The maximum covering problem with travel time uncertainty

Abstract

Both public and private facilities often have to provide adequate service under a variety of conditions. In particular travel times, that determine customer access, change due to changing traffic patterns throughout the day, as well as a result of special events ranging from traffic accidents to natural disasters. This article studies the maximum covering location problem on a network with travel time uncertainty represented by different travel time scenarios. Three model types—expected covering, robust covering, and expected p-robust covering—are studied; each one is appropriate for different types of facilities operating under different conditions. Exact and approximate algorithms are developed. The models are applied to the analysis of the location of fire stations in the city of Toronto. Using real traffic data it is shown that the current system design is quite far from optimality. The best locations for the four new fire stations that the city of Toronto is planning to add to the system are determined and alternative improvement plans are discussed.

Keywords:

• Facility location
• maximum covering problem
• travel time uncertainty
• robust optimization