In this paper, we study a family of time-dependent pickup and delivery problems with time windows to optimize the service of a transportation provider under two dimensions of operational flexibility. In the first, we consider problems wherein the transportation service provider can choose the transportation requests it serves in order to maximize profit. In the second, we consider problems wherein they can take advantage of periods of light traffic by dictating to drivers when their routes should begin. We also consider problems wherein these flexibilities are not present. We propose an exact solution approach for solving problems from this family that is based upon branch and price, wherein columns are generated via a tailored labeling algorithm. We augment the framework with adaptations of various speed-up techniques from the literature, including limited-memory subset-row cuts and route enumeration. With an extensive computational study, we assess the effectiveness of the proposed framework and the impact of the adapted techniques.