Uncertainty in travel and service times poses significant challenges for vehicle routing in logistics systems. This paper proposes a stochastic model predictive control (SMPC) strategy to manage a Vehicle Routing Problem with time windows (VRPTW) under stochastic service times with correlation across customers. The approach combines a dynamic optimization model with single and joint chance constraints and a forecasting tool for updating travel plans as new information becomes available. A deterministic reformulation of the stochastic constraints is developed so that the problem can be solved via mixed-integer programming. The aim of this paper is to demonstrate that the SMPC strategy can maintain a high level of time-window reliability (meeting customer time windows with high probability) at a reasonable cost by re-optimizing routes over a moving horizon. In numerical case studies, the SMPC approach achieves the desired reliability levels while incurring only modest increases in total cost, and it flexibly adjusts the cost–risk tradeoff by switching between single and joint chance constraints. These results illustrate the potential of the proposed method for real-time distribution routing under uncertainty and highlight the novel contribution of integrating chance-constrained optimization with Model Predictive Control in a VRPTW context.
He et al. (2026) studied this question.