A Multi-objective Mathematical Programing Model for the Problem of P-envy Emergency Medical Service Location.

To prevent the great dangers caused by emergency situations, providing rapid and high-quality emergency aid highly depends on the location of emergency medical centers. The purpose of this research is to present a multi-objective mathematical programing model based on the minimum P-envy algorithm to locate and construct emergency medical services (EMS). Maximizing the coverage in order to increase the probability of survival of different categories of patients, minimizing the costs of constructing EMS and optimizing the ratio of regions having the right to emergency medical services is one of the fundamental challenges in the health care system of countries. In this paper, a model for maximum utilization of EMS considering budget limitations is presented. In this study, since the problem is NP-Hard, the Genetic Algorithm (GA) and Simulated Annealing (SA) algorithm were used to solve this problem. The parameters of the metaheuristic algorithms were tuned using the Taguchi method. Several instance problems were solved to compare the performance of 2 algorithms. The results demonstrate that the validity of the proposed model. Also, the mean of the solutions obtained by GA for small, medium, and large-size problems are better than the SA algorithm. Also, the GA algorithm obtained more efficient solutions than the SA algorithm.