Equilibrium models in multimodal container transport systems

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Optimizing the performance of multimodal freight transport networks involves adequately balancing the interplay between costs, volumes, times of departure and arrival, and times of travel. In order to study this interplay, we propose an assignment model that is able to efficiently determine flows and costs in a multimodal network. The model is based on a so-called user equilibrium principle, which is at the basis of Dynamic Traffic Assignment problems. This principle takes into account transport demands to be shipped using vehicles that transport single freight units (such as trucks) or multiple freight units (such as trains and barges, where demand should be bundled to reach efficient operations). Given a particular demand, the proposed model provides an assignment of the demand over the available modes of transport. The outcome of the model, i.e., the equilibrium point, minimizes users’ generalized costs, expressed as a function of mode, travel time and related congestion, and waiting time for bundling sufficient demand in order to fill a vehicle. The model deals with these issues across a doubly-dynamic time scale and in an integrated manner. One dynamic involves a learning dynamic converging towards an equilibrium (day-to-day) situation, reflecting the reaction of the players towards the action of the others. Another dynamic considers the possible departure time that results in minimum expected costs, also due to the fact that players mutually influence each other on the choice of departure times, due to congestion effects and costs for early/late arrival of freight units. This is a choice within a given time horizon such as a day or a week. We present a study on the influence and sensitivity of different model parameters, in order to analyse the implications on strategic decisions, fostering a target modal share for freight transportation. We also study under which conditions the different modes can be substitutes for each other.