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Motivated by the change in mobility patterns, we present a scheduling approach for a vehicle-sharing problem, considering several alternative modes of transport, from a company viewpoint with centralized planning. We consider vehicle-sharing in a company having one or more depots and a fixed number of users, i.e. employees. The users have appointments with a fixed location and fixed start and end times. A vehicle must be used for a full trip of a user from depot to depot. We aim at assigning vehicles to user trips so as to maximize savings compared to other modes of transport. We first consider that only one type of vehicle is used, and second that multiple vehicle types can be used. For the first case, we show that the vehicle-sharing problem can be formulated as a minimum-cost flow problem. Secondly, if multiple types of vehicles are available the problem can be formulated as a multi-commodity flow problem. These formulations make the problem applicable in daily operations due to efficient solution methods. We provide a comprehensive computational study for both cases on instances based on demographic, spatial, and economic data of Vienna. We show that our formulations for this problem solve these instances in a few seconds, which makes them usable in an online booking system. In the analysis we discuss different potential settings. We study the optimal composition of a shared fleet, restricted sets of modes of transport, and variations of the objective function.