Handbook of Optimization in Telecommunications M.G.C. Resende and P.M. Pardalos (Editors) Springer Science + Business Media, 2006.
Chapter 7
Multicommodity network  flow models and algorithms in telecommunications
M. Minoux
Abstract
We present an overview of mathematical optimization models and solution algorithms related to optimal network design and dimensioning in telecommunications. All the models discussed are expressed in terms of minimum cost multicommodity network flows with appropriate choice of link (or node) cost functions. Various special cases related to practical applications are examined, including the linear case, the linear with fixed cost case, and the case of general discontinuous nondecreasing cost functions. It is also shown how the generic models presented can accommodate a variety of constraints frequently encountered in applications, such as, among others, constraints on the choice of routes, robustness and survivability constraints. Finally we provide an overview of recent developments in solution algorithms, emphasizing those approaches capable of finding provably exact solutions, which are essentially based on general mixed integer programming techniques, relaxation, cutting-plane generation techniques and branch & cut.
Keywords: Multicommodity flows, network design, mixed integer programming, relaxation, cutting-planes, constraint generation, branch & cut.