The integrated dial-a-ride problem (IDARP) concerns of the optimal routes of a set of vehicles that serve the first and last miles of in combination journeys such that a fixed transport service may carry out the longest part of the journey. It implies some modeling and practical issues. Practical wise, it only integrates a single fixed-line. It also does not accept any dial-a-ride problem (DARP) request. From the modeling perspective, the transfer node system enlarges quickly with each new request. It also requires more strengthening strategies to be adopted. The proposed integrated dial-a-ride problem fixed-route selection (IDARP-FRS) handles some of these issues. It extends the IDARP to include iterations over a two-line fixed service. An additional set of constraints is devised to easily switch the proposed model to the IDARP and even accommodate users from the dial-a-ride problem. The IDARP-FRS also introduces a set of newly constructed direction-based constraints, for suppressing the number of transfer node arcs. Besides, the symmetry-breaking constraints are brought from the literature to the context of the IDARP-FRS to further strengthen the model. The computational tests are implemented on Gurobi and showed the significant role of the proposed constraints in reducing the problem complexity.