The Quay Crane Scheduling Problem

Abstract The recent growth in worldwide container terminals’ traffic resulted in a crucial need for optimization models to manage the seaside operations and resources. Along with the recent increase in ship size and the container volume, the advancements in the field of Quay Crane Scheduling introduced the need for new modeling approaches. This is the motivation behind the current paper, which focuses on developing a novel yet simple formulation to address the Quay Crane Scheduling Problem (QCSP). The objective of the problem is to determine the sequence of discharge operations of a vessel that a set number of quay cranes will perform so that the completion time of the operations is minimized. The major contribution is attributed to the way that minimization is performed, which is by minimizing the differences between the container loads stacked over a number of bays and by maintaining a balanced load across the bays. Furthermore, important considerations are taken into account, such as the bidirectional movement of cranes and the ability to travel between bays even before completion of all container tasks. These realistic assumptions usually increase model complexity; however, in the current work this is offset by the novel simple objective. This paper presents a mixed-integer programming (MIP) formulation for the problem, which has been validated through multiple test runs with different parameters. Results demonstrate that the problem is solved extremely efficiently, especially for small problem sizes.