This presentation discusses cases of vehicle routing problems where customers can specify multiple locations or time at which he can be visited. We are more specifically interested in variants with time windows where timing aspects are challenging. This includes the Generalized Vehicle Routing Problem with Time Windows (GVRPTW), the Vehicle Routing Problem with Multiple Time Windows (VRPMTW), the Vehicle Routing Problem with Roaming Delivery Locations (VRPRDL), and the Vehicle Routing Problem with Delivery Options (VRPDO). To solve these problems, we present a matheuristic that combines heuristic and exact components. It is based on a Large Neighborhood Search (LNS) that uses large and small destruction steps with different recreate strategies. For exact approaches, we study the integration of a Set Partitioning component and of the Balas-Simonetti neighborhood. The proposed LNS alone already outperforms most of the existing algorithms. The addition of the Set Partitioning Problem or the Balas-Simonetti neighborhood further improves its results on some variants. A study on each problem and a cross-analysis on all considered problems exhibit the impacts of hybridization to solve variants of the GVRPTW.