A Regret Policy for the Dynamic Vehicle Routing Problem with Time Windows

In this work, we present a regret policy for the dynamic vehicle routing problem with time windows (DVRPTW) in which customer order arrivals are revealed over a day and which has been the considered problem in the EURO Meets NeurIPS 2022 Vehicle Routing Competition. The problem requires two types of decisions: Dispatching orders and planning the respective vehicle routes. The objective is to minimize the travel time while dispatching all orders over the day and adhering to the respective time windows. The regret policy we present in this paper focuses on the former decision, namely the dispatching of orders, as the routing can then be performed by a regular VRPTW solver. The basic idea of the policy is to calculate a regret value for each order which represents possible cost savings that we would miss when dispatching the order immediately. To attain this regret value, we make use of the customer distribution from which orders are sampled. If the value is below a predefined threshold, the order is dispatched and routes are planned with a state-of-the-art VRPTW solver. Otherwise, the order needs to be dispatched at a later stage. The proposed policy outperforms several benchmark policies and ranked 6th place among approximately 50 teams. Furthermore, the proposed regret policy has a high level of explainability, is simple to implement, and can be generalized to other problems in the domain of dynamic vehicle routing.