Scientific paper ID 2545 : 2024/3

The problem, which is considered in the paper is how to determine the number of police offices and their area and population coverage according to the time frame of the specified standards. The goal is to find the minimum number of police centers to provide maximum service (coverage), both to the population and to the territory of the city for a given maximum time and/or distance. In order to determine the coverage by districts in the city of Sofia, it is necessary to apply known mathematical models for choosing the location of the police station, and in this paper is used the set covering problem, which is a mixed integer and linear programming problem. The objective function and the constraints and the binary variables are defined in the Microsoft Solver Add-in. These police teams must provide maximum ”coverage” for a limited time to the population of all areas. Considering the population of each area and the service times of existing and potential centers, it is necessary to find additional centers with their respective locations that can provide service within these time frames. As a result of solving the task with a varying number of police centers (1, 2 and 3), their location and degree of coverage (served population) with the previously set time standards for police triage (to 15 min., which s the time for transmission of the signal by the dispatcher (about 2 min.) and the reaction time of the designated team as necessary (between 3-5 min.)).