A Note on Feasible Flows in Lower-Bounded Multicommodity Networks

Abstract

This note considers the feasibility for two types of multicommodity flow problems: maximal flow problems with both upper and lower arc capacities, and capacitated minimal cost trans-shipment problems. Although closed form conditions analogous to those known for single commodity problems cannot be derived, it is shown that feasibility is equivalent to finding a maximal multicommodity flow of a specified value on a related network with zero lower bounds, a direct extension of well-known results for single commodity networks.