Deterministic Operations Research

David J. Rader 지음

Wiley 2013년 06월 07일 출간

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Uniquely blends mathematical theory and algorithm design for understanding and modeling real-world problemsOptimization modeling and algorithms are key components to problem-solving across various fields of research, from operations research and mathematics to computer science and engineering. Addressing the importance of the algorithm design process. Deterministic Operations Research focuses on the design of solution methods for both continuous and discrete linear optimization problems. The result is a clear-cut resource for understanding three cornerstones of deterministic operations research: modeling real-world problems as linear optimization problem; designing the necessary algorithms to solve these problems; and using mathematical theory to justify algorithmic development.Treating real-world examples as mathematical problems, the author begins with an introduction to operations research and optimization modeling that includes applications form sports scheduling an the airline industry. Subsequent chapters discuss algorithm design for continuous linear optimization problems, covering topics such as convexity. Farkas' Lemma, and the study of polyhedral before culminating in a discussion of the Simplex Method. The book also addresses linear programming duality theory and its use in algorithm design as well as the Dual Simplex Method. Dantzig-Wolfe decomposition, and a primal-dual interior point algorithm. The final chapters present network optimization and integer programming problems, highlighting various specialized topics including label-correcting algorithms for the shortest path problem, preprocessing and probing in integer programming, lifting of valid inequalities, and branch and cut algorithms.Concepts and approaches are introduced by outlining examples that demonstrate and motivate theoretical concepts. The accessible presentation of advanced ideas makes core aspects easy to understand and encourages readers to understand ho

목차

Preface.1. Introduction to Operations Research.1.1 What is Deterministic Operations Research?1.2 Introduction to Optimization Modeling.1.3 Common Classes of Mathematical Programs.1.4 About the Book.Exercises.2. Linear Programming Modeling.2.1 Resource Allocation Models.2.2 Work Scheduling Models.2.3 Models and Data.2.4 Blending Models.2.5 Production Process Models.2.6 Multiperiod Models: Work Scheduling and Inventory.2.7 Linearization of Special Nonlinear Models.2.8 Various Forms of Linear Programs.2.9 Network Models.Exercises.3. Integer and Combinatorial Models.3.1 Fixed-Charge Models.3.2 Set Covering Models.3.3 Models Using Logical Constraints.3.4 Combinatorial Models.3.5 Sports Scheduling and an Introduction to IP Solution Technques.Exercises.4. Real-World Operations Research Applications:& An Introduction.4.1 Vehicle Routing Problems.4.2 Facility Location and Network Design Models.4.3 Applications in the Airline Industry.Exercises.5. Introduction to Algorithm.5.1 Exact and Heuristic Algorithms.5.2 What to Ask When Designing Algorithms?5.3 Constructive versus Local Search Algorithms.5.4 How Good is our Heuristic Solution?5.5 Example of a Local Search Method.5.7 Other Heuristic Methods.5.8 Designing Exact Methods: Optimality Conditions.Exercises.6. Improving Search Algorithms and Comvexity.6.1 Improving Search and Optimal Solutions.6.2 Finding Better Solutions.6.3 Convexity: When Does Improving Search Imply Global Optimality?6.4 Farkas&- Lemma: When Can No Improving Feasible Direction be Found?Exercises.7. Geometry and Algebra of Linear Programs.7.1 Geometry and Algebra of &"Corner Points&".7.2 Fundamental Theorem of Linear Programming.7.3 Linear Programs in Canonical Form.Exercises.8. Solving Linear Programs: Simplex Method.8.1 Sim

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“Dr. Phillips has used other texts, but he is especially enthused with this book, influenced by student feedback. He says, “Algorithmic ideas are introduced at a pace that emphasizes and encourages intuitive understanding.”& (Informs Journal on Computing, 1 June 2012)"The book is aimed at serving upper-undergraduate and graduate students of all fields as a comprehensive textbook or as a reference for studies on the subject." (Zentralblatt MATH, 2011)"The result is a clear-cut resource for understanding three cornerstones of deterministic operations research: modeling real-world problems as linear optimization problems; designing the necessary algorithms to solve these problems; and using mathematical theory to justify algorithmic development." (InfoTECH Spotlight - TMCnet, 8 February 2011)&

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저자(글) David J. Rader

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David J. Rader Jr., PhD, is Associate Professor of Mathematics at Rose-Hulman Institute of Technology, where he is also the editor of the Rose-Hulman Institute of Technology Undergraduate Mathematics Journal. Dr. Rader currently focuses his research in the areas of nonlinear 0-1 optimization, computational integer programming, and exam time timetabling.