Optimal loading plan for multiple trains in container terminals

The definition of the train loading plan is one of the decisional aspects to be dealt with in a container terminal [1]. In the literature, few research studies have been devoted to the train load planning problem; among them, in [2] three different integer linear programming formulations are proposed in which the real weight restrictions related to wagons configurations are considered, as in the present work. The model proposed in this paper is the extended version of the models described in [3]; the main new modelling aspects of this work in comparison with [3] refer to considering multiple trains, with different destinations, and taking into account the minimization of the distances between the stocking area and the train. In the proposed model, the trains are supposed to be loaded by cranes sequentially and some rehandling operations in the stocking area are allowed. The decision problem can be defined as follows: given a set of containers characterized by different weights, lengths, commercial values and stowage positions in the yard and a set of trains composed by a set of wagons characterized by different lengths and weight restrictions, the problem is to determine how to assign containers to wagons in order to satisfy the physical constraints of wagons, while maximizing the train utilization and minimizing both the rehandling cost in the stoking area and the distances covered to transfer containers from the stocking area to the wagons.