Shipper-carrier dynamic freight assignment model using a variational inequality approach

This paper develops a dynamic freight assignment model that captures the shipper-carrier mechanism of the freight industry. The shippers minimize their cost by choosing a carrier with the lowest shipping cost for each shipment. The market reaches equilibrium when no shipper can reduce its cost further by changing the carrier for any shipment. Each carrier optimizes its operations so that it can reduce its shipping costs and attract more business from the shippers. An iterative variational inequality (VI) formulation is used to model the market equilibrium including the feedback from the carriers to the shippers. The cost function in the VI is obtained from a carrier submodel that is a dynamic, multimodal, multicommodity network-assignment model based on a linear programming formulation. The formulation and solution algorithms are presented in this paper. A test network is used to implement the solution algorithm to demonstrate the applicability of the model.