Breaking the Linear Barrier: A Deep Learning Approach to Nonlinear Efficiency in Ports

Port efficiency is a critical factor in global trade. Yet, traditional efficiency evaluation methods, such as Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA), rely on linear assumptions that fail to capture the complexities of real-world port operations. Nonlinearity, particularly diminishing returns, often leads to misleading efficiency assessments. This study addresses these limitations by integrating deep learning into a DEA-based variant, Multi-Directional Efficiency Analysis (MEA), creating a framework that better models nonlinear input-output relationships and saturation effects. The proposed deep learning-enhanced MEA framework utilizes neural network-based function approximation to improve the accuracy of efficiency assessments. Using real-world data from the Port of Sines, experimental results show that traditional MEA overestimates efficiency by 69.9% in 2022 and 59.7% in 2023, compared to the deep learning-enhanced MEA model, which successfully accounts for diminishing returns. The findings confirm that machine learning (ML) approaches offer superior performance in capturing complex efficiency structures. This research is significant as it bridges the gap between traditional efficiency modeling and modern ML techniques, offering a more precise tool for port management and industrial efficiency analysis. By enabling more realistic efficiency assessments, this approach supports better decision-making, resource allocation, and operational planning in maritime logistics, ultimately contributing to more sustainable and optimized port operations.