The concept of demand-responsive transport is seen as a promising solution for the necessary changes in the mobility sector in the context of sustainable urban transport. In this work, a model for the Dial-a-Ride problem with public transport integration is presented. The model aims to minimise the sum of waiting times for all passengers, focusing on suburban stations with realistic route data. The model is optimally solvable for small instances, but a heuristic approach based on simulated annealing is proposed for larger instances. The research results suggest that the model is well suited to address the problem discussed and the heuristic approach provides reliable results in a reasonable computational time and is therefore suitable for practical applications.