AbstractIn 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 multiperiod 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 plans for all passengers 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.