The quay crane scheduling problem with non-crossing and safety clearance constraints: An exact solution approach

This paper considers the Quay Crane Scheduling Problem (QCSP) with non-crossing and safety clearance constraints for a single vessel. The problem determines the order of unloading and loading operations that a specific number of quay cranes (QCs) perform to serve a vessel in minimum time. The QCs move on a single rail and therefore cannot cross each other, and every two consecutive cranes must leave a specific safety distance between them. Due to the difficulty of this problem, most researchers have used heuristics to solve it. However, the QCSP is normally used as a building block of bigger ports’ optimization problems that are very difficult to solve without some decomposition techniques like Lagrangian relaxation. For these methods to succeed, the sub-problems must be solved to optimality in reasonable computational time. This paper presents an improvement on a recent novel formulation for the problem, followed by a new exact and computationally fast technique to solve it. The technique is a two-step approach initiated by a partitioning heuristic and terminated by a Branch and Price algorithm. Through computational experiments, we demonstrate that the proposed solution approach can solve real-sized cases in a fast computational time and has low sensitivity to all parameters. Finally, we introduce a method, formulated as a traveling salesman problem, to acquire operationally practical solutions by minimizing crane re-positioning movements and accounting for crane initial positions.