In the context of door-to-door transportation of people with disabilities, service quality considerations such as maximum ride time and service time-consistency are critical requirements. To identify a good trade-off between these considerations and economic objectives, we define a new variant of the multi-period dial-a-ride problem called the time-consistent dial-a-ride problem. A transportation planning is supposed to be time-consistent if for each passenger, the same service time is used all along the planning horizon. However, considering the numerous variations in transportation demands over a week, designing consistent plan for all users can be too expensive. It is therefore necessary to find a compromise solution between costs and time-consistency objectives. The time-consistent dial-a-ride problem is solved using an epsilon-constraint approach to illustrate the trade-off between these two objectives. It computes an approximation of the Pareto front, using a matheuristic framework that combines a large neighbourhood search with the solution of set partitioning problems. This approach is benchmarked on time-consistent vehicle routing problem literature instances. Experiments are also conducted in the context of door-to-door transportation for people with disabilities, using real data. These experiments support managerial insights regarding the inter-relatedness of costs and quality of service.