Robust Data-Driven Vehicle Routing with Time Windows

On-time delivery is of utmost importance in today’s urban logistics. However, travel times are uncertain and classical deterministic routing solutions often fail to ensure timely delivery. In this paper, a robust solution that exploits travel times data to determine the best routes for maximal timely delivery is proposed. A new decision criterion is introduced, the service fulfillment risk index (sri), which accounts for both the late arrival probability and its magnitude. Together with Wasserstein distance–based ambiguity in travel times, sri can be evaluated efficiently in closed form. In addition, an exact branch-and-cut approach and a meta-heuristic algorithm are developed to minimize sri with a given travel cost. Simulation studies demonstrate that handling uncertainty improves service punctuality, and that incorporating ambiguity prevents overfitting. Most importantly, sri outperforms the canonical decision criteria of lateness probability and expected lateness duration.