The Quay Crane Scheduling Problem With Stability Constraints

The quay crane scheduling problem (QCSP) is one of the most important problems for the operations at container ports. The QCSP aims to decide a QC schedule for loading and unloading containers so as to minimize the vessel turnaround time. The QCSP is subject to various kinds of constraints, e.g., task precedence constraints and QC noninterference constraints. This paper extends the QCSP by taking into consideration the stability constraints, which are crucial for the safety reason but often omitted in the existing literature. We provide a mathematical model for the QCSP with stability constraints (QCSPSCs). A bicriteria evolutionary algorithm is proposed to solve the QCSPSC. The algorithm consists of a sliding-window heuristic to fix the schedule, which violates the stability constraints. Extensive experiments are conducted to demonstrate the effectiveness of the algorithm. The computational results of the traditional QCSP and the QCSPSC are also compared and analyzed. Note to Practitioners—Stability is a vital factor for the safety of the ship and the goods inside. At a terminal, when a berthed container ship receives loading and unloading operations performed by quay cranes (QCs), it is required that the ship stability criterion does not exceed a certain threshold. In practice, ship operation managers are keen in minimizing the ship’s turnaround time via an efficient QC schedule for loading and unloading containers without leaning the ship to one side. The schedule is then implemented by automatic scheduling systems or simulation tools in the terminal routines. This paper presents some practical stability constraints and integrates them into the traditional QC scheduling model. The results show that by considering the stability constraints, the ship will become more stable, but the turnaround time will not be affected significantly. We believe that the introduction of ship stability constraints can not only fill in the gap between the research on QC scheduling and the real-world ship handling practices but also enrich the studies on logistics planning and port operations.

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