Development of an Integrated Optimization Model for Container Relocation and Truck Appointment Scheduling (TAS)

Background: The rise in global throughput has created major challenges for container terminals and depots, especially in managing limited storage space and unsynchronized truck pickup schedules from different companies. These conditions complicate the organization, retrieval, and relocation of containers, especially when target containers are located in the middle of stacks. This study aims to develop an integrated optimization model that combines Truck Appointment Scheduling (TAS) and Restricted Block Relocation Problem (RBRP) to minimize container relocations, coordinate pickup schedules, and improve operational efficiency. Methods: An integer programming model is formulated to integrate relocation and scheduling decisions by considering practical operational constraints, including maximum stack capacity, queue length, crane movement capacity, relocation validity, prevention of redundant movements, and efficient slot utilization. Two solution schemes are evaluated, simultaneous RPRP-TAS approaches and sequential TAS-then-RBRP approaches, to minimize relocations. Results: The results show that the simultaneous approach produces fewer relocation and more stable than the sequential approach. Sensitivity analysis also confirms that the simultaneous scheme is more robust to variations in the number of containers and crane movement capacity, while maintaining comparable pickup time-shift performance. Conclusions: The simultaneous integration of RBRP and TAS provides coordinated, practical, and efficient decision support for depot and terminal operations.