Ship fuel consumption prediction is crucial for maritime operations. Experts want accurate models that are also easy to understand. This study introduces two new methods: a physics-informed neural network (PI-NN) and a mixed-integer quadratic optimization (MIO) model. The PI-NN model makes black-box models easier to interpret without losing accuracy. The MIO model allows for more flexible white-box models. By using SHapley Additive exPlanations (SHAP), the researchers show how different features affect fuel consumption predictions. These new methods help balance accuracy and interpretability in predicting ship fuel consumption, making it easier to apply data-driven models in practice.