Solving jointly districting and resource location and allocation problems: An application to the design of Emergency Medical Services

This paper proposes an integrated approach to jointly tackle districting and resource allocation decisions, two interrelated problems that, in most cases, are handled separately. The proposed approach is applied to the context of Emergency Medical Services (EMS), where a large territory needs to be covered by a limited number of resources, i.e., the ambulances. The territory is usually split into districts; each district receives a share of ambulances, which are managed quasi-independently. This paper focuses on the importance of districting decisions, which will impact daily operations and, therefore, the performance of the system. To address the districting and resource location and allocation problems jointly, it proposes an iterative algorithm that exploits the interaction between the strategic (i.e., the districting) and the operational (i.e., the location and allocation of resources) decisions to build compact and balanced districts and, at the same time, find the location and allocation of resources that maximize the performance in terms of system's response time. Starting from an initial set of districts, the iterative algorithm solves the associated resource location and allocation problem for each of them. Then, according to the performance reached by the location-allocation solutions, the districts are modified. Applied to realistic instances inspired by the city of Montreal, Canada, the algorithm produced results that improved simultaneously the system's expected response time and the metrics assessing the quality of the districts.