Logistics systems often face challenges and uncertainties in travel time, customer behavior, and operational issues. These factors highlight the need for reliable delivery prediction to make sure that supply chain resilience is attained. However, existing models mostly ignore uncertainty and only provide single-point estimates, which cause overconfidence and unreliable decision-making. This article introduces a combined approach using both traditional as well as machine learning models for on-time delivery prediction, incorporating uncertainty quantification techniques. Five statistical models and five machine learning algorithms were evaluated in a real-world logistics dataset. Among the models, Gradient Boosting achieved the highest classification accuracy of 95.7%. For quantifying uncertainty, Quantile Regression is used to derive confidence intervals for delivery prediction. This technique helped in identifying high-risk delivery conditions and enhanced model output reliability. This way of modelling not only improves clarity, but also helps in planning when things are uncertain. The findings of this project highlight the need for uncertainty-aware models in stronger and more informed decisions in logistics.