In the Dial-A-Ride Problem with Transfers (DARPT), a passenger may be transfered from the vehicle that picked him up to another vehicle at some predetermined location, called transfer point. Transfers may generate non negligible savings in terms of routing cost. We propose an Adaptive Large Neighborhood Search (ALNS) to solve the Pickup and Delivery Problem with Transfers (PDPT). We present heuristics introduced to integrate transfers in routes and how the ALNS has been adapted to the DARPT. Checking whether a solution of the DARPT remains feasible after inserting a request in one route, or in two routes using a transfer point, becomes a non-trivial problem. Indeed, routes should be synchronized at transfer points and therefore, cannot be scheduled independently anymore. For a set of routes, the feasibility problem given by the DARPT precedence and time constraints can be stated as a Simple Temporal Problem (STP). Since the STP has to be solved after all request insertions, solving it e ciently is a crucial issue. We propose some necessary and su cient feasibility conditions that reduce the time needed to establish feasibility or unfeasibility.