Data-Driven Bunker Refueling Under Price Uncertainty

Abstract

Bunker refueling decisions in international shipping are crucial operational choices. Each ship acts like a movable storage unit navigating through diverse markets, procuring bunker fuels from different ports to sustain its voyage. This involves grappling with challenges posed by varying bunker fuel prices over time and locations. To address this, we propose data-driven structure-prescriptive (SP) approaches that combine the strengths of modern machine learning with the insights from traditional operations research (OR) modeling and optimization. Instead of predicting future fuel prices, our approach directly learns the optimal policy from data and adapts refueling decisions to the current market conditions, including fuel prices, crude oil price, NYSE index, etc. Our focus lies in leveraging the well-established understanding that the optimal refueling decision adheres to a state-dependent base-stock refueling policy. This decision depends on factors such as the port of call, fuel tank capacity, market conditions, and is finite-valued, depending on the ship’s schedule and voyage. We provide a practical framework to incorporate these structural properties into data-driven decision-making. The finite-valued property, for instance, establishes a connection between the refueling problem and multiclass classification, integrating OR modeling with machine learning. We test our approach through experiments under both simulated scenarios and a real-world example involving the Asia–North America Trade Route. The proposed SP approaches successfully recovered the “true” optimal refueling policy in synthetic simulations. Our real-world data experiments further demonstrate that integrating structural properties into the learning process enhances the quality of prescriptions, particularly when training data is limited. Specifically, with one and a half years of training data, the proposed methods outperform current industry practices. With less than three years of training data, our models yield substantial fuel cost savings, approximately 40 US dollars per metric ton, during the testing period.