Health & Biomedicine
This work considers the ambulance location problem for the Red Cross in Tijuana, Baja California, Mex-ico. The solution to the ambulance location problem is to optimally locate all available ambulances withinthe city such that coverage of the city population is maximized and a quick response to any emergency isensured. The problem is posed using three different coverage models, these are: the Location Set CoveringModel (LSCM), Maximal Covering Location Problem (MCLP) and Double Standard Model (DSM). Usingreal-world data recovered from over 44 thousand emergency calls received by the Red Cross of Tijuana,several scenarios were generated that provide different perspectives of the demand throughout the city,considering such factors as the time of day, work and off-days, geographical organization and call priority.These models are solved using Integer Linear Programming, and solutions are compared with the current coverage provided by the Red Cross. Results show that coverage and response times can be substantially improved without additional resources.
One of the core problems for Emergency Medical Services (EMS) is the location problem of available ambulances [?]. The capability of these services to save lives depends greatly on the time it takes foran ambulance to arrive on the scene of an emergency. Hence, it is important to position all available ambulances in such a way that any emergencies that arise may be dealt with promptly.
The population in the city of Tijuana, Baja California, Mexico is approximately 1.6 million inhabitants [?].Currently, the Red Cross of Tijuana (RCT) has 11 ambulances in service and 8 bases, that cover about 98%of the medical emergencies throughout the city [?]. On average, there is one ambulance for every 145,000inhabitants. In 2013 the RCT provided EMS to 37,000 people. Average response time was approximately14 minutes with a standard deviation of 7 minutes. In 75% of all incidents the ambulance arrived within 18minutes and in 90% of all incidents it arrived within 23 minutes. In an emergency situation, the probabilitythat a patient survives depends on the time it takes for the ambulance to arrive, if response time was notquick enough the patient may suffer permanent injury. Therefore, it is very important to ensure that all emergencies can be responded to as fast as possible, by properly locating all available ambulances in the city.
To solve the ambulance location problem in Tijuana, three models are used in this work. These are theLocation Set Covering Model [?], Maximal Covering Location Problem[?] and Double Standard Model[?]. Using the LSCM, MCLP and DSM models, several scenarios were solved to determine the optimalambulance locations during different hours of the day and days of the week, in the city of Tijuana. Twosets of demand points were considered. The first is based on the locations of 92 neighborhoods and ismerely artificial while the second was created from EMS records from the Red Cross using clustering.Both sets offer different perspectives of the demand throughout the city. Accounting for the priority ofEMS requests, ambulance locations that favor demand points with higher priority requests were obtained.Generally speaking, solving all these scenarios with these three models has shown that demand coverage and response times can be improved with the resources currently available.
The LSCM experiments have shown that all demand could be covered using about half the number of ambulances currently in service, with a response time of 14 minutes. With the MCLP experiments, it has been shown that demand coverage, with a response time of 10 minutes, could be improved by as much as22% only by relocating the current 8 bases of the Red Cross. Also, almost all demand could be coveredby properly locating all 11 ambulances in service. As for the DSM experiments, with these 11 ambulancesit would be possible to cover all demand with a response time of 14 minutes, 95% of all demand within10 minutes and still provide double coverage to more than 85% of all demand. However, all of this istheoretical, and, in practice, real coverage and response times may vary, as they depend on many otherfactors beyond what has been considered in this work so far, such as time dependent travel times, weatherconditions, roadblocks, etc. Nonetheless, the results of this work may be used as tools to aid in the decision making about the location of ambulances in the city.
So far the ambulance location problem has been addressed, leaving the relocation problem to be solved.This arises when an ambulance is dispatched to the scene of an emergency and it becomes necessary torelocate one or more ambulances to maintain adequate coverage of the city population
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