A High-level Category Survey of Dial-a-Ride Problems

Sevket G

okay

1,2

, Andreas Heuvels

and Karl-Heinz Krempels

1,2

Informatik 5 (Information Systems), RWTH Aachen University, Aachen, Germany

CSCW Mobility, Fraunhofer FIT, Aachen, Germany

Keywords:

Demand-Responsive Transport, Dial-a-Ride, Ride-Sharing.

Abstract:

Dial-a-Ride Problem (DARP) is an active research ﬁeld since 1980. Many on-demand transport concepts like

Dial-a-Ride (DAR) services, Demand-Responsive Transport (DRT) and ride-sharing share the common objec-

tive of solving DARP. Along with its application areas changing over the years, the problem continues to draw

increasing attention with growing diversity of requirements, constraints and features. This paper examines the

research on DARP with respect to the feature categories the solutions consider in order to discover DARP

variants that most works focus on.

1 INTRODUCTION

Personal transport can be divided into two basic

groups: Private and public. Both forms have their

advantages and disadvantages. While private trans-

port is ﬂexible (w. r. t. time and location) and there-

fore convenient, public transport utilizes ﬁxed routes,

schedules and stops. Since public transport is based

on predetermined network and infrastructure, it can

achieve a higher throughput (i. e. bringing a larger

number of people from A to B in a period of time) and

therefore be more cost-efﬁcient. On the other hand,

its quality of service can be poor in rural communities

and off-peak times. Much attention has been given

to developing transport services that can combine the

advantages of both groups. On-demand transport or

DAR services pick up their customers at their desired

time and bring them from any location to any loca-

tion. In this sense, from a convenience perspective,

they are similar to private transport. They also resem-

ble public transportation, since passengers with simi-

lar journeys may share the vehicle, which contributes

to their cost-efﬁciency.

The initial applications included door-to-door

transportation of elderly/disabled people and trans-

portation at night and in rural areas to complement

public transport. However, with technological ad-

vancements like smartphones with Global Positioning

System (GPS) and Internet capabilities, it became

apparent that these applications can be broadened.

This gave rise to ride-sharing (i. e. carpooling, taxi-

sharing) and companies like Uber

and Lyft

1.1 Motivation

The underlying problem that DAR services address,

namely DARP, can be summarized as follows. Ac-

cording to (Cordeau and Laporte, 2007), DARP con-

siders designing vehicle routes and schedules for

• m users who specify trip requests between origins

and destinations,

• where there are n vehicles based at k depot(s),

• while minimizing vehicle route costs and accept-

ing as many requests as possible

• under a set of constraints.

DARP generalizes Pick-up and Delivery Problem

(PDP) and Vehicle Routing Problem with Time Win-

dows (VRPTW) which are prominent problems dealt

with in logistics and operations research.

Many real-world practices necessitate various re-

quirements and variants of DARP. In this paper, we

identify the feature categories that are derived from

the requirements and give a high-level overview of

the DARP landscape over the last 40 years w. r. t. fea-

ture categories the solutions consider. By doing so,

we aim to unlock aspects that get more attention from

the scientiﬁc community. In this paper, the following

terminology is used:

https://www.uber.com

https://www.lyft.com

594

Gökay, S., Heuvels, A. and Krempels, K.

A High-level Category Survey of Dial-a-Ride Problems.

DOI: 10.5220/0007801605940600

In Proceedings of the 5th International Conference on Vehicle Technology and Intelligent Transport Systems (VEHITS 2019), pages 594-600

ISBN: 978-989-758-374-2

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

595

is the meeting point between the driver and a cus-

tomer, which might reduce the overall costs, even

if there are no nearby location visits. The latter

is an active research area in the context of car-

pooling, where a driver has a speciﬁc journey and

accepts to make detours and extra stops to pick-up

and drop-off riders with similar journeys in order

to divide the travel expenses.

• With/without user preferences: Solutions can

consider user preferences, if users can inﬂuence

the decision making process (w. r. t. vehicle-trip

assignments and route calculation) by providing

extra constraints. Traditionally, a trip request

model consists of a pick-up and drop-off location,

a pick-up or drop-off time, time constraints and

the number of passengers. A model extending this

deﬁnition can be considered as a trip request with

user preferences. Some examples are as follows:

Fastest or cheapest ride, riding alone (i. e. no ride-

sharing), intermediate stops, vehicle type, seating

preference, baggage allowance. Since some pref-

erences directly imply selection of vehicle fea-

tures (which is already expressed by heterogene-

ity of vehicles category), herein we consider pref-

erences that are not covered by heterogeneous ve-

hicles in order to minimize the functional overlap

between the two.

3 RELATED WORK

A comprehensive survey and analysis of DARP land-

scape (i. e. models and solutions) up to 2007 and

thereafter can be found in (Cordeau and Laporte,

2007) and (Ho et al., 2018), respectively. The re-

view in (Cordeau and Laporte, 2007) categorizes the

solutions according to the single/multi vehicle and

static/dynamic variants and annotates whether a solu-

tion incorporates additional constraints like time win-

dows and vehicle capacity. The survey in (Ho et al.,

2018) categorizes the solutions according to static/

dynamic and deterministic/dynamic variants and an-

notates whether a solution considers single/multi de-

pots, single/ multi vehicles, homogeneous/ heteroge-

neous vehicles, time windows and vehicle capacity.

Unfortunately, both works fall short of giving a com-

plete overview of the DARP taxonomy, for example

as the work in (Psaraftis et al., 2016) does for VRP.

In recent years, ride-sharing started to emerge as

a new form of transportation with the rise of services

like Uber and Lyft. The authors of (Czioska et al.,

2017) differentiate ride-sharing from DARP with re-

gard to ride-sharing drivers having unique origins and

destinations whereas DARP utilizes depots. Never-

Table 1: DRT stop visit types according to (Ambrosino

et al., 2004). The higher the level, the higher the ﬂexibil-

ity.

Level Location Visit time

Required

visit?

1 predetermined predetermined yes

2 predetermined predetermined no

3 predetermined ﬂexible no

4 arbitrary ﬂexible no

theless, ride-sharing can be modeled as DARP, where

every vehicle starts at one unique depot and returns

to another unique depot (similar to multi-depot and

backhauls). Due to this close relationship between

the two domains, we include works addressing ride-

sharing as part of our study.

Some variants of DRT services can be considered

as another application of DARP. Table 1 illustrates

the four types of DRT stop visits identiﬁed by (Am-

brosino et al., 2004). Based on this observation, we

can determine ﬁve groups of DRT services:

• Fixed routes and schedules consisting of only

Level-1 stop visits (e. g. a conventional bus ser-

vice)

• Free routes and schedules consisting of only

Level-3 stop visits (e. g. DARP with pretermined

locations)

• Free routes and schedules consisting of only

Level-4 stop visits (e. g. taxi service, DARP with

arbitrary locations)

• Fixed routes and schedules with divergence/devi-

ation: In this group, the routes are only partially

deﬁned (Level-1) and can contain stop visits of re-

maining levels. It is allowed to deviate from the

route based on customer demand.

• Other mixed forms

4 CATEGORIZATION

Section 2 gave an overview of descriptions of dif-

ferent DARP feature categories in isolation. How-

ever, solutions almost never consider only one cate-

gory but a combination thereof. In order to recog-

nize some major trends, this section provides statistics

about studies addressing different combinations.

4.1 Research Methodology

We used Google Scholar

as the database to search

for the keywords dial-a-ride and ride-sharing. We

https://scholar.google.com

VEHITS 2019 - 5th International Conference on Vehicle Technology and Intelligent Transport Systems

596

Table 2: Analysis about the percentage of papers that ad-

dress different feature categories (without combinations).

Category Percentage of papers

Multi-vehicle 86%

Deterministic 86%

With time constraints 82%

Homogeneous vehicles 68%

Single-depot 64%

Static 64%

With backhauls 63%

With transfers 8%

With electric vehicles 5%

With user preferences 4%

With meeting points 3%

considered only the results of which the full text

was accessible from our organization network. Many

variants mentioned in Section 2 are studied in re-

lated problem domains as well, e. g. (Shang and Cuff,

1996) addresses Pick-up and Delivery Problem with

Transfers (PDP-T). Even though problem models

and solution approaches are similar and adaptable to

our examined domain, we intentionally leave such re-

search out of our scope. In total, we analyzed 154

publications between 1980 and 2019 with regards to

DARP categories they consider. Due to the high num-

ber of publications, we have made the paper refer-

ences only publicly available

, along with our anal-

ysis of each paper for all categories.

4.2 Results and Discussion

Figure 1 depicts the distribution of number of DARP

papers over the years. We can see that it started to get

more attention from the scientiﬁc community since

2000. Table 2 summarizes the percentage of papers

which consider different feature categories. We can

recognize 3 groups of percentages: Category aspects

above 80% that most papers consider, aspects in 60-

70% band where the complementary aspect receives

non-negligible attention and aspects with less than

10% percentage. DARP with transfers, electric vehi-

cles, user preferences and meeting points only gained

momentum in the recent years. Due to the low num-

ber of papers in these categories we omit them from

further inspection.

Figures 2a to 2g visualize the distribution of num-

ber of papers for each category over the years. As

we can see from Figures 2a to 2d, one category as-

pect received continuous attention from the commu-

nity over the years and dominates its complementary

https://github.com/goekay/DARP-variants/tree/

54422a1

aspect. On the other hand, Figures 2e to 2g illustrate

that the aspects dynamic, multi-depot and backhauls

started to receive increasing attention (arguably due

to the rise of ride-sharing).

Moreover, we wanted to analyze which combina-

tions of category aspects are addressed the most in

DARP landscape and what their percentages are. In

order to achieve this, we calculated the power set of

7 remaining categories to ﬁnd out the subsets with 2

to 7 categories. Table 3 summarizes the combinations

with the highest percentage in their respective subsets

with up to 6 categories. One interesting observation is

that the most popular n-combination builds upon the

most popular n − 1-combination.

Finally, Table 4 depicts most popular 4 combina-

tions in the subset with 7 categories. They all have

in common that they build upon the multi-vehicle,

deterministic, static DARP with time constraints and

backhauls. We conclude our analysis with the fol-

lowing results: The most popular DARP variant with

19% percentage of papers considers single-depots and

homogeneous vehicles aspects, additionally. More-

over, the dynamic DARP variant with the highest

percentage has only 5% share and addresses multi-

vehicle, deterministic, multi-depot DARP with time

constraints and homogeneous vehicles without back-

hauls.

5 CONCLUSION

In this work, we analyzed the research on DARP since

1980 w. r. t. various feature categories the studies con-

sider. We provided a taxonomy of the variants and la-

belled DARP publications accordingly. In doing so,

we were able to discover some new trends and that

some feature category aspects remained focal points

over the years. Finally, we can derive that multi-

vehicle, single-depot, deterministic, static DARP with

time constraints, backhauls and homogeneous vehi-

cles is the most studied DARP variant.

5.1 Outlook

We envision that DARPs with electric vehicles, user

preferences and meeting points will receive increas-

ing attention in the forthcoming years. For exam-

ple, one real-world application of meeting points is

already introduced by Uber as Express POOL (Stock,

2018). The service reduces detours by having the cus-

tomer walk to/from a location nearby the start/end-

point of the initial request. The so-called Express

spots change based on popular routes at the time of

request.

A High-level Category Survey of Dial-a-Ride Problems

597

Table 3: Most popular combinations with 2 to 6 categories. Each row represents the combination with the highest percentage

of papers in its respective subset.

Category combinations

Percentage

of papers

Multi-vehicle & deterministic 75%

Multi-vehicle & deterministic & time constraints 67%

Multi-vehicle & deterministic & time constraints & backhauls 51%

Multi-vehicle & deterministic & time constraints & backhauls & static 43%

Multi-vehicle & deterministic & time constraints & backhauls & static & homogeneous vehicles 27%

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

2016

2018

2019

Figure 1: Number of DARP papers per year.

Table 4: Most popular 4 combinations with 7 categories.

All papers commonly consider the multi-vehicle, determin-

istic, static DARP with time constraints and backhauls.

They differ from each other in 2 categories which are de-

picted.

Category combinations

Percentage

of papers

Homogeneous vehicles & single-depot 19%

Heterogeneous vehicles & multi-depot 10%

Homogeneous vehicles & multi-depot 9%

Heterogeneous vehicles & single-depot 6%

Autonomous Vehicles (AVs) are a research area

that is in experimental stages, but may be considered

by the DARP research community in future. Classi-

cal DARP concentrates on calculating optimal sched-

ules and routes, but not on who executes them or how

they are executed. Therefore, the entity that moves

the vehicle (i. e. a computer in case of AVs or a hu-

man) is mostly orthogonal to DARP. However, taking

into account additional constraints like crew schedul-

ing (e. g. work shifts) is only applicable in variants

with human drivers. Similarly, it is possible that spe-

ciﬁc constraints arise with the advent of AVs.

Most DARP solutions assume that shortest path

information between origins and destinations exists,

and that the lookup of shortest paths between two lo-

cations is fast and therefore negligible. Consequently,

they focus on the multi-criteria combinatorial opti-

mization aspect of DARP. Fast shortest path lookup

is possible, if a shortest path matrix between all lo-

cations can be pre-calculated and cached. This is

feasible either in static variants or in variants with

predetermined locations. With the popularity of on-

demand real-time ride-sharing, the research focus will

shift from static to dynamic DARP solutions. A pre-

determined set of locations for pick-up and drop-off

reduces the ﬂexibility to Level-3 (see Table 1) and

forces the customers to walk to/from a pick-up/drop-

off location. However, real door-to-door mobility is

provided by DARP solutions with arbitrary locations.

In these variants, the number of locations is virtually

inﬁnite (depends on the underlying map), which pre-

vents pre-calculation

and makes path calculations a

performance bottleneck. This is an issue that needs to

be addressed by DARP research community.

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1980

1988

1996

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Multi-vehicle

Single-vehicle

(a)

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Stochastic

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(f)

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