Determining capacity of multimodal multi-commodities freight transportation network from critical link volumes

The commodity transportation capacity between all origin-destination (OD) pairs over the multimodal multi-commodities freight transportation network (MMFTN) is determined. A multi-objectives mathematical model is formulated for determining the OD capacity over the MMFTN according to a transporting capacity matrix that increased from the reference matrixes. The corresponding incremental factor for estimating the capacity matrix is obtained via the maximal likelihood estimation method that samples data of differences between the estimated commodity volumes and carrying capacities of the critical links. The proposed formulations are tested by an experimental highway and railroad freight transportation network in an existing literature. The relevant results of OD capacities are displayed and applicability of the algorithm is certified.