This paper discusses an approach to compute a lower bound on fleet-size in variable-schedule fleet-size problem. The lower bound is computed in two stages. In stage one, a fixed-schedule fleet-size problem is solved for a relaxed set of trips where each trips is assumed to be departing at its latest permissible departure time and yet arrive at earliest arrival time resulting in reduced elapsed time. In second stage the lower bound is augmented by the minimum additional fleet-size required to make each trip individually restorable to its original elapsed time.