In this paper we consider the daily aircraft routing and scheduling problem (DARSP). It consists of determining daily schedules which maximize the anticipated profits derived from the aircraft of a heterogeneous fleet. This fleet must cover a set of operational flight legs with known departure time windows, durations and profits according to the aircraft type. We present two models for this problem: a Set Partitioning type formulation and a time constrained multi-commodity network flow formulation. We describe the network structure of the subproblem when a column generation technique is applied to solve the linear relaxation of the first model and when a Dantzig-Wolfe decomposition approach is used to solve the linear relaxation of the second model. The linear relaxation of the first model provides lower bounds. Integer solutions to the overall problem are derived through branch-and-bound. By exploiting the equivalence between the two formulations, we propose various optimal branching strategies compatible with the column generation technique. Finally we report computational results obtained on data provided by two different airlines. These results show that significant profit improvement can be generated by solving the DARSP using our approach and that this can be obtained in a reasonable amount of CPU time.