The enriched median routing problem and its usefulness in practice

Emergency response fleets often have to simultaneously perform two types of tasks: (1) urgent tasks requiring immediate action, and (2) non-urgent preventive maintenance tasks that can be scheduled upfront. In Huizing et al. (2020), Huizing et al. proposed the Median Routing Problem (MRP) to optimally schedule agents to a given set of non-urgent tasks, such that the response time for urgent tasks remains minimal. They proposed both an exact MILP-solution and a fast, scalable and accurate heuristic. However, when implementing the MRP-solution in a real-life pilot with a Dutch railway provider, we found that the model needed to be extended by including additional practical objectives and constraints. Therefore, in this paper, we extend the MRP to the so-called Enriched Median Routing Problem (E-MRP), making the model much better aligned with considerations from practice. Accordingly, we extend the MRP-based solutions to the E-MRP. This allows us to compare the performance of our proposed E-MRP solutions to performance obtained in the current operational practice of our partnering railway infrastructure company. We conclude that the E-MRP solution leads to a strong reduction in emergency response times compared to current practice by smartly scheduling the same volumes of non-urgent tasks.