Models for relocation of emergency medical stations

Abstract

The paper presents a mathematical programming model for the deployment of stations where the ambulances are kept. The model deals with the reliability of service. Reliability in emergency systems is based on the individual level of service at each demand point. The system operates, if there is an available ambulance that can respond immediately to each emergency call. However, the probability that vehicles are available can hardly be determined before the stations are located. That is why an upper bound on the failure probability is used in presented location model instead of the probability itself. This upper bound is calculated using a Poisson distribution of arriving calls and the maximum time duration of a vehicle service trip. The model maximizes an average reliability that can be achieved on a given territory with a limited number of vehicles. Such a model may be useful when the issue is a reorganization of the current emergency system. A computer simulation model was used to verify vehicle location provided by the mathematical model. Both models were implemented under the conditions of the Slovak Republic. Travel times were calculated using the transportation network data from the OpenStreetMap project. The paper compares the proposed vehicle location with the current one in terms of the objective function and performance characteristics resulting from computer simulation.