Risk based optimization for improving emergency medical systems

Abstract

In emergency medical systems, arriving at the incident location a few seconds early can save a human life. Thus, this paper is motivated by the need to reduce the response time - time taken to arrive at the incident location after receiving the emergency call - of Emergency Response Vehicles, ERVs (ex: ambulances, fire rescue vehicles) for as many requests as possible. We expect to achieve this primarily by positioning the "right" number of ERVs at the "right" places and at the "right" times. Given the exponentially large action space (with respect to number of ERVs and their placement) and the stochasticity in location and timing of emergency incidents, this problem is computationally challenging. To that end, our contributions building on existing data-driven approaches are three fold: 1. Based on real world evaluation metrics, we provide a risk based optimization criterion to learn from past incident data. Instead of minimizing expected response time, we minimize the largest value of response time such that the risk of finding requests that have a higher value is bounded (ex: Only 10% of requests should have a response time greater than 8 minutes). 2. We develop a mixed integer linear optimization formulation to learn and compute an allocation from a set of input requests while considering the risk criterion. 3. To allow for "live" reallocation of ambulances, we provide a decomposition method based on Lagrangian Relaxation to significantly reduce the run-time of the optimization formulation. Finally, we provide an exhaustive evaluation on real-world datasets from two asian cities that demonstrates the improvement provided by our approach over current practice and the best known approach from literature.