A Tailored Two-Stage Algorithm for Quay Crane and Automated Guided Vehicle Scheduling Problems

The integrated scheduling problem of cranes and automated guided vehicles (AGVs) in automated container terminals is a crucial area of concern for ports. In the terminal with AGV-supports in the yard, AGVs can autonomously place or pick up containers without waiting for yard cranes. Therefore, in such a terminal, meticulous scheduling and coordination between quay cranes (QCs) and AGVs are core for efficient and orderly operations. However, managing the operation of QCs and AGVs is complex as numerous factors affect the operational performance, such as QC interference, vehicle congestion, and limited capacity of handover points. To address the problem, we formulate a mixed-integer linear programming model that explicitly considers the above realistic factors. As the model is computationally inefficient even for small-scale instances, we develop a tailored two-stage algorithm, where the first stage is branch-and-bound for QC operations and the second is column generation for AGV operations. To validate the solution quality, we compare the proposed algorithm with some benchmark methods, and the numerical experiments confirm the effectiveness of the proposed approach.