The Mobility Allowance Shuttle Transit (MAST) system is a type of public transportation where vehicles may deviate from a fixed route to serve clients who wish to get on or off within a service area. In this area, the system provides an on-demand service. We use Mixed-Integer Linear Programming to tackle the MAST system and consider often neglected realistic constraints, as those linked to vehicle capacity and fleet availability. We perform a sensitivity analysis to understand how the system performance varies as a result of changing client priorities.