently the two most-used optimization models in business and industry. Each chapter of the book is designed to be the continuation of the "story" of how to both model and solve optimization problems by using the specific problems (linear and integer programs) as guides. This enables the reader (and instructors) to see how solution methods can be derived instead of just seeing the final product (the algorithms themselves). Numerous examples and problems as well as relevant historical summaries can be found throughout the text. Each chapter contains at least 20 problems per chapter, with some chapters having many more problems.

Preface
Introduction to Operations Research
What is Deterministic Operations Research?
Introduction to Optimization Modeling
Common Classes of Mathematical Programs
About this Book
Exercises
Linear Programming Modeling
Resource Allocation Models
Work Scheduling Models
Models and Data
Blending Models
Production Process Models
Multiperiod Models: Work Scheduling and Inventory
Linearization of Special Nonlinear Models
Various Forms of Linear Programs
Network Models
Exercises
Integer and Combinatorial Models
Fixed-Charge Models
Set Covering Models
Models Using Logical Constraints
Combinatorial Models
Sports Scheduling and an Introduction to IP Solution Techniques
Exercises
Real-World Operations Research Applications: An Introduction
Vehicle Routing Problems
Facility Location and Network Design Models
Applications in the Airline Industry
Exercises
Introduction to Algorithm Design
Exact and Heuristic Algorithms
What to Ask When Designing Algorithms?
Constructive versus Local Search Algorithms
How Good is our Heuristic Solution?
Examples of Constructive Methods
Example of a Local Search Method
Other Heuristic Methods
Designing Exact Methods: Optimality Conditions
Exercises
Improving Search Algorithms and Convexity
Improving Search and Optimal Solutions
Finding Better Solutions
Convexity: When Does Improving Search Imply Global Optimality?
Farkas' Lemma: When Can No Improving Feasible Direction be Found?
Exercises
Geometry and Algebra of Linear Programs
Geometry and Algebra of "Corner Points"
Fundamental Theorem of Linear Programming
Linear Programs in Canonical Form
Exercises
Solving Linear Programs: Simplex Method
Simplex Method
Making the Simplex Method More Efficient
Convergence, Degeneracy, and the Simplex Method
Finding an Initial Solution: Two-Phase Method
Bounded Simplex Method ?.
Computational Issues
Exercises
Linear Programming Duality
Motivation: Generating Bounds
Dual Linear Program
Duality Theorems
Another Interpretation of the Simplex Method
Farkas' Lemma Revisited
Economic Interpretation of the Dual
Another Duality Approach: Lagrangian Duality
Exercises
Sensitivity Analysis of Linear Programs
Graphical Sensitivity Analysis
Sensitivity Analysis Calculations
Use of Sensitivity Analysis
Parametric Programming
Exercises
Algorithmic Applications of Duality
Dual Simplex Method
Transportation Problem
Column Generation
Dantzig-Wolfe Decomposition
Primal-Dual Interior Point Method
Exercises
Network Optimization Algorithms
Introduction to Network Optimization
Shortest Path Problems
Maximum Flow Problems
Minimum Cost Network Flow Problems
Exercises
Introduction to Integer Programming
Basic Definitions and Formulations
Relaxations and Bounds
Preprocessing and Probing
When are Integer Programs "Easy?"
Exercises
Solving Integer Programs: Exact Methods
Complete Enumeration
Branch-and-Bound Methods
Valid Inequalities and Cutting Planes
Gomory's Cutting Plane Algorithm
Valid Inequalities for 0-1 Knapsack Constraints
Branch-and-Cut Algorithms
Computational Issues
Exercises
Solving Integer Programs: Modern Heuristic Techniques
Review of Local Search Methods: Pros and Cons
Simulated Annealing
Tabu Search
Genetic Algorithms
GRASP Algorithms
Exercises
Background Review
Basic Notation
Graph Theory
Linear Algebra
Reference
Index

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