David Bernstein

Terry L. Friesz

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.

Foundations of Network Optimization and Games

Tan C. Miller

Roger L. Tobin

This is a book about the simultaneous location, production and distri bution decisions of a firm entering a competitive market whose spatial nature is describable by a network in which the market either achieves an equilibrium or is equilibrium tending. As such, the problem is of clear theoretical and practical importance, for it is a rather general version of the problem faced by real firms every day in deciding where to locate. Further, the timeliness of this subject manifests itself in the growing excitement and interest found both in the research/academic communities and in the practitioner/private industry communities for more comprehensive approaches to competitive facility location analy sis and equilibrium modeling of networks. The desire both for new conceptual approaches yielding enhanced insights and for practical methodologies to capture these insights drives this interest. While nor mative, deterministic facility location modeling techniques currently provide valuable input into the location decision-making process, re searchers and practitioners alike have realized the vast and relatively untapped potential of more advanced location decision making tech niques. In this book, we develop what we believe represents a major new line of research in the field of competitive facility location analysis; namely, equilibrium facility location modeling. In particular, this book offers a number of innovations in the mathe matical analysis and computation of solutions to location models which we have pioneered and which are collected under a single cover for the first time.

Terry L. Friesz

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