Improved Fuel Consumption Estimation for Sailing Speed Optimization: Eliminating Log Transformation Bias

Sailing Speed Optimization (SSO) is a crucial problem in shipping operations management, aiming to reduce both operating costs and carbon dioxide emissions. The ship’s sailing speed directly impacts fuel consumption, where fuel consumption is generally assumed to follow a power function with respect to sailing speed. Previous studies have used transformation-based fitting methods, such as logarithmic transformations, to investigate the relationship between sailing speed and fuel consumption using historical data. However, these methods introduce estimation bias and heteroskedasticity, violating the core assumptions of Ordinary Least Squares (OLS) used for general linear regression. To address these issues, we propose two novel fitting methods that directly optimize the original nonlinear model without relying on transformations. By analyzing the characteristics of the objective function, we derive parameter constraints and integrate them into a discrete optimization framework, resulting in improved fitting accuracy. Our methods are validated through extensive case studies, demonstrating their effectiveness in enhancing the reliability of SSO decisions. These methods offer a practical approach to optimizing fuel consumption in real-world maritime operations.