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Feature Category. DARP studies address multiple
problem dimensions that are orthogonal to each
other. A feature category corresponds to a prob-
lem dimension. For example, the decision about
the number of vehicles a DARP study makes con-
stitutes a feature category.
Category Aspect. In our analysis, each feature cat-
egory is three-valued. The values correspond to
category aspects. The special value NULL is used
to express that a study does not address the fea-
ture category. For example, the feature category
about the number of vehicles contains two as-
pects, namely single- and multi-vehicle.
DARP Variant. A DARP variant is a combination of
aspects from all feature categories, fully describ-
ing the study w. r. t. decisions it makes about the
problem dimensions.
2 TAXONOMY
This section gives an overview of different feature cat-
egories that can be found in DARP studies:
• Static/dynamic (i. e. offline/online): In static
variants all trip requests are known a priori.
The decisions about vehicle-trip assignment and
routes are made before operation. In dynamic so-
lutions, the trip requests are revealed while the ve-
hicles are in operation. Such variants process re-
quests as they appear in real-time without knowl-
edge about the future and constantly update the
decisions.
• Deterministic/stochastic: In deterministic vari-
ants, it is assumed that all necessary informa-
tion to solve the problem is known with cer-
tainty. However, practical applications have to
work around unexpected events, such as some
customer demands being only revealed when they
are visited or potential customers not showing
up. Such solutions have to deal with information
uncertainty or imperfectness when decisions are
made. They, therefore, fall into the category of
stochastic variants.
• Single/multi vehicle: Solving multi-vehicle
DARP increases the problem complexity, since
trip-vehicle assignment optimality has to be con-
sidered.
• Single/multi depot: In single-depot variants, the
vehicles start their routes at the same depot and,
if backhauls are wanted, return to the same de-
pot after servicing all requests. With multi-depot
variants, the vehicles are initially located at mul-
tiple depots. The cost-effectiveness of the first
(and last, if backhauls are wanted) route leg has
to be considered. In addition to that, a vehicle
might start at one depot and return to another de-
pot, which adds another level of complexity.
• With/without time constraints: Earlier DARP so-
lutions derive from PDP and therefore have no
time constraints. Recent works employ time
constraints for customer pick-up/drop-off events,
even though their definitions vary. Most works
explicitly use the concept of time windows, which
enforces an event to happen between an earliest
and latest time. The concepts like maximum wait-
ing time, maximum ride time and maximum travel
delay are also in use. Basically, they all describe
the temporal boundaries to ensure customer con-
venience. Moreover, some works use soft time
windows, where violation is allowed to some de-
gree.
• Homogeneous/heterogeneous vehicles: Most
multi-vehicle DARP studies consider a homoge-
neous fleet and the vehicle capacity as the only
constraint. However, some real-world use cases
(e. g. transferring patients or elderly) require ve-
hicles with heterogeneous features and constraints
(e. g. vehicle type, equipment, capacity).
• With/without backhauls: Solutions with back-
hauls require the vehicles returning to a depot af-
ter servicing all requests.
• With/without transfers: Classical DARP solu-
tions transport a customer from a pick-up to a
drop-off location in one vehicle. Some recent
works started to investigate the possibility of ve-
hicle transfers in order to reduce travel costs.
• With/without Electric Vehicles (EVs): The uti-
lization of electric vehicles introduces the chal-
lenge of considering the state of charge of the bat-
tery and service pauses for battery charging when
planning the routes and schedules. This variant
seems to get a lot of attention in the context of
Vehicle Routing Problem (VRP), but not DARP.
• With/without meeting points (location flexibil-
ity): In DARP variants with arbitrary locations,
vehicles are typically routed via the exact loca-
tions that the customers specify. This might cause
inefficiency due to high number of small detours
or multiple unnecessary stops if locations are
nearby. In such situations, it is desirable to com-
bine a vehicle’s nearby location visits (whether for
pick-up or drop-off) into one (i. e. meeting points
between customers). A variation of the same idea
A High-level Category Survey of Dial-a-Ride Problems
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