Multicommodity network flows—A survey

TLDR

The multicommodity flow problem naturally models shipping or transmitting commodities, vehicles, or messages across network nodes, and recent applications of mathematical programming to traffic equilibrium and computer network analysis have renewed interest. The report surveys the literature on the multicommodity flow problem and discusses solution techniques for both linear and nonlinear flow problems. Solution techniques include decomposition, partitioning, compact inverse methods, primal‑dual algorithms for linear problems, and various feasible‑direction methods for nonlinear problems. The survey concludes with applications and computational experience for both linear and nonlinear multicommodity flow problems.

Abstract

Abstract This report aims at a comprehensive survey of the literature dealing with the multicommodity flow problem. This problem arises naturally in network modelling wherever commodities, vehicles, or messages are to be shipped or transmitted from certain nodes of an underlying network to some others. Recent applications of mathematical programming techniques to traffic equilibrium problems in transportation studies as well as computer networks analysis has renewed considerable interest in this problem. This report discusses solution techniques for both linear and nonlinear flow problems. The former includes decomposition, partitioning, compact inverse methods, and primal‐dual algorithms. We describe a variety of feasible direction methods for the latter. The report concludes by giving applications and computational experience for both types of problems.