Network Optimization

Linear Network Optimization presents a thorough treatment of classical approaches to network problems such as shortest path, max-flow, assignment, transportation, and minimum cost flow problems.

Using strategic supply chain network design, companies can achieve dramatic savings from their supply chains. Now, experts at IBM and Northwestern University have brought together both the rigorous principles and the practical applications you need to master. You’ll learn how to use supply chain network design to select the right number, location, territory, and size of warehouses, plants, and production lines; and optimize the flow of all products through your supply chain even if extends around the globe. The authors present better ways to decide what to manufacture internally, where to make these products, which products to outsource, and which suppliers to use. They guide you in more effectively managing tradeoffs such as cost vs. service level, improving operational decision-making by integrating analytics throughout supply chain management; and re-optimizing regularly for even greater savings. Supply Chain Network Design combines best practices, the latest methods in optimization and analytics, and cutting-edge case studies: everything you need to maximize the value of supply chain network design. For all supply chain executives, managers, strategists, and analysts; and for all students, instructors, and researchers in advanced supply chain management and/or logistics courses.

Network models are critical tools in business, management, science and industry. “Network Models and Optimization” presents an insightful, comprehensive, and up-to-date treatment of multiple objective genetic algorithms to network optimization problems in many disciplines, such as engineering, computer science, operations research, transportation, telecommunication, and manufacturing. The book extensively covers algorithms and applications, including shortest path problems, minimum cost flow problems, maximum flow problems, minimum spanning tree problems, traveling salesman and postman problems, location-allocation problems, project scheduling problems, multistage-based scheduling problems, logistics network problems, communication network problem, and network models in assembly line balancing problems, and airline fleet assignment problems. The book can be used both as a student textbook and as a professional reference for practitioners who use network optimization methods to model and solve problems.

Network optimization is important in the modeling of problems and processes from such fields as engineering, computer science, operations research, transportation, telecommunication, decision support systems, manufacturing, and airline scheduling. Recent advances in data structures, computer technology, and algorithm development have made it possible to solve classes of network optimization problems that until recently were intractable. The refereed papers in this volume reflect the interdisciplinary efforts of a large group of scientists from academia and industry to model and solve complicated large-scale network optimization problems.

This text describes a series of models, propositions, and algorithms developed in recent years on time-varying networks. References and discussions on relevant problems and studies that have appeared in the literature are integrated in the book. Its eight chapters consider problems including the shortest path problem, the minimum-spanning tree problem, the maximum flow problem, and many more. The time-varying traveling salesman problem and the Chinese postman problem are presented in a chapter together with the time-varying generalized problem. While these topics are examined within the framework of time-varying networks, each chapter is self-contained so that each can be read – and used – separately.

This text presents a modern theory of analysis, control, and optimization for dynamic networks. Mathematical techniques of Lyapunov drift and Lyapunov optimization are developed and shown to enable constrained optimization of time averages in general stochastic systems. The focus is on communication and queueing systems, including wireless networks with time-varying channels, mobility, and randomly arriving traffic. A simple drift-plus-penalty framework is used to optimize time averages such as throughput, throughput-utility, power, and distortion. Explicit performance-delay tradeoffs are provided to illustrate the cost of approaching optimality. This theory is also applicable to problems in operations research and economics, where energy-efficient and profit-maximizing decisions must be made without knowing the future. Topics in the text include the following: - Queue stability theory - Backpressure, max-weight, and virtual queue methods - Primal-dual methods for non-convex stochastic utility maximization - Universal scheduling theory for arbitrary sample paths - Approximate and randomized scheduling theory - Optimization of renewal systems and Markov decision systems Detailed examples and numerous problem set questions are provided to reinforce the main concepts. Table of Contents: Introduction / Introduction to Queues / Dynamic Scheduling Example / Optimizing Time Averages / Optimizing Functions of Time Averages / Approximate Scheduling / Optimization of Renewal Systems / Conclusions

This is a book about infrastructure networks that are intrinsically nonlinear. The networks considered range from vehicular networks to electric power networks to data networks. The main point of view taken is that of mathematical programming in concert with finite-dimensional variational inequality theory. The principle modeling perspectives are network optimization, the theory of Nash games, and mathematical programming with equilibrium constraints. Computational methods and novel mathematical formulations are emphasized. Among the numerical methods explored are network simplex, gradient projection, fixed-point, gap function, Lagrangian relaxation, Dantzig-Wolfe decomposition, simplicial decomposition, and computational intelligence algorithms. Many solved example problems are included that range from simple to quite challenging. Theoretical analyses of several models and algorithms, to uncover existence, uniqueness and convergence properties, are undertaken. The book is meant for use in advanced undergraduate as well as doctoral courses taught in civil engineering, industrial engineering, systems engineering, and operations research degree programs. At the same time, the book should be a useful resource for industrial and university researchers engaged in the mathematical modeling and numerical analyses of infrastructure networks.

Problems in network optimization arise in all areas of technology and industrial management. The topic of network flows has applications in diverse fields such as chemistry, engineering, management science, scheduling and transportation, to name a few. Network Optimization introduces the subject to undergraduate and graduate students in computer science, mathematics and operations research. The focus is mainly on developing the mathematical underpinnings of the techniques that make it possible to solve the several optimization problems covered in the text. The text discusses such topics as optimal branching problems, transshipment problems, shortest path problems, minimum cost flow problems, maximum flow problems, matching in bipartite and nonbipartite graphs and many applications to combinatorics. Also included is a large number of exercises.