Dynamic routing with real-time traffic information

We consider the vehicle routing problem (VRP) with real-time traffic information, where stochastic intermediate times (travel times and service times) are assumed to be realized with probability distributions at the end of each customer's service and before determining the next customer to visit. We propose a dynamic VRP (DVRP) model addressing the varying intermediate times and show that the DVRP can significantly reduce the total duration than the static or priori VRP model. To solve the DVRP model, we develop an approximate dynamic programming algorithm based on a semi-infinite linear programming, which can be derived from a class of affine time-to-go approximation functions and generate lower bound only dependent on the expected duration and the description of support set of the stochastic time vectors. We also propose a greedy heuristic time-directed policy to produce good solutions and improve computational efficiency even for the worst-case condition, and prove that it can be solved within polynomial time. The results show that our approach is of high applicability for the VRP with dynamic and real-time traffic.