Who is more likely to get a ride and where is easier to be picked up in ride-sharing mode?

Abstract

The ubiquity of information and communication technology (ICT) and application of global positioning system (GPS) enabled cell phones provide new opportunities to implement ride-sharing in many ride-hailing platforms, where matching proposals with multiple riders are established on very short notice. In this paper, the travelers joining in the ridesharing are assumed to be homogeneous in terms of having their own vehicles. When they have announced their travel requests, the ride-sharing platform will check whether they can be picked up by any other travelers. If failed, they will drive by themselves and become a driver who would like to pick up other passengers in the system. To solve this problem, the ride-matching problem is formulated as a set-partitioning problem and a so-called ordered greedy (OG) method is presented to get the approximately optimum under the large-scale circumstance. The results of simulation examples prove that the proposed method can achieve a reasonable matching result through Cplex within a few seconds but at most 3.8% worse than the exact optimum. Furthermore, several interesting results are also found via simulating generated data and the real-world data of Chengdu in China. In simulation experiments, with a higher level of demand density, the easiest place to find a ride is not in the center but a ring close by it, which is determined by traffic flows, OD distance and vehicles’ utilization. As a contrast, the optimal strategy for participants to be a rider is going to other specific regions rather than staying in the city center in real-world experiments.

Full text

Journal Pre-proof
Who is more likely to get a ride and where is easier to be picked up in ride-sharing
mode?
Yue Yang, Qiong Tian, Yuqing Wang
PII: S2096-2320(20)30044-5
DOI: https://doi.org/10.1016/j.jmse.2020.09.003
Reference: JMSE 35
To appear in: Journal of Management Science and Engineering
Please cite this article as: Yang Y., Tian Q. & Wang Y., Who is more likely to get a ride and where is
easier to be picked up in ride-sharing mode?, Journal of Management Science and Engineering, https://
doi.org/10.1016/j.jmse.2020.09.003.
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1
Who is more likely to get a ride and where is easier to be
picked up in ride-sharing mode?
Yue Yang, Qiong Tian*, Yuqing Wang
School of Economics and Management, Beihang University, Beijing 100191, China
* Correspondence:
tianqiong@buaa.edu.cn
Abstract: The ubiquity of information and communication technology (ICT) and
application of global positioning system (GPS) enabled cell phones provide new
opportunities to implement ride-sharing in many ride-hailing platforms, where
matching proposals with multiple riders are established on very short notice. In this
paper, the travelers joining in the ridesharing are assumed to be homogeneous in terms
of having their own vehicles. When they have announced their travel requests, the
ride-sharing platform will check whether they can be picked up by any other travelers.
If failed, they will drive by themselves and become a driver who would like to pick up
other passengers in the system. To solve this problem, the ride-matching problem is
formulated as a set-partitioning problem and a so-called ordered greedy (OG) method
is presented to get the approximately optimum under the large-scale circumstance.
The results of simulation examples prove that the proposed method can achieve a
reasonable matching result through Cplex within a few seconds but at most 3.8%
worse than the exact optimum. Furthermore, several interesting results are also found
via simulating generated data and the real-world data of Chengdu in China. In
simulation experiments, with a higher level of demand density, the easiest place to
find a ride is not in the center but a ring close by it, which is determined by traffic
flows, OD distance and vehicles’ utilization. As a contrast, the optimal strategy for
participants to be a rider is going to other specific regions rather than staying in the
city center in real-world experiments.
Keywords: ride-matching; heuristic algorithm; passenger ratio; Chengdu data.
1 Introduction
With the growing concern for traffic congestion, fuel shortage and environmental
pollution, people alternatively using transportation modes in a flexible way.
Ridesharing which is for the purpose of taking the great use of the existing
passenger-movement capacity on the vehicles has been widely adopted by citizens.
While sharing a vehicle, individual travelers split travel costs such as gas, toll, and
parking fees with people who have similar itineraries and time schedules and thus
saving part of their travel costs. Aside from participants, ridesharing is also beneficial
to the society by mitigating traffic congestion, conserving fuel, and leading to a low
carbon economy through cutting down motor vehicle exhaust. (Ferguson, 1997;
Kelley, 2007; Morency, 2007; Chan et al., 2012).
Over the past few years, traditional taxi industries have experienced and
witnessed radical changes. One representative is these widely used online ride-hailing
platforms, such as Uber, Lyft and Didi Chuxing, enable idle taxi drivers to be
automatically matched with passengers without spending amount of time searching on
the street. Specifically, these platforms would collect all the idle drivers and the new
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coming requests during each short time slot (say one or two seconds), and then make
decisions based on a combinatorial optimization algorithm. Under this circumstance,
the taxis’ ride-matching optimization problems of E-hailing platforms naturally fall
into the category of bipartite matching problems, which have been widely discussed in
some researches (Agatz et al. 2012; Zhan et al., 2015; Xu et al., 2018). Some
well-known solution approaches for maximum bipartite matching has been employed
to solve these problems in both academic researches and industrial application.
Compared to taxi-matching problem, ride-sharing matching problems will be more
complex and intractable due to the nature of service mode. To begin with, there will
be more than one rider picked up in a ridesharing trip, to reduce the operating cost and
boost total revenue, the platform needs to schedule the route and determine the order
of serving riders. In addition, the participants in ridesharing do not work as agency
employees of the platform but have their own vehicle and would like to share the ride
with others with limited detour. In this case, the platforms will determine their roles
(rider or driver) and provide them with schedules to satisfy their demands. The above
facts show that the matching process in ridesharing systems is similar to traditional
carpooling and dial-a-ride problem (DARP). Although carpooling is a regular,
advanced, and cost-effective means of transportation (Ferguson, 1997; Morency,
2007), it does not accommodate unexpected changes of schedule. By contrast, DARP
provides shared seats to response to the advanced requests between any origins and
destinations within specific depots (Berbeglia et al., 2010), whereas in a ridesharing
system each driver may have a unique and flexible origin–destination (OD) pair.
From the perspective of travelers, overly long waiting time is essentially caused
by the imbalance and mismatching among travelers, in other words, travelers’
personal preferences, including travel distance and origin locations, will exert a
critical effect on the performance of ride-sharing system. Upon tackling the
inefficiency in this stage, Santi et al. (2014) suggested a mathematical framework for
the understanding of the tradeoff between collective benefits of sharing and individual
passenger discomfort is lacking. Stiglic et al. (2016) demonstrated the time flexibility
of each participant in ridesharing will results in different efficiencies of the system.
Long et al. (2018) also proved that the serval factors, including unit cost of driving,
travelers’ VOTs, travel time uncertainty, have significant impacts on the performance
of the proposed ride-sharing system with travel time uncertainty. Nonetheless,
compared to these aforementioned factors, the spatial distribution of participants’
origins also has intense impacts on the outcomes of ride-sharing system, while there
are few studies focus on this topic.
To ameliorate the matching efficiency in ridesharing, in this paper we
concentrate our attention on figure out the optimal strategies for each traveler to find a
ride as soon as possible. Firstly, we consider a ride-sharing system setting in which all
the trips are known in advance and suppose each trip own a vehicle. With information
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of location and time requirements provided by each participant, the ride-sharing
system automatically match potential drivers and passengers over time via ordered
greedy (OG) algorithm. Secondly, according to the spatial distribution of “passenger
ratio” in aforementioned system, we discover several factors affecting the matching
efficiency. Finally, combining with real-world identification in Chengdu, we figure
out the optimal choices of origins for each participant based on extensive simulations.
The main contributions of this paper can be summarized as follows:
 A new heuristic method is introduced to solve the ride-sharing matching
problem, and results prove that our method achieves remarkable performance (about
3.8% worse than the verified exact optimum which is solved by Cplex within a few
seconds).
 Based on the outcomes of ridesharing system, several factors affecting
matching efficiency have been discovered to offer recommendations to ridesharing
participants to find a ride but also help the platforms to improve the ride-sharing
service.
 Comprehensive numerical experiments are also conducted based on
simulation data and the real-world taxi data to identify who is more likely to be a
passenger and where is easier to find a ride in ridesharing.
The rest of paper is organized as follows. In Section 2, we give a review of the
related works refer to ride-sharing models and ride-matching methods. Then we
propose a reduction mechanism and set-partitioning model in Section 3. In Section 4,
the solution algorithm is developed. And in order to identify the performance of
proposed algorithm and further explore that who and in where is easier to be a
passenger in ride-sharing, extensive experiments are conducted in Section 5. Finally, a
conclusive discussion is presented in Section 6.
2 Literature review
2.1 Shared Taxi, Carpooling and Dial-a-Ride problem
Several types of ridesharing systems have been proposed in the research
literature and many of them are being used in Taxi-sharing, Carpooling and
Dial-a-Ride problem (DARP).
Taxis are a private mode of demand-responsive transportation alternative. Along
with higher cost, the door-to-door transportation provided by taxi is not affordable for
everyone. While nowadays, shared taxi services make it possible for passengers to cut
down the cost of the journey by sharing their trips and potentially result in a reduction
in the total miles traveled in the network. In many researches, lots of different
shared-use mobility services have been designed. Flexible itinerary transit systems
(Quadrifoglio et al. 2008; Li and Quadrifoglio 2010; Qiu et al. 2014), and
High-Coverage Point-to-Point Transit (HCPPT) (Cortés and Jayakrishnan, 2002) are a
few examples.
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Carpooling is another concept of using shared cars by persons with similar travel
needs who decide to carry out common car journeys between certain origins and
destinations.
The carpooling problem can be divided into two main types in practice:
the traditional carpooling problem and the flexible (casual) carpooling problem.
Traditional carpooling requires a long-term commitment among two or more people
to travel together on recurring trips for a particular purpose, often for traveling to
work (Baldacci et al., 2004; Wolfler et al., 2004). And the other type is characterized
by no prearrangements or fixed schedules for matching drivers and passengers.
Example of flexible carpooling is showed in the Washington D.C. area, where the
participants are free of charge (LeBlanc, 1999; Spielberg and Shapiro, 2000), and
casual carpooling is in San Francisco Bay Area and Houston, with a fixed-price for
each rideshare itinerary (Burris and Winn, 2006; Kelley, 2007).
Dial-a-ride services are offered in the context of demand responsive
transportation. Users are transported from a specific origin (e.g., from home) to a
specific destination (e.g., to a medical facility). Typically, a user has two related
transport requests on a single day: an outbound request from home to the desired
destination and an inbound request, i.e., the return trip home. DARP is a
generalization of vehicle routing problem with picking-up and delivery under a time
window (VRPPDTW), where people are transported instead of goods. Usually, DARP
optimizes the pick-up and delivery of passengers in special settings including
door-to-door transportation and is commonly used in para-transit systems or
shuttle-like services. In the basic form of DARP, vehicles and riders are assumed to be
homogeneous. All vehicles start from and return to the same depot (Savelsbergh et al.,
1995; Cordeau et al., 2007; Mahmoudi et al., 2016).
In recent years, traditional Dial-a-ride problems have experienced and witnessed
radical changes. One representative is these widely used online ride-hailing platforms,
which enable idle taxi drivers to be automatically matched with passengers without
spending amount of time searching on the street. To facilitate the implement of
ride-hailing application, Alonso-Mora et al. (2017) proposed a real-time multitask
framework to tackle the large-scale real-world taxi assignment. Given a collection of
trips, Vazifeh et al. (2018) also provide a network-based solution to determine the
minimum number of vehicles needed to satisfy all the trips in the city.
2.2 Ride-matching problem
With effective use of new communication modes including mobile technology
and global positioning system (GPS), the ride-matching problem was concerned by
scholars in recent years (Furuhata et al. 2013; Agatz et al. 2012). Ride-matching
problems share some of the characteristics of the more advanced DARPs and
VRPPDTW, such as multiple depots, heterogeneous vehicles and passengers. Drivers
in ridesharing systems are traveling to perform activities and have distinct origin and
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destination locations (multi-depot), different vehicle capacities (heterogeneity), and
rather narrow travel time windows. Generally, these factors may lead the matching in
ridesharing systems into a spatiotemporally sparse problem. In its simplest form, the
ride-matching problem matches a single rider to each driver. This can be modeled as a
maximum-weight bipartite matching problem that minimizes the total rideshare cost
(Agatz et al., 2011).
There are new trends in modeling the ride-matching problem recently.
(1) Variations of ridesharing through introducing meeting points: Stiglic et al.
(2015) introduced a ridesharing system with meeting points instead of pickups or
drop-offs at a series of points and validated the efficiency in terms of the number of
shared trips and system wide travel distance savings. This idea was first mentioned by
Kaan and Olinick (2013) while considering vanpooling. All the commuters gathered
at one park-and-ride location and ride to another, but the destination was fixed by then,
which made the problem simpler. The application of meeting points can also be found
in school bus transportation, Schittekat et al. (2013) gave a comprehensive
consideration of the station and itinerary choices by means of a new hybrid
parameter-free metaheuristic. More relevant to our study, Varone and Aissat (2015)
narrowed down to individual riders. Setting limitations to the meeting points on each
way and keeping the detour constraint in mind. Aïvodji et al. (2016) considered the
cost of ridesharing user privacy while setting meeting points, and developed a privacy
preserving procedure to deploy meeting points without sacrificing the ridesharing
usage.
(2) Scaling to large system through partitions and developing three types of
partitions, geography based, user based, and model based: Ma et al. (2015) and Pelzer
et al. (2015) proposed to partition the study area into small homogeneous sub-regions
based on predefined grids and road network topology, by which real-time sharing
requests could be well arranged under time, capacity and cost limitations. Apart from
geography-based matching and scheduling, personal preference, the number of
passengers for instance, was also considered by Lyu et al. (2017) as a basic condition
while grouping. Moreover, Masoud et al. (2017) located users and potential available
drivers in a narrow search space and model in each subset to reduce problem size. As
for model-based development, Bent and Van Hentenryck (2006) creatively divided the
matching process into two stages, minimized the fleet size and total distance in turn.
As a result, larger instances could be solved faster through a population-based
metaheuristic (Cherkesly et al. 2015). Also, for neighborhood search (VNS), Parragh
et al. (2010) added a competitive variable into heuristic method. Hosni et al. (2014)
applied the Lagrange decomposition approach to reduce the mixed integer
ride-matching problem into smaller problems and solved them separately.
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3 Model formulation
In this section, we consider a ride-sharing platform serves for a particular
metropolitan area, where a sequence of
travel requests generated over time from
potential participants. All the participants sending their trip request to the ride-sharing
platform imply their willingness to share the ride with others. Every trip request 
has an earliest departure time, 



, from her/his origin 

and a latest arrival time,




, at her/his destination 

. The participants can decide to either be a driver, who
serve as many as possible passengers considering her/his time and the vehicle
capacity constraints, or be a passenger if any driver can pick up and drop off in her/his
time window 







. Let  denotes the set of participants, which is
divided into two sub-sets, namely representspassengers who are looking
for rides and ,stands for the set of drivers who are willing to provide rides along the
journey. Each vehicle is homogeneous in terms of the same capacity  and constant
travel speed . It is assumed that all the travel requests are known in advance before
the execution of the ride-matching process. The platform, for some purpose (for
instance minimizing the total vehicle-km) decides how to sort the travel requests into
itineraries. Let’s considering a typical participant  who acts as a driver. After a
series of matching processes, driver  totally serves  passengers. Let  !
denotes the itinerary of driver, which includes " #$! nodes:
 !%

&

'
&

'
&

(
The itinerary  ! is an ordered sequence which consists of origins and
destinations not only of the driver  but also of other passengers sharing the ride with
. To focus on the ride matching process and without any loss of generality, the
network structure is ignored in the model and the vehicle travel along straight line
between successive nodes. Due to the simplicity, the rest of the paper will use )
*
to
represent the +, node in the itinerary .
For any itinerary -)
.
&)
*
&)
/01/
2, the number of occupied seats is
denoted as a vector 3-4
.
&4
*
&4
/01/
2, where 4
*
is the number of
occupied seats of itinerary  after visiting the + th node along the itinerary. In
addition, because each travel request has its own earliest departure time and latest
arrival time, for each node of an itinerary there are four types of time constraint. Let
56, 5, 76 and 7 respectively denote the sets of the earliest arrival time, the
earliest departure time, the latest arrival time and the latest departure time for the
itinerary. 56-89
.
&89
*
&89
/01/
2
5-8
.
&8
*
&8
/01/
2
76-:9
.
&:9
*
&:9
/01/
2
7-:
.
&:
*
&:
/01/
2
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Obviously, the earliest departure time 8
.
of the first node is 

;

and the latest
arrival time :9
/01/
of the final node is 

;

. It is essential to note that there are no
arriving time existing at 

;
and no departure time existing at 

;
, and for simplicity,
we can assume that 89
.
<:
/01/
=. Thus, 56
>
,5
>
,76
>
,7
>
can be derived
from: 89
*
8
*?.
#
>
@A;
>
@
(1)
8
*
89
*
#B
>
@
(2)
:
*
:9
*1.
C
>
@
>
@D;
(3)
:9
*
:
*
C9
>
@
(4)
where 
>
@A;
>
@
is the travel time from )
*?.
to )
*
, and B
>
@
9
>
@
indicate the probable
waiting time and probable advance time at the node )
*
, respectively.
As intuitively depicted in Fig. 1, it is compulsory for the driver to wait at )
*
if
89
*
is earlier than 
>
@

, that is, the time gap B
>
@
between 
>
@

and 89
*
(
>
@

E89
*
) is
the waiting duration when driver arrives at )
*
. Meanwhile, compared to latest
departure time :
*
, the driver has to reach )
*
no later than 
>
@

. In other words, the
gap 9
>
@
between 
>
@

and :
*
(
>
@

F:
*
) is length of time to calculate the latest
arrival time. Specifically, we should note that waiting time B
>
@
will only exist at
origin node, while advance time 9
>
@
will happen only at destination node. As a
consequence, B
>
@
9
>
@
can be represented as:
B
>
@
G <+H)
*
+8++
49IJ<
>
@

C89
*
K+H)
*
+)+L+ (5)
9
>
@
G <+H)
*
+)+L+
49IJ<:
*
C
>
@

K+H)
*
+8+9+ (6)
Specifically, the equation (1) represents the earliest arrival time 89
*
of )
*
is
generated from 8
*?.
of previous node )
*?.
, and the equation (2) indicates the
earliest departure time 8
*
of )
*
is derived from 89
*
and B
>
@
. Moreover, the
equation (3) shows the latest departure time :
*
of )
*
is calculated from :9
*1.
of
latter node )
*1.
, finally the equation (4) indicates the latest arrival time :9
*
of :9
*
is
deduced from :
*
and 9
>
@
. The detailed procedure of acquiring four sets is depicted
in Fig. 1:
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Fig. 1. The procedure of calculating 56
>
,5
>
,76
>
,7
>
After constructing the capacity and time constraints, we realize that the location
)
*
and )
*1.
, the earliest departure time 8
*
and the latest arrival time :9
*1.
can be
used to define a serving region in the network, which is the so-called time-space range
(Masoud et al., 2017). In this paper, we put all the spatial nodes into two-dimension
coordinate, that is, each node in itinerary  will own horizontal and vertical
coordinates. Consequently, the time-space range will be formed as an ellipse, whose
focal points o are two adjacent nodes )
*
and )
*1.
. In addition, the length of the major
axes is the Euclidean distance between )
*
and )
*1.
, and the transverse diameter is an
upper bound of the travel (detour) distance between )
*
and )
*1.
(see Fig. 2).
According to ,76,5, we can easily obtain the time-space range set M of the
itinerary, which states the detour (serving) range of driver
.
without conflicting
with the time constraints. See as follows:
M-N
.
&N
*
&N
/01.
2O+P-$&"#$2
where N
*
O+P-$&"#$2 is the detour range when the driver starts from )
*
.
Obviously, if a new nodecan be covered by any of subrange N
*
in M, hence this
node can be visited by the itinerary  without violating its time constraints.
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Fig. 2. The example of acquiring the time-space range set M
Note that the range of N
*
is also determined by the new coming node, assume
that there is a new coming node IQR! with a coordinate IQ! and a time buffer
R, which represents a probable waiting time or a probable advance time at this node.
In particular, since the new node can be origin or destination, for taking time
characters of the current node into consideration, here we introduce a different
notation R, which is equivalent to a probable waiting time if the node is origin,
otherwise a probable advance time. Therefore, the subrange N
*
covering the new
coming node can be defined as the following form:
N
*
G IQR!STUJ
ICI
>
@
K
"
#
V
QCQ
>
@
W
"
#
UJ
ICI
>
@D;
K
"
#
V
QCQ
>
@D;
W
"
X
F
:9
*1.
C
8
*
CR!
Y
Z (7)
where V
I
>
@

Q
>
@
W,V
I
>
@D;

Q
>
@D;
W are the two-dimension coordinates of the node )
*
and
)
*1.
, respectively. In particular, the time buffer R defined here will be further
discussed in the next section.
To mathematically model the ride-matching problem, we use three sets of
decision variables, as defined in (7)-(9). And the mathematical notations used in the
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paper are summarized in Table. 1.
[
\

]$)+8)9^8,8++8)9)Q
<_,8)B+8 (8)
`
>
@
>
@D;

]$)+8))98:,89)aH)4)
*
)
*1.
+
<_,8)B+8 (9)
b
\
c
]$98L8)d9^89)+8+)+8eQ
<_,8)B+8 (10)
Table. 1. Notations
The Description of Notations

The set of ridesharing drivers.

The set of passengers.
f
The set of candidate routes.

A feasible itinerary and

P
f
.
3
The occupied seats vector of the itinerary

.
5
The earliest departure time vector of the itinerary

.
56
The earliest arrival time vector of the itinerary

.
7
The latest departure time vector of the itinerary

.
76
The latest arrival time vector of the itinerary

.
M
The time-space range set of the itinerary


.

The capacity of a vehicle, which is constant in this paper.

>
@

The departure time of node
)
*
in the itinerary

.

>
@
g
The arrival time of node
)
*
in the itinerary

.
R

h
The probable waiting time at origin

c
of passenger
d
.
R

h
The compulsory advanced arriving gap at origin

c
of
passenger
d
.
a
\
The cost saving of the itinerary

.

\
All the passengers joining the itinerary

.
i
\
The total time buffer of the itinerary

.
[
\

A binary decision variable.
`
>
@

>
@
D
;

A binary decision variable.
b
\


c
A binary decision variable.
j
\
A binary decision variable.
Therefore, the ridesharing matching problem can be modeled as follows:
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11
39I+9a8k9+Ll a
\
Yl[
\

P
!
\Pf
(11)
Subject to:
l`
>
@
>
@D;

>
@
m

Cl`
>
'A;
>
'

>
'
m

[
\

OPO)
*
)
n
P (12)
l`
>
'A;
>
'

>
'
m

Cl`
>
@
>
@D;

>
@
m

[
\

OPO)
*
)
n
P (13)
l`
>
@
>
@D;

>
@D;
Cl`
>
@D;
>
@Do

>
@D;
<OPO)
*1.
Pp-



2 (14)
l`
>
@
>
@D;

>
@
m
h
Cl`
>
'A;
>
'

>
'
m
h
b
\
c
OPOdPO)
*
)
n
POPf (15)
l`
>
'A;
>
'

>
'
m
h
Cl`
>
@
>
@D;

>
@
m
h
b
\
c
OPOdPO)
*
)
n
POPf (16)
8
*
F
>
@

F:
*
O)
*
P (17)
89
*
F
>
@
g
F:9
*
O)
*
P (18)
4
*
FO)
*
P (19)
b
\
c
F[
\

OPOdPOPf (20)
[
\

Fl`
>
@
>
@D;

>
@
OPO)
*
POPf (21)
Equation (11) presents the objective function of the problem. A ride-matching
problem may have various objectives, ranging from maximizing profits to minimizing
the total system-wide vehicle-miles. This objective can vary among the nature of the
agency who is managing the system (public or private).
If the system is private and
operates for profit, the platform may pursue to maximize the number of participants
because revenues are linked to the number of successful ride-sharing arrangements.
However, public systems may have a societal objective like minimal system-wide
vehicle-miles, which is important from a societal point of view since it helps to reduce
pollution and congestion. Hence, in this paper we suppose that the ride-sharing system
attempts to minimize a system-wide vehicle-miles driven by all potential participants
traveling to their destinations, specifically, this objective also coincides with
maximizing total travel distance savings.
The sets of constraints that define the ridesharing system are presented in (12)
-(21). Constraint sets (12)-(14) route drivers in the network. Constraint set (12) directs
drivers in set D out of their origin 

, and (13) ensures that they end their trips at their
destination 

. Moreover, constraint set (14) is for flow conservation, which enforces
that a driver entering a passenger’s origin or destination, will exit this node and
continue his trip. Constraint sets (15)-(16) route riders in the network and are
analogous to (12)-(13), except for a small variation. While the optimization problem
generates itineraries for all drivers, matched or not, this is not the case for riders. Only
riders who are successfully matched will receive itineraries. This difference is
reflected in the formulation by replacing 1 on the ride hand side of constraint sets (12)
and (13) by b
\
c
in constraint sets (15) and (16). Constraints (17)-(18) guarantee the
departure time 
>
@

should fall into time windows 8
*
:
*
 and arrival time 
>
@
g
also
need to satisfy time windows 89
*
:9
*
, and Constraint (19) ensure occupied seats
does not exceed the vehicle capacity.
Constraint sets (20) and (21) register drivers
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12
who contribute to each passenger’s itinerary. Finally, all decision variables of the
problem defined in (8)-(10) are binary variables.
In particular, a
\
in this paper indicates the travel distance saving of itinerary,
which is defined as:
a
\
l+J
c
q
K
cPr
s
#+ 
q
!C+ ! (22)
where + t! indicates the function calculating the travel distance (Euclidean
distance) of the given itinerary, and 
q
represents the itinerary when the driver
drives alone.
3.1 Set Partitioning Formulation
Therefore, based on the feasible itineraries set f satisfying constraints(12-19),
the ride-sharing assignment problem in equation (11) can be converted to a
set-partitioning problem as follows:
39I+9a8k9+Lua
\
\Pf
Yj
\
Subject to: lj
\\Pf
h
$OdP (23)
lj
\\Pf

$OP (24)
j
\
P-<$2OPf (25)
where j
\
is the binary decision variable equals to 1 if the itinerary is included in
the final schedule f
v
and 0 if not. As shown in equation (23)-(24), each
participantcan join only one itinerary whether he acts as a driver or a passenger, and
f
c
,f

respectively represents the subset of itineraries sets containing the passengerd
and driver .
3.2 Reduction mechanism
In the previous sections, we have constructed a mathematical model to solve the
optimal assignment of ridesharing problem. To acquire the feasible itineraries set f,
we further introduce a reduction mechanism to limit the number of matching
relationships among the participants and eliminate drivers who cannot be part of a
rider’s itinerary due to lack of spatiotemporal compatibility between their trips. It
should be noted, this procedure does not limit the search space of the optimization
problem, but only narrows it by cutting down practically infeasible ranges, and
therefore it does not affect the optimality of the solution.
Suppose there is a feasible itinerary -)
.
&)
*
&)
/01/
2O+P-$&"#
"2 and a new arriving request d with an origin 
c
, a destination 
c
and time
window w

h



h

x, we need to identify whether d can be a passenger to join the
itinerary . To do so, we propose a reduction mechanism with four steps as follows:
Step1: Identify whether the origin 
c
of the participant can join the itinerary
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13
) if it can be covered by any of subrange N
*
O+P-$&"#$2 in M.
Firstly, given the subrange N
*
, the origin 
c
can be converted to VI

h
Q

h
R

h
W,
where R

h
is the probable waiting time at 
c
:
R

h
49IV<

h

C8
*
C
>
@

h
W (26)
Secondly, we will check the origin 
c
whether can be cover by N
*
:
yzV
I

d
CI
)
+
W
/
#V
Q

d
CQ
)
+
W
/
#zV
I

d
CI
)
+#$
W
/
#V
Q

d
CQ
)
+#$
W
/
{
FV
:9
+#$
C
8
+
CR

d
WY
(27)
Finally, if the origin 
c
can be visited in N
*
without violating time
constraints, we need to verify the capacity constraints as below:
4
*
#$F (28)
Step2: If 
c
satisfies the constraints mentioned in equation (27) and (28), we
can obtain a new itinerary 
1
h
, which indicates 

has been inserted into the
itinerary , and then the corresponding sets 3
1
h
,56
1
h
,5
1
h
,76
1
h
,7
1
h
,
M
1
h
can be easily derived from equation (1)-(7).
Step3: Suppose 
c
is the ^th node of the itinerary 
1
h
, we need to identify
whether the destination 
c
of the request d can be visited by the itinerary 
1
h
if
it can be covered by any of subrange N
n
O|P-^&"#"2in M
1
h
.
Initially, we also need to represent 
c
as a form VI

h
Q

h
R

h
W according to
the subrange N
n
, where R

h
defined as:
R

h
49IV<:9
n1.
C

h
>
'D;
C

h

W (29)
Last, the required covering condition should be verified:
yzV
I

d
CI
)
|
W
/
#V
Q

d
CQ
)
|
W
/
#zV
I

d
CI
)
|#$
W
/
#V
Q

d
CQ
)
|#$
W
/
{
FV
:9
|#$
C
8
|
CR

d
WY
(30)
Step4: If 
c
satisfies the constraint mentioned in equation (30), we can obtain a
new itinerary 
1
h
1
h
, which indicates 
c
has been inserted into the itinerary 
1
h
,
and then the corresponding sets 3
1
h
1
h
,56
1
h
1
h
,5
1
h
1
h
,76
1
h
1
h
,7
1
h
1
h
,
M
1
h
1
h
can be easily derived from equation (1)-(7).
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14
Fig. 3. The procedure of reduction mechanism
Consequently, if a request d satisfies all the verification in the four steps
mentioned above, namely he can join the itinerary ) to establish a new feasible
itinerary scheme 
1
h
1
h
(summary of the reduction mechanism can be seen in Fig
3). In this paper, the objective of ridesharing matching problem is to obtain the
optimum schedule f
v
among the feasible itinerary set f.
4 Algorithm
Since the ILP model mentioned in Section 3.1 is NP-hard, even with a small
number of requests, the feasible itineraries set f may be large and the decision
variable j
\
results in an exponentially large search space. Hence in this section we
propose a heuristic approach to arrive at the approximately optimal ride-matching
assignment, which aims to reach the best compromise between solution quality and
computational efficiency for large-sized real-world instances.
The philosophy of the heuristic approach is to reduce the value of the exponential
growth of decision variables j
\
. Ferrari et al. (2003) has proposed a straightforward
application of well-known greedy heuristic to solve the set partitioning problem.
In
addition, Huang et al. (2013) applied a kinetic tree algorithm capable of scheduling
dynamic requests and adjusting itineraries on-the-fly. Furthermore, Qian et al. (2017)
introduced a graph conversion method to acquire the optimal solution. However, the
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15
exact algorithm may work efficiently for small or medium sized instances,
nevertheless, it will fail with growing size. Xing et al. (2018) also proposed to apply
the greedy strategy in solving the one-to-one ride-matching problem combining
stability of matching.
Therefore, in order to efficiently solve the large-scale ridesharing cases in this
paper, we develop an improved heuristic algorithm so-called ordered greedy (OG)
algorithm, and the process of the OG Algorithm can be summarized as follows:
Step1. Initialize: Given the participants set -
.

/
&
}
2, we can construct
the candidate assignment f
v
~

;

q


o
q
&

•
q
€, which comprised of the
itinerary driven alone by each participant in set . Moreover, the driver set  and
passenger set  are initially set to •.
Step2. Order: Given the candidate assignment f
v
, then we need to sort the
itinerary  from largest to smallest in set f
v
based on i
\
, which can be denoted as:
i
\
 :9
/01/
C8
.
!Cl
>
@A;
>
@
*P-/&/01/2
(31)
where :9
/01/
C8
.
! is the totally extra time of the driver and l
>
@A;
>
@
*P-/&/01/2
represents the sum of travel time consuming. Hence, we can observe the remaining
time (to serve other participants if feasible) of the itinerary  via introducing i
\
.
Step3. Select: Given the ordered candidate assignment f
v
, we select the
itinerary 
*
from f
v
in order, and further obtain a feasible subset f
\
@
1.
deriving
from 
*
inserted only one participant. In particular, all the itineraries in f
\
@
1.
will
have a positive distance saving (the itineraries with a negative distance saving will be
also seen as infeasible and remove from f
\
@
1.
). Hence:
 If f
\
@
1.
is nonempty, we will go directly to Step4.
It’s also should be
noted that if 
*
is selected for the first time, the driver of 
*
will be
removed from the set .
 If f
\
@
1.
is empty, which means the itinerary 
*
can’t share a ride with
any other participants in remaining set , we will select the next itinerary in
f
v
and repeat Step3.
Step4. Update: Based on local greedy strategy, we can easily obtain the itinerary

v
in f
\
@
1.
with maximum travel distance saving as:

v
9)L49I
\
J~a
\
OPf
\
@
1.
€K (32)
Compared to 
*
, the new joined passenger in f
v
will be added into the
passenger set  and removed from the set . Moreover, the itinerary driven alone by
this passenger will also be removed from the set f
v
. Consequently, 
*
will be
updated to 
v
.
Step5. Iterate: Repeat the Step2, Step3, Step4 until set  is empty.
Step6.Terminate: Final the assignment set f
v
will be an approximately
optimal solution. (more detailed procedure can be referred in Table. 2 )
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16
Table 2. Pseudo-code of OG algorithm
Algorithm OG Algorithm
Initialize

f
v

~


;

q



o
q

&



•
q
€

B
,
8)8



-

.


/

&


}
2
.


•



•
‚
Input:






f
v
Output:
f
v
1
+
ƒ
$
2 While

„
•
do
3 Sort the itinerary set

f
v
based on the time gap
i
\

O

P

f
v
.
4 Select the
+
th itinerary

*
in the set

f
v
5 If driver in

*
is selected for the first time do
6


ƒ

the driver of

*
7

ƒ
9dd8



+


,


ƒ
)848



H)4


8 End
9 Enumerate feasible schedules set
f
\
@

1
.
10 If
f
\
@

1
.
„
•
do
11 Calculate the travel distance saving set
~
a
\

O

P
f
\
@

1
.
€
for each

P
f
\
@

1
.
12

v
ƒ
_e9+8

eQ

…†‡ˆ‰Š‹Œ

•Ž
!
13
d

ƒ

the new joined passenger in

v
compared to

*
14

ƒ
9dd8

d

+


,


ƒ
)848

d

H)4


,


15

v
ƒ
)848


c
q

H)4


f
v
16 Replace

*
with

v
in the set

f
v
17
+
ƒ
$
18 Else
19
+
ƒ
+
#
$
20 End
21 End
22 Return
f
v
In order to explain the OG algorithm mentioned above from a more intuitive
view, then we construct the following example to demonstrate the procedure of the
Algorithm1 in detail. As shown in the Fig. 4.A, we suppose that participants
set-
.

/

•

•

‘

’
2, the steps for applying OG Algorithm to assign the
announcements are as below:
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17
Fig. 4. The example of OG algorithm
Firstly, suppose i
\
of each itinerary in
f
v
equal to 60,50,40,30,20,10 minutes,
respectively, and we can construct the candidate itinerary set
f
v
from the biggest to
the smallest as follows:
f
v

%


$
:


"
:


“
:


”
:


•
:


–
:
(
Secondly, 

;
q
will be selected and suppose
f

$
:
1.
-

$
#
"


$
#
”


$
#
•
2,
and 
.
will be assigned as a driver, hence, -
.
2 and -
/

•

•

‘

’
2.
Thirdly, suppose a
\
of each  in
f

$
:
1.
are 2.5, 1.5 and 1 km, respectively,
and according to the local greedy strategy (

;
1
o
owns the maximum saving), thus

/
will be a passenger and -
/
2, -
•

•

‘

’
2. Aa a consequence,
f
v

%


$
#
"


“
:


”
:


•
:


–
:
(
(shown in Fig. 4.B).
Fourthly, suppose i
\
of each itinerary in
f
v
equals 15,40,30,20,10 minutes,
respectively. Then the set
f
v
will be sorted as:
f
v

%


“
:


”
:


•
:


$
#
"


–
:
(
Accordingly, 

—
q
will be selected and suppose n
f

“
:
1.
-

“
#
•
2, 
•
will
be assigned as a driver and obviously 
‘
will be a passenger, hence, -
.

•
2,
-
/

‘
2, -
•

’
2 and
f
v

%


$
#
"


“
#
•


”
:


–
:
(
(shown in Fig. 4.C).
Fifthly, suppose i
\
of each itinerary in
f
v
equals 15,15,30,10 minutes,
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respectively. Then the set
f
v
will be sorted as:
f
v

%


”
:


$
#
"


“
#
•


–
:
(
Obviously, 

˜
q
will be selected and
f

”
:
1.
is supposed to be empty.
Therefore, both 
•
and 
’
will be assigned as drivers, and further
-
.

•

•

’
2, -
/

‘
2.
Consequently, • and the
f
v

%


$
#
"


“
#
•


”
:


–
:
(
(shown in Fig.
4.D) will be obtained as the approximately optimal assignment.
5 Numerical Study
We now present the results of a set of computational experiments, designed to
generate the performance of the proposed algorithm and analyses upon where is easier
to get a ride. The algorithm was coded in Matlab2015b, and the experiments were
conducted on a desktop with @1.60 GHz processor, and 4 GB RAM. Each result
reported in the following sections are averaged over 10 runs for each problem instance.
The origins and destinations of participants in this experiment will be randomly
generated in a circle with a 7 mile radius. Besides, the rule of time window of each
participant can be set as ™







#šY




›, where 



is generated randomly
within <B, and 



simply equals to the sum of 



and šY




. Note that
the parameter š is a travel time budget factor, which indicates the degree of tightness
of travel time (Masoud et al., 2017).
In the next three sections, we will use the proposed algorithm to find the optimal
solutions for the randomly generated problems and real-world problems through
simulations. In section 5.1, we will compare the performance of the proposed
algorithm with Cplex in terms of computation time and solution quality. And an
in-depth analysis upon which factors affected ridesharing participants to become
riders is conducted in section 5.2. Finally, the numerical experiments are carried out
by using multiple real-world datasets from Chengdu in China to identify the practical
results in comparison to Section 5.2. In addition, we introduce three indicators in this
paper as below:
(1) The request density œ œSS •t7
/
tB!
ž (33)
(2) The passenger ratio Ÿ ŸSSSS
ž (34)
(3) The distance ratio
l+ !
\Pf
v
l+J
q
K
P¡
¢ (35)
In equation (33), •t7
/
represents the area size of the given region and B is
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the length of the time range, thus œ also indicates the arriving rate of the requests per
minute per square kilometer. Moreover, SS and SS in equation (34) are the number
of participants and passengers, respectively. Furthermore, l+ )!
>P\
v
is the total
distance after ridesharing while l+ )
q
!
P¡
is the total distance without
ridesharing in equation (35). It should be noted, that the objective mentioned in ILP
model can be equivalent to maximizing the distance ratio .
For more detailed parameters, see the following Table 3:
Table 3. Parameter setting
Parameter Values
7
5 km
B
30 min
š
2

4
5.1 Algorithm Comparison
For the first experiment, in order to gain a comprehensive comparison of the
algorithm in terms of computation time and solution quality, we generate and solve
five random instances with various œ<‚<$<‚<"<‚<•<‚$<‚", ten runs for each. As
shown in Table 4, The passenger ratio Ÿ, total distance and computation time cost are
compared between proposed method and IBM Cplex.
It can be observed that the Cplex is better than our method in minimizing the
total distance. However, it will take much more seconds to find the optimal solution
f
v
compared to proposed algorithm. Specifically, even with small increase of œ
(such as œ<‚<"<‚$), the computation time may differ significantly. The reason for
the huge differences is mainly because of the increase of the feasible itinerary set f.
For instance, œ<‚<" has only 917 feasible itineraries due to the loosely matched
relations among participants, which can be easily solved by enumerating within 3
seconds. As œ increases to 0.1, it becomes harder to enumerate 34233 feasible
itineraries for a large amount of computation time. In addition, when œ equals to 0.2,
the computing cost is too high to arrive at the optimal solutions by Cplex.
On the contrary, it can be illustrated that the proposed OG algorithm not only
performs efficiently for all the cases, but also obtains reasonably good solution quality.
It generates optimal or approximately optimal solutions for cases with verified
optimal solution and solves œ<‚" case in less than 20s. In particular, the solutions
of heuristic algorithm are optimal solution in œ<‚<$ case and are from 2.0%
(œ<‚<") to 3.8% (œ<‚$) worse than the optimal solutions in other cases.
Consequently, the heuristic algorithm is proved to be efficient and effective for
solving large-scale ride-matching instances based on our numerical experiments.
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Table. 4. Comparison of algorithm’s performance
S

S
œ
S
f
S
Cplex OG algorithm
Ÿ
Total
Distance(km) Time
Cost(s)
Ÿ
Total
Distance(km) Time
Cost(s)
30 0.01 83 0.26 141.75 3.52 0.26 141.75 0.96
60 0.02 917 0.4833 220.85 248.24 0.55 225.38 2.93
150 0.05 2758 0.4800 504.59 2465.06 0.57 517.59 9.09
300 0.1 34233 0.5733 901.73 53456.35 0.59 937.14 10.17
600 0.2 - - - - 0.64 1689.28 19.13
Table. 5. The result of 11 additional instances with œ<‚$&$‚•
S

S
œ
Ÿ
S

S
S

S
Total distance(km)
Time cost(s)
300 0.1 0.596 178.8 121.2 937.14 0.593818 10.16928
600 0.2 0.642667 385.6 214.4 1689.28 0.536523 19.13027
900 0.3 0.661778 595.6 304.4 2384.21 0.508735 35.4628
1200 0.4 0.678667 814.4 385.6 3043.66 0.487774 73.9648
1500 0.5 0.686333 1029.5 470.5 3704.49 0.474363 113.8377
1800 0.6 0.6965 1253.7 546.3 4344.61 0.463184 156.251
2100 0.7 0.70481 1480.1 619.9 4971.99 0.453732 257.574
2400 0.8 0.710458 1705.1 694.9 5576.22 0.444812 377.086
2700 0.9 0.714185 1928.3 771.7 6174.31 0.437665 563.427
3000 1.0 0.717467 2152.4 847.6 6809.35 0.434076 738.268
4500 1.5 0.731467 3291.6 1208.4 9675.83 0.412705 1239.95
Since the efficiency and effectiveness of the heuristic algorithm has been shown,
we further generate and solve 11 additional instances with œ<‚$&$‚•. The
results are shown in Table 5, and Fig. 5. A measures the passenger ratio Ÿ and the
distance ratio based on different level of œ. As intuition suggests, for the given
region and time scale, the passenger ratio Ÿ increases with the participant density œ
in the system. This implies that the higher density will result in much more riders in
ridesharing system, which also means more income for a platform. On the other hand,
the distance ratio £ presents a downward trend with the increase of œ, which
suggests that system-wide vehicle-miles will significantly reduce when the participant
density œ is high enough. Another interesting observation is that there is a downward
trend in both the increase rate of Ÿ and the decrease rate of £, moreover, it’s depicted
in Fig. 6. B that the computation cost will also become expensive when œ is too high.
As a result, the figure and table lead to the conclusion that ride-sharing platform
should collect the appropriate requests (e.g. œ can be set to 0.8 in Fig. 5) before
executing assignments to achieve at a better condition.
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Fig. 5. The curves of Ÿ, and time consuming under different
œ
5.2 Mining the factors affecting Passenger ratio
In the previous section, we have presented the overall results of the ridesharing
system and introduced the indicator so-called “passenger ratio” Ÿ. Obviously in the
system, Ÿ may vary among places in the given region and higher Ÿ can reflect more
probabilities for participants to find a ride. Therefore, in order to investigate the
changes of Ÿ in ridesharing system, we will observe its performance in terms of
spatial distribution based on grid-level and ring-level in this section. In the case of this
scenario, the region will be divided into 100 grids, which are 1 kilometer long and 1
kilometer wide. Furthermore, we divide the grids into five rings based on the distance
away from the center, and notice that a ring can be approximately considered as the
sub-region with same distance to the center.
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Fig. 6. Ÿ percentage varies among different grids.
Fig. 6 depicts the heatmaps of Ÿ in each grid, in this experiment the origin 

will be used to represent a participant  for simplistic, that is, Ÿ will be equivalent
to the ratio between the number of passengers’ origins and the number of participants’
origins in each grid. From the figure we can observe that the distribution of Ÿ shows
an irregular trend because of randomness in the small participant size (such as 300
and 600 participants). However, the increase in participant size (such as 3000
participants) results in uniform-distributed Ÿs among the grids of inner four rings.
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Fig. 7. Ÿ varies among different rings.
Furthermore, Fig. 7 displays Ÿ upon each ring, for a given small participant size
(such as 300 and 600 participants), the passenger ratio Ÿ will decrease with the ring
number (equivalent to the distance to the center of the region), which suggests that the
participants in places closed to the center are easier to find a ride. While we set more
participants (such as 1500 or 3000 participants), along with the increase in ring
number, Ÿ reaches a peak value at the third rings and then reduces. This result
suggests that the participants who start from the third ring will be more likely to be a
passenger.
Despite the intuitive difference in Fig. 6 and Fig. 7, there is little knowledge of
which factors will affect the spatial distribution of Ÿ. However, understanding the
significance of each factor and its quantitative influence will not only offer
recommendations to ridesharing participants to find a ride but also help the platforms
to improve the ride-sharing service. To achieve this goal, we utilize the several factors
as below:
Definition 1: Given a specific sub-region, ¤
*
is the flow per participant of grid
+:
¤
+


@
S¡
@
S
(36)
where 
*
denotes the flows (the number of drivers) passing grid +, and 
*
is the set
of participants originating from grid +.
Definition 2: Given a specific sub-region, ¥
*
is the average OD distance of
passengers in grid +:
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¥
*

l

:
P+
S

+
S
(37)
where 
*
is the set of passengers originating from grid +, and l
q
Pr
@
indicates
the sum of solo distance of all passengers in the given sub-region
+
.
Definition 3: Given a specific sub-region, ¦
+
is the rate of vehicles’ utilization
in grid +:
¦
*

l
4
+
P+
S

+
S
t
(38)
where 4
*
represents the occupied seats when driver  visits grid
+,
thus
l4
*
P
@
is the sum of total occupied seats of all the drivers passing grid +.
The distributions of ¤, ¥, ¦ are depicted in Fig. 8, Fig. 9, Fig. 10, respectively.
As an intuition suggests, both ¤ and ¦ decrease with the distance to the center,
while ¥ drops down as the increasing of the distance to the center. Here we further
investigate the correlations between factors and Ÿ in Fig. 11. In the first place, there
exists a rough linear rise for Ÿ with ¤ in four cases, and another interesting
observation is that Ÿ will keep stable when ¤ reaches 2 as requests are sufficient
(such as 3000 trips). This is due to the fact that ¤ is no longer the major determinants
if given enough trips. In the second place, Ÿ significantly decreases with ¥ in four
cases, which means that the participant with a short distance is easier to find a ride in
the system. Finally, Ÿ also demonstrates an increasing trend with ¦, and as a same
trend, Ÿ will fluctuate within a small range if ¦ exceeds 0.5 when we collect
enough requests (such as1500 or 3000 trips).
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Fig. 8. ¤ varies among different grids.
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Fig. 9.
¥
varies among different grids.
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Fig. 10.
¦
varies among different grids.
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Fig. 11. The correlations between factors and Ÿ
5.3 Real-world Experiments
Compared to the random distributions of origins and destinations in simulation
experiments, the commercial and business districts are usually denser within certain
geographical regions and are distinct from residential areas in reality. As depicted in
Fig. 12, we pick a spatial range with 5 km wide and 5 long in Chengdu, and
specifically, the center of our region is set as Tianfu Square. Thus, in this section we
use taxi datasets in Chengdu provided by DiDi chuxing
1
to comprehensively
understand the performance of our algorithm and the distribution of the passenger
ratio.
1
https://outreach.didichuxing.com/research/opendata/
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Fig 12. The sketch map of selected region in Chengdu
In this experiment, all the data are pre-processed to remove erroneous records,
such as coordinates located outside the city boundary or trips whose length is shorter
than 1 min. After cleaning, we conduct the experiments within specific region
centered at Tianfu Square with the same size compared to the previous experiments.
In particular, we extract trip dataset during off-peak hours (00:00-00:30), morning
peak hours (09:00–09:30), and evening peak hours (17:00–17:30) on November 2nd,
2016, which are regarded as representative time frames covering typical traffic states.
And all the other parameters are identical with settings in Table 3.
Table 6 presents the result for different extracted intervals, similar to our
previous simulation the passenger ratio Ÿ demonstrates an increasing trend and the
distance ratio presents a down trend with the increase of the density œ. Another
interesting point is that there is always a trade-off between the solution quality and the
computational efficiency for this ride-matching problem, that is, higher income
(higher Ÿ) and lower vehicle-mile cost (lower ) means more expensive
computational cost for a platform. Apparently, compared to other scenarios, the result
of morning peak (09:00-09:30) is optimal but it takes more than 17 minutes, which
may beyond the participants’ endurance. As a consequence, platforms in real-world
should make a matching decision under an appropriate participant density.
Table. 6. The result generated by Chengdu data
Interval
S

S
œ
Ÿ
Total distance(km)
Time cost(s)
00:00-00:30 1126
0.3753
0.6687 1682.96 0.4896 102
09:00-09:30 3755
1.2517
0.7217 4700.51 0.4194 1073
17:00-17:30 3532
1.1773
0.7197 4434.58 0.4392 954
To further investigate the passenger ratio under different locations in Chengdu,
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firstly, we plot the spatial distribution of origins and passenger ratio in Fig. 13.
Contrast to our simulations, the origins in Chengdu display a high central tendency
which is mainly concentrated in inner two rings.
The main factors lead to the spatial
concentration in ridesharing are the residential distribution and commuting pattern in
real-world. Also shown in Fig. 14, we combine the passenger ratios among girds
locating at the same ring, we can observe that the city center is not the places with the
highest Ÿ during 09:00-09:30, which suggests that the people close to the Tianfu
Square (the central ring) need to go to other specific regions (the second ring) rather
than staying in the center.
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Fig. 13. The distribution of origins and Ÿ in Chengdu
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Fig. 14. Ÿ varies among different rings in Chengdu
6 Conclusion
Nowadays ride-sharing has the potential to provide huge societal and
environmental benefits, which is also an effective way to balance the demand and
supply during the peak periods without increasing the number of vehicles. Hence in
this paper, we consider a ride-sharing system setting in which all the trips are known
in advance and suppose each trip is supposed to be made for self-interest. Therefore,
the ride-matching problem in this study is formulated as a set partition problem and
we further propose a heuristic method to solve the ride-matching problem, and the
results prove that our method achieves remarkable performance (about 3.8% worse
than the verified exact optimum and solve the problem within a few seconds).
We also conduct extensive numerical experiments to answer the question “Who
is more likely and where is easier to be picked up in ride-sharing mode?” based on
simulation data and Chengdu data. All these experiments demonstrate the platform
should collect a proper level of density of trips before executing the matching process.
the best place to find a ride changes with the demand density in the simulation
experiments, which is significantly affected by traffic flow and vehicles’ utilization.
In addition, the optimal strategy for participants to be a rider is going to other specific
regions rather than staying in the city center from real-world experiments.
In the future, the proposed method could be applied to the online-hailing
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platforms, such as DiDi and Uber, and we believe that our findings could be beneficial
for these platforms or governments to develop strategies in ridesharing and further
significantly improve the level of ridesharing service.
Acknowledgements
This research is jointly supported by the National Key R&D Program of China
(2018YFB1600900) and National Natural Science Foundation of China (No.
71890971/71890970, 71961137001). We also thank the participants at the 11th
International Workshop on Computational Transportation Science
for helpful
comments.
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