AbstractThe minimum‐cost formulation of the problem of determining multicommodity flows over a capacitated network subject to resource constraints has been treated in previobs papers. In those treatments only capacitated arcs were assumed and a uniform unit of measure like short tons was used for all commodities. This paper treats the effect of constraints on the nodes of the network, allows the commodities to be measured in their “natural” units and allows the network capacities to be expressed in vehicles per time period‐in some cases giving a more accurate representation of the capacities of the network. This paper describes the solution procedure which uses the column generation technique; it also discusses computational exp