A discrete transportation network design problem with combined trip distribution and assignment

Three network design problems are formulated for optimizing discrete additions to link capacities. Trip distribution and assignment are functions of travel expenditure in each problem. A reformulation of Wilson's doubly-constrained trip distribution problem, in which entropy instead of total travel expenditure is constrained, provides zone-to-zone flows in each problem. Entropy is interpreted as a measure of zone-to-zone trip-making interaction. Computational results for a toy network are reported.