Modeling Uncertainty for the Double Standard Model Using a Fuzzy Inference System

Abstract

This paper studies the issue of uncertainty in the ambulance location problem to cover the maximum number of demand points in a city. The work is based on the double standard model (DSM), a popular coverage model where two radii are considered to cover a percentage of the demand points twice. Uncertainty is introduced in the expected travel time between an ambulance and a demand point, before computing the optimal placement of ambulances in potential bases by solving the linear program posed by the DSM. The following three approaches are considered: (1) solving the DSM without uncertainty; (2) uncertainty in the travel time is based on triangular fuzzy set; and (3) a fuzzy inference system (FIS) with a rule base derived from the problem properties, which is the main contribution of this work. Results show that considering uncertainty can have a significant effect on the solutions for the DSM, with the solutions produced with the FIS approach achieving a higher total coverage of the demand. In conclusion, the proposed strategy could provide a reliable and effective tool to support decision making in the ambulance location problem by considering uncertainty in the ambulance travel times.Keywords: ambulances, emergency medical services, bases, double standard model, triangular fuzzy set, fuzzy inference system inTrODUcTiOn In recent years, the development of computational support systems for emergency medical services (EMS) has attracted a growing amount of attention from researchers. In EMSs, a crucial factor that must be considered is response time. For example, let us consider cardiac arrest, the American Heart Association concluded that in the first 4-6 min after a person suffers a cardiac arrest she (he) can begin to suffer from permanent brain damage or even brain death. However, normal heart rhythm can be restored if advanced life support (ALS) is provided early. Studies have shown that the probability of a patient surviving is reduced by 7-10% with each passing minute in which defibrillation and ALS are not provided, and resuscitation is mostly unsuccessful after 10 min (EMSWorld.com, 2014).Another example is traffic accident, where the number of deaths was estimated to be 1.25 million in 2013. Half of all fatalities caused by traffic accidents are pedestrians, cyclists, and motorcyclists. Death rates from such accidents are considerably higher in developing countries (OMG, 2015). Therefore, appropriate and timely response times to such incidents are indispensable in highly urban areas.In 2013, the Red Cross of Tijuana (RCT) covered about 98% of the EMS requests (Cruz Roja de Tijuana, 2012), providing medical attention to 37,000 emergency calls. It does this with 13 ambulances that are distributed in 8 bases that cover a population of approximately 1.6 million people in an area of 1,243 km 2 (INEGI, 2010). This means that, on average, each ambulance serves about 123,000 people and each base must cover an average of 155 km 2 . This contrasts, for instance, with the US, where by the 1990s there was about 1 am...