Load balancing location of emergency medical service stations

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Technická Univerzita v Liberci
Technical university of Liberec, Czech Republic
When we want to design a successful and efficient emergency medical system, the crucial task is to determine the number of ambulances operating in a given region and the deployment of stations where the ambulances are kept. In the Slovak Republic, the number and locations of stations are specified by the Ministry of Health for the whole state territory. In the Czech Republic, the network of stations is established by the local authority for each administrative region. Due to geographical and population diversity, there are significant differences in population served by individual ambulances. Assuming that the number of ambulances is given, we want to investigate whether a different location of the ambulances might result in a more even distribution of their workload and, consequently, shorter response time. The problem is modelled as a capacitated p-median problem and solved using mathematical programming. The capacitated p-median problem is known to be NP-complete. As a consequence, it cannot be solved to optimality even for moderate-sized problem instances. However, we face a large-scale problem instance consisting of almost 3,000 demand nodes. Therefore heuristic approaches need to be used to get a sufficiently good solution in an acceptable time. Two decomposition mathematical heuristics are described in the paper and a new heuristic method based on previously developed approaches is presented. A redeployment of existing EMS stations in the Slovak Republic is calculated using these methods. The results are compared mutually and with the current deployment. The benefits and limitations of the presented methodology are discussed.
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