A multi-criteria districting approach for ambulance fleet management

Emergency Medical Services (EMS) play an important role in modern healthcare systems. They provide fast response to any person requiring medical assistance in case of emergency, and ensure a safe transportation to the selected healthcare facility. The performance of an EMS, generally defined in terms of the response time, is strongly impacted by the many decisions related to the ambulance fleet management, which involve all decision levels, i.e., strategic, tactical and operational. At the strategic level, some organizations divide their territory into districts. A given number of vehicles is assigned to a district, and each district is managed independently. Such decentralized management aims at easing fleet management, but it can also result in poorer performance if districts are not carefully designed. However, in the practice, districts are often defined a priori, without considering the dynamics of the system. This may lead to undesirable consequences during operations, e.g. ambulances may be sent to serve out-of-district calls to compensate local criticalities and keep a good service level. In this work, we propose a solution framework to deal with the districting problem in EMS, with the goals of minimizing out-of-district assignments and balancing the workload among the districts. The approach consists of an iterative matheuristic in which, at each iteration, the ambulance location and dispatching problem is solved given a layout of districts, to determine locations and assignments of ambulances. Then, redistricting decisions are performed based on the solution found at the operational level. The proposed approach is applied to a set of realistic instances representative of the city of Montréal, Canada, in order to validate its potential. Results show that the layout of districts strongly affects the quality of the solution and that our approach improves the solution with respect to an a priori districting.