Nonlinear Predictive Control for the Management of Container Flows in Maritime Intermodal Terminals

The increase of efficiency in the management of container terminals is addressed via a predictive control approach to allocate the available handling resources. The predictive control action results from the minimization of a performance cost function that measures the lay times of carriers over a forward horizon. Such an approach to predictive control is based on a model of container flows inside a terminal as a system of queues. Binary variables are included into the model to represent the events of departure or stay of a carrier, thus the proposed approach requires the on-line solution of a mixed-integer nonlinear programming problem. Two techniques for solving such a problem are proposed that account for the presence of binary variables as well as nonlinearities into the model and the cost function. The first relies on the application of a standard branch-and-bound algorithm. The second is based on the idea of dealing with the decisions associated with the binary variables as step functions. In this case, real nonlinear programming techniques are used to find a solution. Finally, a third approach is proposed that is based on the idea of approximating off line the feedback control laws that result from the application of the two previous approaches. The approximation is made using a neural network, which allows one to construct an approximate feedback control law and generate the corresponding on-line control action with a small computational burden. Simulation results are reported to compare such methodologies.