Abstract
A freight forecast model that assigns commodity flows to cyclic commercial vehicles is proposed in this study. The commercial vehicles are formulated to traverse in cycles and include loading and unloading costs at zone centroids. Empty hauls can be tracked, as can transshipment flows by commodity type and by inbound and outbound modes. A linear programming formulation is proposed as well as nonlinear objectives for link and transshipment congestion. An inverse nonlinear programming approach using Karush-Kuhn-Tucker conditions is formulated to calibrate the congestion parameters of this model such that observed flow variables are optimal. Because the forward problem is convex and composed of only equality or non-negativity constraints, it can be readily solved with classical nonlinear optimization methods instead of treating the inverse problem as a nonlinear complementarity problem. The models are tested on a 6-node network with up to 54 transshipment activities. The model is shown to be sensitive to supply side changes on links and transshipment facilities or to fuel cost changes. The appendix includes an inverse traffic assignment problem using the inverse nonlinear programming method.