The design of more sustainable transportation systems is an achievement that modern societies are aiming to reach. In effect, the realization of transportation supply systems and services that can help reducing the number of private vehicles is a challenge that have attracted the attention not only of researchers, but also of administrations. In this framework, particular attention is devoted to the design and the management of cheap and flexible transportation modes that can significantly boost the modal shift towards more sustainable modes. The model proposed in this paper represents an improvement of the Generalize Ride Sharing (GRS) system introduced in  by means of the statement of a new optimization problem for determining the optimal departure and arrival times of users in addition to the optimal user/mode matches. Additional aims of this work are the completion of the dynamic models of the considered transportation modes and the discussion of new simulation results.
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