This article introduces the round-trip dial-a-ride problem (RT-DARP). In this variant of the dial-a-ride problem (DARP), each user has a round-trip demand with one morning request and one afternoon request. The novelty of this approach is that a user's maximum ride time is shared between the two requests, creating a dependency between the morning routes and the afternoon routes. The RT-DARP is solved using the small and large neighbour-hood search (SLNS) metaheuristic and further speed up by an improved feasibility testing procedure. Results from this new formulation are compared with results from solving separately the morning and afternoon DARP. The experiments are performed on a new benchmark generated for the RT-DARP. The results from the RT-DARP always outperform the results from the separated formulation. From a managerial perspective, the RT-DARP makes it possible to improve the quality of service without changing the transportation cost.