Optimizing Container Terminal Operations: A Robust Scheduling Framework Under Uncertainty

Container terminals play a central role in global logistics, and acts as the essential nodes in the network of maritime transportation. The efficient operation of these terminals is important for the smooth flow of goods across continents. The scheduling of terminal equipment such as quay cranes (QCs), internal vehicles (IVs), and yard cranes (YCs) is vital to the operational efficiency of container terminals, directly impacts loading and unloading times, terminal throughput, and the overall cost of maritime logistics. For instance, QCs are the primary interface between the ship and the port, responsible for the transfer of containers to and from vessels. The scheduling and allocation of QCs are critical because they directly affect the vessel turnaround time. Efficient QC scheduling can minimize the time ships spend at berth, which is a significant factor in shipping schedules and operational costs. Delays and inefficiencies in QC operations can lead to bottlenecks, and cause delays not just at the terminal but throughout the supply chain. Once containers are offloaded from the ship, they must be transported to the yard for storage or directly to trucks or trains for onward movement. IVs, such play a crucial role in this process and the effective scheduling of IVs ensures that containers are moved efficiently from the quay to the yard or delivery points, reducing internal transit times and minimizing the risk of congestion within the terminal. On the other hand, YCs are responsible for stacking containers in the yard and retrieving them for delivery or loading onto vessels. The scheduling of YCs affects the storage capacity and retrieval efficiency of a terminal. Proper coordination between YCs and IVs is necessary to avoid delays in container retrieval and to maximize the use of yard space. Efficient YC scheduling is particularly important for terminals dealing with high volumes of transshipment cargo, where containers need to be moved and organized efficiently to ensure smooth transshipment processes. Indeed, the necessity for effective scheduling of QC, IV, and YC operations cannot be overstated. It requires sophisticated optimization algorithms and real-time decision-making systems to adapt to the dynamic nature of terminal operations, and the critical role of container terminals in global logistics highlights the necessity for effective scheduling of terminal equipment like QCs, IVs, and YCs.  To this account, a new study published in Computers & Industrial Engineering and led by Professor Wenfeng Li from the School of Transportation and Logistics Engineering at the Wuhan University of Technology and conducted by Lei Cai, Wenjing Guo, and Lijun He, the authors addressed the challenges of integrated scheduling in container terminals, particularly under the condition of uncertain operation times. They proposed a novel approach that combines a mixed integer nonlinear programming model, a genetic algorithm for solving the model, and a framework for generating robust scheduling plans against uncertainties.   The team designed a series of experiments to validate the efficacy of their proposed methods. The experiments aimed to test the robustness and effectiveness of the scheduling plans generated by their framework in an uncertain operational environment typical of container terminals. They created a simulated container terminal environment, incorporating the operational dynamics of QCs, IVs, and  YCs, along with the uncertainties in operation times influenced by factors like weather conditions and manual operations. Moreover, they generated different problem instances varying in size and complexity (number of containers, QCs, IVs, YCs) to assess the model’s scalability and robustness across different operational scenarios. They also treated operation times as stochastic variables to simulate the uncertainty. The researchers modeled these times based on a normal distribution, reflecting real-world variability in the duration of equipment operations. The proposed method (PM-AERI) was benchmarked against traditional scheduling approaches, including Robust Optimization Method (ROM), Stochastic Programming Method (SPM), Triangular Fuzzy Number Method (TFNM), and Maximum Gap Method (MGM), to demonstrate its superiority in handling uncertainties.

The researchers conducted extensive simulations, iterating each problem instance 1000 times to ensure statistical significance. The authors found that the PM-AERI method consistently outperformed the traditional scheduling approaches in terms of handling operational uncertainties. The schedules generated by PM-AERI exhibited greater resilience to the cascading effects of operation time fluctuations, leading to more reliable and efficient terminal operations. Across different problem sizes and degrees of uncertainty, the PM-AERI method demonstrated superior performance which suggest its applicability and effectiveness in a wide range of operational conditions encountered in container terminals. The schedules produced by the PM-AERI method not only managed uncertainties better but also optimized the makespan (the total time required to complete all operations), showcasing the method’s ability to enhance operational efficiency. Moreover, the introduction of an anti-cascade effect and robustness evaluation index based on complex network structural entropy theory proved to be a novel and effective tool for assessing and comparing the robustness of different scheduling plans.

Indeed, the PM-AERI framework, with its focus on the anti-cascade effect and robustness analysis, offers a significant methodological advancement over traditional approaches, particularly in environments characterized by high uncertainty. Additionally, the research highlights the practical applicability of the proposed method in improving the resilience and efficiency of container terminal operations, potentially leading to significant economic benefits and enhanced service levels.  The authors’ findings also open up new avenues for future research, including the exploration of other uncertainty types, optimization objectives, and the application of the proposed method to other scheduling problems. In summary, the experiments conducted by Professor Wenfeng Li and team provide compelling evidence of the advantages of their proposed scheduling framework in managing uncertainties in container terminal operations. The study successfully applied complex network theory and robustness analysis, and addressed a gap in the existing literature and provided a practical framework for improving the resilience and efficiency of port operations worldwide.