Robust multi-equipment scheduling for U-shaped container terminals concerning double-cycling mode and uncertain operation time with cascade effects

The integrated scheduling of quay cranes, internal vehicles, and yard cranes in container terminals aims to improve port operations and often requires scheduling robustness under uncertainty with cascade effects. In container terminal operations, uncertainty in equipment operating time poses challenges to effective scheduling, as even small fluctuations can create cascade effects throughout the operations, rendering the original schedule ineffective. This research aims to develop a new method that enables a balance between optimization and robustness in container terminal scheduling. Additionally, the double-cycling operation mode and U-shaped port layout, known for their improved efficiency in container terminals, are gaining increasing attention and hence are incorporated into this study. It creates a three-stage hybrid flow shop scheduling problem with bi-directional flows, waiting time, and uncertain operation time. To address the complex problem, a mixed integer programming model is proposed to characterize the integrated scheduling problem, and an index based on complex network structure entropy is designed to evaluate the anti-cascade effect as well as the robustness of the schedule. The index and makespan serve as the bi-objectives, transforming the original problem into a bi-objective optimization one. The non-dominated sorting genetic algorithm-II with appropriate coding and decoding rules is utilized to solve the model and obtain a set of Pareto frontier solutions. The feasibility of the new method is verified through a real case analysis. Specifically, comparative analysis with basic stochastic programming, basic robust optimization, triangular fuzzy programming, and maximum gap method are used to demonstrate the effectiveness of the new method. The paper also provides insightful practical implications for port managers, and the genericity of the method could also contribute to its practical values spreading to a wider scope of beneficiaries, such as manufacturing warehousing and distribution management.