Multi-criteria assignment problems for optimising the emergency medical services (EMS), considering non-homogeneous speciality of the emergency departments and EMS crews.

Dispatching of the EMS crews (ambulances) to awaiting patients and then directing the patients, that are already onboard, to appropriate Emergency Departments (ED), is a nontrivial decision problem. In many emergency medical systems it is handled by the Medical Dispatcher using various strategies-sometimes preferring the closest unit. However, applying a wrong strategy may result in transferring acute-state patients, who require very specialised medical aid, to low-speciality EDs with insufficient treatment capabilities. Then, they would need to be re-transferred to referential units, prolonging substantially the time to receive treatment. In some cases such a delay might make the treatment less effective or even impossible. In this work we propose two multi-criteria mathematical optimisation problems-the first one allows us to calculate the ambulance-to-patient assignment, the second one-to establish the patient-to-hospital assignment. These problems not only take the time-to-support criterion into consideration but also optimise for the speciality of care received by each patient. The ED dispatching problem proposed allows both for direct transfers of patients to referential units and for re-transferring them from non-referential EDs. The performance of the proposed approach is tested in simulations with real-life emergency cases from the NEMSIS data set and compared with classic assignment strategies. The tests showed the proposed approach is able to produce better and more fit-for-purpose dispatching results than other strategies tested. Additionally, we propose a framework for embedding the proposed optimisation problems in the current EMS/ED dispatching process.