Multicommodity Network Flows: A Survey, Part II: Solution Methods

Abstract

The multicommodity network flow (MCNF) problem is an important and challenging topic in many scheduling and routing applications. As a follow-up survey paper to the previous one that focus on the MCNF applications and formulations, this paper first introduces the conventional MCNF solution methods such as price-directive, resource-directive, and basis partitioning methods, then summarizes recent progress in applying approximation algorithms, interior-point algorithms, quadratic programming algorithms, and heuristics to solve the linear or integral multicommodity network flow problems. Finally the computational performance of different solution methods in literature is compared and directions for future research are suggested.