  Some of today's most significant challenges in urban environments concern
individual mobility and rapid parcel delivery. With the surge of e-commerce and
the ever-increasing volume of goods to be handled, new logistic solutions are
in high demand. The share-a-ride problem (SARP) was proposed as one such
solution, combining people and parcel transportation in taxis. This is an
NP-hard problem and thus obtaining optimal solutions can be computationally
costly. In this paper, we work with a variation of SARP for ride-hailing
systems, which can be formulated as a multi-depot open generalised vehicle
routing problem with time windows. We present and solve a mixed-integer linear
programming (MILP) formulation for this problem that bundles requests together,
and we compare its results to a previously proposed two-stage method. The
latter solves the so-called freight insertion problem (FIP) in the second
stage, for which we consider two versions, and the problem consists of
inserting parcels into predefined passenger routes obtained in the first stage.
We tested the methods in three sets of instances. The developed bundle-based
approach outperformed both FIP versions in solution quality and in the service
of parcels. Our method also compares favourably when it comes to reducing the
amount of deadheading distance.
