The median routing problem for simultaneous planning of emergency response and non-emergency jobs

This paper studies a setting in emergency logistics where emergency responders must also perform a set of known, non-emergency jobs in the network when there are no active emergencies going on. These jobs typically have a preventive function, and allow the responders to use their idle time much more productively than in the current standard. When an emergency occurs, the nearest responder must abandon whatever job he or she is doing and go to the emergency. This leads to the optimisation problem of timetabling jobs and moving responders over a discrete network such that the expected emergency response time remains minimal. Our model, the Median Routing Problem, addresses this complex problem by minimising the expected response time to the next emergency and allowing for re-solving after this. We describe a mixed-integer linear program and a number of increasingly refined heuristics for this problem. We created a large set of benchmark instances, both from real-life case study data and from a generator. On the real-life case study instances, the best performing heuristic finds on average a solution only 3.4% away from optimal in a few seconds. We propose an explanation for the success of this heuristic, with the most pivotal conclusion being the importance of solving the underlying p-Medians Problem

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