A model for the fleet sizing of demand responsive transportation services with time windows

We study the problem of determining the number of vehicles needed to provide a demand responsive transit service with a predetermined quality for the user in terms of waiting time at the stops and maximum allowed detour. We propose a probabilistic model that requires only the knowledge of the distribution of the demand over the service area and the quality of the service in terms of time windows associated of pickup and delivery nodes. This methodology can be much more effective and straightforward compared to a simulation approach whenever detailed data on demand patterns are not available. Computational results under a fairly broad range of test problems show that our model can provide an estimation of the required size of the fleet in several different scenarios.