  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.
