An Integer Programming Model for Locating Vehicle Emissions Testing Stations

Connecticut and other states not in compliance with federal air quality standards are required to implement a motor vehicle inspection program to test vehicles for pollutants---hydrocarbons and carbon monoxide. The problem is to determine the number, size, and locations of stations given constraints on the maximum travel distance from each town to its nearest station and the average waiting time at a station. In this paper we use simulation to find the maximum allowable arrival rates (in vehicles per hour) of stations of different sizes and formulate the station location problem as a set covering model. We generate a range of solutions through sensitivity analysis, varying both the average waiting time and maximum distance constraints. Comparing the current configuration of stations in Connecticut to our integer programming solutions we find that the integer programming approach reduces the objective function by at least $3 million. The current configuration has more stations than the IP solutions but they are not as well distributed.