  With ongoing developments in digitalization and advances in the field of
autonomous driving, on-demand ride pooling is a mobility service with the
potential to disrupt the urban mobility market. Nevertheless, to apply this
kind of service successfully efficient algorithms have to be implemented for
effective fleet management to exploit the benefits associated with this
mobility service. Especially real time computation of finding beneficial
assignments is a problem not solved for large problem sizes until today. In
this study, we show the importance of using advanced algorithms by comparing a
fast, but simple insertion heuristic algorithm with a state-of-the-art
multi-step matching algorithm. We test the algorithms in various scenarios
based on private vehicle trip OD-data for Munich, Germany. Results indicate
that in the tested scenarios by using the multi-step algorithm up to 8$\%$
additional requests could be served while also 10$\%$ additional driven
distance could be saved. However, computational time for finding optimal
assignments in the advanced algorithm exceeds real time rather fast as problem
size increases. Therefore, several aspects to reduce the computational time by
decreasing redundant checks of the advanced multi step algorithm are
introduced. Finally, a refined vehicle selection heuristic based on three rules
is presented to furthermore reduce the computational effort. In the tested
scenarios this heuristic can speed up the most cost intensive algorithm step by
a factor of over 8, while keeping the number of served requests almost constant
and maintaining around 70$\%$ of the driven distance saved in the system.
Considering all algorithm steps, an overall speed up of 2.5 could be achieved.
