  Ridepooling services play an increasingly important role in modern
transportation systems. With soaring demand and growing fleet sizes, the
underlying route planning problems become increasingly challenging. In this
context, we consider the dial-a-ride problem (DARP): Given a set of
transportation requests with pick-up and delivery locations, passenger numbers,
time windows, and maximum ride times, an optimal routing for a fleet of
vehicles, including an optimized passenger assignment, needs to be determined.
We present tight mixed-integer linear programming (MILP) formulations for the
DARP by combining two state-of-the-art models into novel
location-augmented-event-based formulations. Strong valid inequalities and
lower and upper bounding techniques are derived to further improve the
formulations. We then demonstrate the theoretical and computational superiority
of the new model: First, the formulation is tight in the sense that, if time
windows shrink to a single point in time, the linear programming relaxation
yields integer (and hence optimal) solutions. Second, extensive numerical
experiments on benchmark instances show that computational times are on average
reduced by 49.7% compared to state-of-the-art event-based approaches.
