A multi-modal supply-demand equilibrium model for predicting intercity freight flows

In this paper a new approach to intercity freight transportation system modeling is developed. Modeling formulation considers supply-demand equilibrium, where the demand side represents the behavior of shippers (cargo owners) and the supply side represents the behavior of carriers (transportation operators). Shippers decisions considered include choice of destination, mode, carrier for pure modes and transfer point for combined modes. Carriers take routing decisions over a multi-modal, multi-product and multi-operator network. A new mathematical formulation, not known before, is proposed to find consistent equilibrium solutions for modal O-D shipments, network flows and levels of service. Necessary conditions are deduced to show that the solutions obtained, from the mathematical formulations proposed, satisfy the behavioral principles assumed in each case. It is shown that special rationality conditions are required, with respect to fares charged and network routing decisions, to obtain consistent supply-demand equilibrium solutions. Sufficient conditions for the existence and uniqueness of solutions to diagonalized versions of the mathematical problem formulated are deduced. Finally, a general solution approach is proposed and an application example is developed to illustrate the characteristics of the model and solution algorithm.