The fixed-route vehicle-refueling problem is a daily scheduling problem used by truck companies that seeks the best set of refueling stations (truck stops) for a given route. The paper introduces valid inequalities, lower bounds, as well as methods to reduce the number of stops that can be visited directly after a given stop. We show in a comprehensive computational study that our model formulation reduces the average computation times in comparison with a standard MIP formulation by over 78% on average and by 95% for instances with 2000 truck stops. Instances with 2000 truck stops are solved in less than 0.3 s.