A robust linear model for the maximum expected coverage location problem considering the relative coverage

Emergency medical services (EMS) stations reduce mortality and irreparable damage from injuries through the timely treatment of patients. After performing the initial measures at the scene of the accident, if necessary, they transfer the patient to the hospital. In such cases, the goal is to save human lives. Thus, suggestions and solutions that can improve the performance of these centers are very welcome. One of the most important parameters in providing high-quality EMS is the timing of these services. Therefore, the location of these centers plays a key role in diminishing the response time to demand. In that regard, the location of these centers in cities, especially large and densely populated cities, is very important. In this study, in order to answer the mentioned questions, a linear mathematical model based on the maximum expected coverage model is presented. In this model, by considering the relative coverage conditions, the best locations in the city, as well as the coverage of demand points and distance traveled by the vehicles will be obtained. Furthermore, robust optimization (RO) is used to provide better situations for the operation of the model. Finally, according to the results, it is found that the proposed model has a better resolution time than nonlinear models and is also able to solve cases with high input data. The proposed model is implemented in District 10 of Tehran, Iran.