Uniquely blends mathematical theory and algorithm design for
understanding and modeling real-world problems
Optimization 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 how to think about
the problem, not just what to think. Relevant historical summaries
can be found throughout the book, and each chapter is designed as
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. The book's various examples are
accompanied by the appropriate models and calculations, and a
related Web site features these models along with Maple(TM) and
MATLAB(R) content for the discussed calculations.
Thoroughly class-tested to ensure a straightforward, hands-on
approach, "Deterministic Operations Research" is an excellent book
for operations research of linear optimization courses at the
upper-undergraduate and graduate levels. It also serves as an
insightful reference for individuals working in the fields of
mathematics, engineering, computer science, and operations research
who use and design algorithms to solve problem in their everyday
work.
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