iBusiness, 2013, 5, 84-89
http://dx.doi.org/10.4236/ib.2013.53B018 Published Online September 2013 (http://www.scirp.org/journal/ib)
An Algorithm to Vehicle Scheduling Problem of AirPort
Pickup and Delivery Service
Zhengzheng Xu1,2*, Jiafu Tang2
1School of Business Administration, Northeastern University, Shenyang 110819, China; 2State Key Laboratory of Integrated Auto-
mation for Process Industries, Northeastern University, Shenyang 110819, China.
Email: *xuzz99@sina.com
Received July, 2013
ABSTRACT
This paper studies the vehicle scheduling problem in cities for the pickup and delivery service. Considering customer
point as vehicle collaboration point, we propose a two-stage algorithm based on customer point collaboration through
the theory of optimization. In additio n to considering the problem whether the isolated customer point is collabo rative,
the algorithm also takes into account the problem whether the customers on the vehicle (picking up multiple customer
points) can transfer its customers to the other basic vehicle. Moreover, the selection of the type of basic vehicles is no
longer single; we can choose different types of vehicles suitable for different vehicle capacities according to the total
number of people to carry. Finally, we perform simulation analysis and simulation results show that th e algorithm pro-
posed in this paper is feasible and effective.
Keywords: Pickup and Delivery Service; Vehicle Collaboration; Satisfaction Degree; Isolated Customer Point
1. Introduction
The airport pickup and delivery service is a value-added
service for the air ticket corporation to attract customers
and enhance market competitiveness. The vehicle sched-
uling in the airport pickup and delivery service is sig-
nificantly important for the modern logistics engineering
and transportation. And it has received the extensive at-
tention and studied well. The vehicle routing and sched-
uling problem of pickup and delivery of customers to
airport belongs to the vehicle routing problem [1]. Some
vehicles and trip number are unnecessary for the whole
pickup and delivery service [2]. The vehicle scheduling
problem is similar to the routing prob lem in communica-
tion networks where we are to find the optimal route ac-
cording to the origin-destination flows [3, 4]. In the
pickup and delivery service for customers, the vehicle
scheduling via vehicle collaborations has received exten-
sive attentions from academic and industrial circles.
Some vehicle scheduling methods have been proposed
to this problem. Belfiore et al. studied the long-haul ve-
hicle scheduling problems with working time rules [2].
Pop et al. used the integer programming to model the
generalized vehicle routing problem and proposed two
new models [1]. Wy et al. investigated the rollon-rolloff
vehicle routing problem and brought forth a hybrid
metaheuristic approach to overcome it [5]. Mester et al.
studied both capacitated vehicle routing problem and
vehicle routing problem with time window constraints,
and then they presented an efficient evolution strategies
algorithm to solve them [6]. The set-partitioning model
was used to find the optimal vehicle routing and sched-
uling in the free pickup and delivery service in flight
ticket sales companies [7]. Yan et al. studied the cash
transportation vehicle routing and scheduling, and they
developed a model to ensure cash conveyance safety and
minimize the transportation cost [8].
This paper studies the vehicle scheduling problem in
cities for the pickup and delivery service. We propose the
concept of the isolated customer point through taking
customer satisfaction and bypass limit as constraints.
Considering customer point as vehicle collaboration
point, we propose the vehicle collaboration rules about
customer transfer. And a two-stage algorithm based on
customer point collaboration is put forward through the
theory of optimization. In addition to considering the
problem whether the isolated customer point is collabo-
rative, the algorithm also takes into account the problem
whether the customers on the vehicle (picking up multi-
ple customer points) can transfer its customers to the
other basic vehicle. Moreover, the selection of the type of
basic vehicles is no longer single; we can choose differ-
ent types of vehicles suitable for different vehicle capac-
ity according to the total number of people to carry. Fi-
nally, taking the airport p ick up an d deliv ery serv ice of air
Copyright © 2013 SciRes. IB
An Algorithm to Vehicle Scheduling Problem of AirPort Pickup and Delivery Service 85
ticketing company as a study case, we perform simula-
tion analysis. Simulation results show that the algorithm
proposed in this paper is feasible and effective.
2. Problem Statement
Consider as the research object the traveling passengers
of a city to pickup and deliver in a plan period (one day).
According to the basic traveling information of passen-
gers (such as the traveling time and the pickup location
of customers) in the plan period, air ticketing company is
to arrange the number of vehicles dispatched, the depar-
ture time of each vehicle, customers to be picked up by
each vehicle, pickup order for these customers, customer
points to collaborate, selection of collaboration location s,
and the pickup time. As a result, the company can
achieve the high customer satisfaction degree and low
operation cost. Basic vehicles are the vehicles that pick
up customers from the depot to the airport. Collaborative
vehicles refer to the vehicles that assist the basic vehicle
to finish the pickup task from the depot but not arriving
at the airport. Hence, for the characteristics of the prob-
lem itself, we give the following assumptions:
In the pickup service, there is only one depot and
one airport.
Take the customers with the same pickup time in
same location as the same customer point; the number of
customers at each customer point is no more than the
carrying capacity of each vehicle.
Each vehicle serves one trip loop, and the whole
process that the vehicle departs from the depot, arrives at
the airport, and finally returns to the d epot is regarded as
one trip.
Employ two kinds of vehicles, and collaborative
vehicles select the vehicles with smaller vehicle capacity.
The number of customers in basic vehicle is greater
than or equal to the number of customers in its collabora-
tive vehicle.
During the whole pickup process, vehicles keep a
constant speed and provide the service on time. Ignore
the boarding time, and do not consider the delay and
wait.
Do not take the time required to transfer customers
in the case of vehicle collaboration.
Basic vehicles and collaborative vehicles will meet
in the ideal state, namely without the waiting time.
Based on the above assumptions, this paper will study
how to perform the collaboration between basic vehicles
and collaborative vehicles at customer point during the
pickup service of the single trip, in order to obtain the
optimal routing and scheduling methods of the single trip
and multiple vehicles.
In this section, the customers’ satisfaction degree
about the time arriving at the airport is used to measure
whether customers are satisfied with the pickup service
or not. And we can use the satisfaction degree function to
describe the satisfaction degree of customers [8]. Con-
sidering the factor of vehicle collaboration and the satis-
faction degree of customers at customer points, the satis-
faction degree function of the customers at customer
point i based on the vehicles collaboration at customer
points ca n be defined as:
''
'
''
'
''
1 [,]
(1) [,]
()
(1) [,]
0 [,]
ii
ii iii
ii
i
ii iii
ii
iii
pt
et ptee
ee
St lt ptll
ll
tel



ii
i
i
el
1
(1)
where pi is a constant and ; when the cus-
tomers at customer point i need not transfer, pi = 0, oth-
erwise pi >0;
0
i
p
,
ii
el and
,
ii
el

eel
, respectively, indicate
the soft time window [9] and hard time window [10] of
reaching the airport, meeting .
iiii
Assume that U represents the duration of the work
plan within a planning period (typically one day),
l

C
1, 2,, n indicates the customer point set, 0 represents
the depot,
0NC denotes the set of customer
points and the depot, –1 represents the airport,
01NC
 denotes the set of all geographical
locations during the customer pickup, i
represents the
number of customers at customer point i,
is the level
value of satisfaction degree that can be accepted by cus-
tomers,
1, 2,,
B
K
n represents the basic vehicle
set,
1, 2,,
C
K
m
Q is the collaborative vehicle set,
C denotes the passenger capacity of collaborative ve-
hicles,
B
Q represents the maximum passenger capacity
between the two kinds of basic vehicles, ij is the travel
time from customer point i to customer point j, dij repre-
sents the path distance form customer point i to customer
point j, ik
T
denotes the arrival time of vehicle k to cus-
tomer point i,
represents the bypass coefficient of
customer pickup. Additionally, we assume that zk, yik, xijk,
and vijk are the 0-1 variables and they are the decision
variables of vehicle k. When vehicle k is used, 1
k
z
;
when the customers at customer point i is picked up by
vehicle k, 1
ik
y
; when basic vehicle k arrives form
customer points i to j, 1
ijk
x
; when collaborative vehi-
cle k arrives form customer points i to j, 1
ijk
v
. In the
collaboration process, the following constraints of col-
laboration are considered:
(),
i
Sti C
 (2)
,
iik BB
iC
yQ kK

(3)
,
iik Cc
iC
y
QkK

(4)
Copyright © 2013 SciRes. IB
An Algorithm to Vehicle Scheduling Problem of AirPort Pickup and Delivery Service
86
(1)
() ,
BC
iikiki
kK K
tyTi


C (5)
Equation (2) denotes the constraints of customers’ sat-
isfaction degree. Equation (3) describes the constraints of
the basic vehicles’ capacity. Equation (4) denotes the
constraints of the collaborative vehicles’ capacity. Equa-
tion (5) is the limit of bypass time.
This paper designs a two-stage heuristic algorithm
based on customer point collaboration. Customer point
collaboration refers to the collaborative method that the
collaborative vehicle transfers customers in it to the basic
vehicle at a certain customer point. The first stage ex-
ploits the time sorting-based heuristic algorithm of prior
clustering to generate the initial vehicle trips and access
order of the customer points in each trip. The algorithm
steps are as follows:
Step 1: Give the information of customer points, the
lower limit
of satisfaction degree, and bypass limit
coefficient
. Calculate the time window of arriving at
airport that meets the lower limitation of satisfaction de-
gree according to Equations (1) and (2).
Step 2: Sort the customer points in order according to
the lower limit of the time window of arriving at airport.
And form the sequence K.
Step 3: If K is empty, stop and output the results.
Step 4: Select the first customer point in K as the clus-
tering point. Generate the set i according to the sort-
ing sequence of other customer points and the capacity
limit of basic vehicles shown in Equation (3). Here the
capacity of basic vehicle is limited to .
S
B
Step 5: if i is not empty, we conduct full array of
the customer pints in i, select the route with the short-
est driving distance and denote it as , and examine
whether customer point
Qx
SSi
r
j
i () meets
the bypass limitation in Equation (5). If
cr1,2,j...,||
i
r
j
c meets the
constraint, then keep it in i. Or otherwise remove r
j
c
S
from i and i and put it into the set E. After finishing
the whole process, put i into the route set R. When
i, put this customer point into the set E, delete i,
and delete this customer point from K. This is because
the customer point is considered as the isolated customer
point and is put into E if there is only one custo mer poin t
in the route.
S
1
rr
||S
Step 6: Delete from K the customer points that have
formed the cluster.
Step 7: Put the customer points in E in the time order
according to the lower limit of time window of arriving
at airport and form the sequence L. According to the
constraints in Equations (2)-(5), select the customer point
j to insert the route in R. Then form the new route,
update the route set R, delete the customer points
eE
j
e
from E and L, and go back to Step3.
Step 8: Conduct the second clustering for the cus-
tomer points in E. Namely, repeat th e ab ov e Step s 2-7 for
the customer points in E. If the customer points in E can
form the new routes, then put these new routes into set R
and delete the corresponding customer points from E and
L. At the first stage, we get the basic path set R and iso-
lated point set E. At the second stage, we mainly con-
sider the customer satisfaction degree, vehicle capacity
limitation, and bypass constraint based on the first stage.
Using the selection rules of collaborative points, rear-
range the route for the isolated points in a collaborative
way. Then we take into account the possible collabora-
tion between the collaborative vehicle picking up the
customers of multiple customer points and the basic ve-
hicle, and make the appropriate scheduling. The heuristic
algorithm steps at the second phase are as follows:
Step 1: According to the isolated points in set E, con-
sider the change of customers’ satisfaction degree due to
the vehicle collaboration. And recalculate the time win-
dow of arrive at the airport.
Step 2: If L is empty, then remove all the basic path in
path set R collaborated by the isolated point to set R2,
output the result, and exit.
Step 3: Take out the isolated point from L in order,
insert the basic path that has the same time window with
this isolated point and meet the vehicle capacity con-
straints. According to the above Rules 1-3, select the
appropriate the collaborative point, build the corre-
sponding collaborative path, write down the basic path
collaborated with isolated point, mark the collaborative
customer point, remove this isolated point from set E to
collaborative path set 1, update the arrival time win-
dow and the total number of the basic path which has
been collaborated in set R. If not meeting the Rules 1-3,
the isolated point does not participate in collaboration,
separately construct the path, and place the built path into
the path set R.
R
Step 4: Delete isolated points which have collaborated
with basic path from L and E, and then go back to Step 2.
Step 5: Reorder the path in R according to the lower
limit of the arrival time window.
Step 6: Take the path form R. If is empty,
output the result and exit. i
Ri
R
Step 7: Calculate a
i
wf
where denotes arrival
time window of the path i and f represents penalty
factor. Build the intersection set i of and the
time window of the existing path in . If i is not
empty and the vehicle capacity constraint is satisfied, go
to Step 4, or otherwise go back to Step 6.
a
i
w
2R
RUa
i
wfU
Step 8: Select the customer point r in as the col-
laborative point. According to Rules 1-3, choose the col-
laborative point i which make the collaborative mile-
age shortest and all customer points in i meet the by-
pass restrictions. if i is found, construct the collabora-
tive path, write down the basic path and collaborative
2R
R
C
C
Copyright © 2013 SciRes. IB
An Algorithm to Vehicle Scheduling Problem of AirPort Pickup and Delivery Service
Copyright © 2013 SciRes. IB
87
customer points collaborated by , and remove r from
R to the collaborative path set , update the arrival
time window and the total customer number of the basic
path collaborated in . If i is not found, the path
remains in R, and go back to Step 6.
i
R3R
R
R
2R
i
C
f
i
R
points. Thus the optimal adjustment is performed for the
vehicle scheduling result formed at the first stage. The
vehicle routing and scheduling problem of the single trip
and multiple vehicles with the hybrid vehicle kinds is
solved.
Step 9: Take i from R. If i is empty, remove all
the basic paths in R collaborated by the other basic paths
into the path set , output the result and exit.
R
5R3. Simulation Results and Analysis
Here we use the pickup and delivery service of the air-
port as a study case to validate our algorithm. Assume
there are 30 customer points to pick up for the flights of a
period of 8:00 - 20:00, these customer points are distrib-
uted in the 55 55km km
rectangular area, soft time
window width is 20 minutes, hard time window width is
40 minutes, maximum capacity of basic vehicles is
8
B
Q
, maximum capacity of collaborative vehicles is
4
C
Q
, depot coordinate is (35,37), airport coordinate is
(50,50), vehicle speed is , lower limit of cus-
tomers’ satisfaction degree is
60 /km h
0.8
, bypass restriction
coefficient is 1.5
and . 0.1
i
p
Step 10: If has been collaborated, go to Step 9.
i
Step 11: Calculate where denotes the
arrival time window of the path i and f represents the
penalty factor. Build the intersection set
Ra
wa
i
w
i
U of a
i
wf
and the time window of the basic paths in R except i.
If R
i
U is empty or the vehicle capacity constraint is not
satisfied, go back to Step 9.
Step 12: Select the customer point z from the basic
paths in R except i in order as the collaborative point.
By Rules 1-3, choose the collaborative point i
R
Z
which
make the collaborative mileage shortest and all customer
points in i meet the bypass restrictions. If i
R
Z
is
found, construct the collaborative path, write down the
basic path and collaborative customer points collaborated
by i, and remove z from R to the collaborative path set
, update the arrival time window and the total customer
number of the basic path collaborated in R. If i
R
The corresponding information of 30 customer points
is shown in Table 1. To facilitate the statement, we give
the abbreviations in the follow tables as follows: CP:
Customer Point; VCP: Vehicle Coordination Point; LCP:
Location of Customer Point; LHW: Lower bound of
Hard time Windows; LSW: Lower bound of Soft time
Windows; USW: Upper bound of Soft time Windows;
UHW: Upper bound of Hard time Windows; NC: Num-
ber of Customers; VN: Vehicle Number; COP: Collabo-
ration Point. Using the first-phase algorithm without the
vehicle collaboration, we generate the initial trip and the
access sequence of customer points in each trip. Then the
minimum running mileage and average utilization ratio
of vehicle capacity are attained when not considering the
vehicle collaboration. Average utilization ratio of vehicle
capacity can be denoted as:
4R
Z
is not
found, the path remains in R, and go back to Step 9.
i
In summary, through the three parts at the second
phase, we finally get the set of the basic
paths not participating collaboration, collaborative set
collaborating with the basic paths, the
collaborated basic path set
R
'
R
5R
RR
DR
13CR RR42
. Consequently,
according to the number of customers on each path of R
and D, we can determine how to choose the kinds of ba-
sic vehicles. According to the information in C, we can
determine the collaborative path and co llaborative custo mer
Table 1. Information of customer points.
CP 1 2 3 4 5 6 7 8 9 10
LCP (42,34) (43,45) (30,25) (35,44)(39,36)(31,50)(34,30)(44,16)(29,51) (45,52)
LHW 7:25 7:35 8:50 7:20 7:30 9:05 8:30 8:45 8:50 8:55
LSW 7:35 7:45 9:00 7:30 7:40 9:15 8:40 8:55 9:00 9:05
USW 7:55 8:05 9:20 7:50 8:00 9:35 9:00 9:15 9:20 9:25
UHW 8:05 8:15 9:30 8:00 8:10 9:45 9:10 9:25 9:30 9:35
NC 2 1 1 1 2 1 3 1 1 1
CP 11 12 13 14 15 16 17 18 19 20
LCP (27,33) (32,21) (42,40) (35,40)(14,10)(47,35)(35,40)(38,30)(26,30) (46,38)
LHW 11:40 18:00 17:25 10:25 16:15 17:00 17:15 15:40 12:25 11:05
LSW 11:50 18:10 17:35 10:35 16:25 17:10 17:25 15:50 12:35 11:15
USW 12:10 18:30 17:55 10:55 16:45 17:30 17:45 16:10 12:55 11:35
UHW 12:20 18:40 18:05 11:05 16:55 17:40 17:55 16:20 13:05 11:45
NC 2 1 1 2 1 1 1 2 2 2
CP 21 22 23 24 25 26 27 28 29 30
LCP (39,27) (28,40) (32,32) (43,43)(29,44)(40,30)(47,37)(55,25)(39,29) (30,36)
LHW 17:25 10:25 12:00 12:25 11:05 13:25 13:35 13:30 13:30 18:15
LSW 17:35 10:35 12:10 12:35 11:15 13:35 13:45 13:40 13:40 18:25
USW 17:55 10:55 12:30 12:55 11:35 13:55 14:05 14:00 14:00 18:45
UHW 18:05 11:05 12:40 13:05 11:45 14:05 14:15 14:10 14:10 18:55
NC 1 1 1 1 1 1 4 1 2 2
An Algorithm to Vehicle Scheduling Problem of AirPort Pickup and Delivery Service
88
,
bc
bb cc
NN
nsns
 (6)
where b and c denote the number of the total cus-
tomers delivered by basic and collaborative vehicles,
respectively, b, b
N N
n
s
, c, and c
n
s
represent the trip
number and seat number of basic and collaborative vehi-
cles, respectively. When not considering the collabora-
tion, and .
0
c
N0
c
Simulation results show that without collaborations,
the total running mileage of vehicles is: 1051.4km and
average utilization ratio of vehicle capacity 57.89%.
Based on the results at the first stage, we perform the
heuristic algorithm at the second stage. By optimizing the
results at the first stage, we can obtain the collaborative
information of collaborative vehicles. Simulation results
indicate that with collaborations, the total vehicle mile-
age is 1008.5 km and average utilization ratio of vehicle
capacity is 61.90%.
n
Here we, respectively, use the study cases with 10, 30,
50, 100, 150, 200, 400, 600, 800 and 1000 customer
points to validate further the performance of our algo-
rithm. The depot coordinate is at point (35, 37), while
airport coordinate is at point (50, 50). According to the
distribution of the customer point locations, we discuss
the two cases, namely customer points mainly distributed
near the depot or airport. And the locations of all the
customer points are randomly distributed in the circle
whose center is the depot or airport with radi us by 20 km.
For collaborations and non-collaborations, we obtain
the vehicle total mileage, the average utilization ratio of
basic vehicles, and average satisfaction degree of cus-
tomers for the different study case. From Figures 1-4, we
can see that in contrast to collaborations, average satis-
faction degree of customers decrease a little after col-
laborating. However, Figures 1-4 also tell us that the
0100 200300 400 500 600 700 800 900 1000
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2x 10
4
Number of customer points
Tota l mileage (km)
Customer points mainly distributed near the depot
without collaboration
with collaboration
Figure 1. Total mileage with customer points mainly near
the depot.
0100 200 300400 500 600 700 800 900100
0
0
0.4
0.8
1.2
1.6
2
2.4
2.8x 10
4
Number of customer points
Total
mileage(km)
Customer points mainly distributed near the airport
without collaboration
with collaboration
Figure 2. Total mileage with customer points mainly near
the airport.
0100 200300 400 500 600 7008009001000
0.95
0.96
0.97
0.98
0.99
1
1.01
1.02
1.03
1.04
1.05
Number of customer points
A vera ge satis faction degree of customers
Customer points mainly distributed near the depot
without collaboration
with collabora tion
Figure 3. Average satisfaction degree of customers with
customer points mainly near the depot.
0100 200 300 400 500600 700 800 9001000
0.95
0.96
0.97
0.98
0.99
1
1.01
1.02
1.03
1.04
1.05
Number of customer points
Average satisfaction degree of customers
Customer points mainly distriuted near the airport
without collaboration
with collaboration
Figure 4. Average satisfaction degree of customers with
customer points mainly near the airport.
Copyright © 2013 SciRes. IB
An Algorithm to Vehicle Scheduling Problem of AirPort Pickup and Delivery Service
Copyright © 2013 SciRes. IB
89
total mileage with collaborations is much less than that
without collaborations. And we also find that the reduced
total mileage is up to 4%. This is what we expect. By the
vehicle collaborations, the satisfaction degree of custom-
ers in the collaborative vehicles is to decrease. As a result,
this is to affect the average satisfaction degree of cus-
tomers. The reduced mileage is mainly because the col-
laborative vehicles need not go to the airport. After using
the heuristic algorithm at the second stage, although the
average satisfaction degree of customers decreases a little,
the total running mileage of vehicles is reduced. And
thus the vehicle scheduling cost is also reduced. Hence,
simulation results indicate that the algorithm proposed in
this paper can be used for all the study cases. This tells us
that the algorithm proposed in this paper is effective and
feasible.
4. Conclusions
This paper studies the two vehicle kinds’ collaborative
problems of the pickup and delivery service. By intro-
ducing the vehicle collaborations, a two-stage heuristic
algorithm is proposed. Considering the collaborations
between isolated customer points and basic vehicles, we
make the basic vehicle picking up the customers at the
multiple customer points collaborating with other basic
vehicles. And the customers at the different customer
points are put into the same basic vehicle as possible and
then are picked up to the airport. In such a case, the av-
erage utilization ratio of vehicle capacity is improved.
Moreover, simulation results that in the case of keeping
the appropriate customers’ satisfaction degree; we can
perform the better vehicle scheduling. As a result, the
cost of the company can be significantly reduced. Future
studies need to consider the actual situations, such as
multiple trips, waiting time when transferring, global
collaboration, and dynamic insertion customers.
5. Acknowledgements
This work was supported in part by the National Natural
Science Foundation of China (Nos. 71021061,
61273204), and the Fundamental Research Funds for the
Central Universities (No. N090204001). The authors
wish to thank the reviewers for their helpful comments.
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