As quantum hardware increases in complexity, successful algorithmic execution relies more heavily on the awareness of existing device constraints. In particular, the limited connectivity of quantum hardware can be overcome with the appropriate routing of quantum information across the machine. Previous approaches addressed the problem for each two-qubit gate separately and then imposed the compatibility of the different routes. Here we present an approach that shifts the focus onto the set of all routing operations that are possible at any given time and favors those that most benefit the global pattern of two-qubit gates. We discuss our optimization technique applied to a specific transmon architecture, that we will describe in detail, and benchmark its performance by scheduling variational algorithms. Finally, we apply our scheduler to the design problem of quantifying the impact of manufacturing decisions: how does the number of distinct qubit frequencies in superconducting architectures affect the algorithmic performance of the quantum Fourier transform?