The enormous amount of containers handled at ports hampers the efficiency of terminal operations. The optimization of crane movements is crucial for speeding up the loading and unloading of vessels. To this end, the premarshalling problem aims to reorder a set of containers placed in adjacent stacks with a minimum number of crane movements, so that a container with an earlier retrieval time is not below one with a later retrieval time. In this study, we present a series of constraint programming models to optimally solve the premarshalling problem. Extensive computational comparisons show that the best proposed constraint programming formulation yields better results than the state-of-the-art integer programming approach. A salient finding in this paper is that the logic behind the model construction in constraint programming is radically different from that of more traditional mixed integer linear programming models.

在港口处理的大量集装箱阻碍了码头运营的效率。起重机运动的优化对于加快船舶装卸速度至关重要。为此，预编组问题旨在以最少的吊车移动次数对放置在相邻堆垛中的一组集装箱进行重新排序，以便取回时间较早的集装箱不会低于取回时间较晚的集装箱。在这项研究中，我们提出了一系列约束规划模型来优化解决预编组问题。广泛的计算比较表明，最好的约束规划公式比最先进的整数规划方法产生更好的结果。