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

Abstract

a b s t r a c tThis 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

“…Our research builds directly on the work by Huizing et al on the MRP (Huizing et al, 2020) and the proposed MDSA-heuristic for solving the MRP. This problem has similarities to both the p-Median Problem and the Distance-Constrained Vehicle Routing Problem.…”

“…Therefore, a fast heuristic is needed that provides good solutions within a few minutes. In Huizing et al (2020), MDSA was found to be the most effective heuristic for MRP. Roughly, MDSA consists of four steps, which are outlined below for later reference.…”

“…This way, proper coordination of non-emergency tasks (over time and space) over multiple agents can help to reduce emergency response times and at the same time increase the efficiency of non-urgent tasks. To enable this coordination, Huizing, Schäfer, van der Mei, and Bhulai (2020) proposed the Median Routing Problem (MRP) and a fast, scalable yet accurate heuristic for optimally planning nonurgent tasks, or "jobs", while staying responsive to incidents requiring immediate action. Throughout, this heuristic is called the mediate-dividesequence-agree (MDSA) method.…”

Integrated multi-item packaging and vehicle routing with split delivery problem for fresh agri-product emergency supply at large-scale epidemic disease context

“…(2019) proposed a multi-compartment vehicle routing model to solve the cold-chain distribution problem. Huizing et al. (2020) studied the emergency logistics with non-emergency jobs, and formulated it as a median routing problem to minimize the expected response time.…”

The Traveling k-Median Problem: Approximating Optimal Network Coverage

“…For example, the agents might correspond to an 'emergency fleet' (e.g., police patrol force, emergency medical coverages, railway emergency responders) that one needs to schedule to provide a good emergency response time over a pre-specified time horizon. In fact, we arrived at the Traveling k-Median Problem introduced in this paper through our (more applied) investigations in the domain of emergency logistics; more specifically, the Traveling k-Median Problem considered here is a stylized variant of the so-called Median Routing Problem studied in [12].…”