Special Issue Article
Optimization of transport network in
the Basin of Yangtze River with
minimization of environmental
emission and transport/investment
costs
Advances in Mechanical Engineering
2016, Vol. 8(8) 1–10
Ó The Author(s) 2016
DOI: 10.1177/1687814016660923
aime.sagepub.com
Haiping Shi, Pengfei Xu and Zhongzhen Yang
Abstract
The capacity of the ship-lock at the Three Gorges Dam has become bottleneck of waterway transport and caused serious congestion. In this article, a continual network design model is established to solve the problem with minimizing the
transport cost and environmental emission as well as infrastructure construction cost. In this bi-level model, the upper
model gives the schemes of ship-lock expansion or construction of pass-dam highway. The lower model assigns the containers in the multi-mode network and calculates the transport cost, environmental emission, and construction investment. The solution algorithm to the model is proposed. In the numerical study, scenario analyses are done to evaluate
the schemes and determine the optimal one in the context of different traffic demands. The result shows that expanding
the ship-lock is better than constructing pass-dam highway.
Keywords
Network design, environmental load, ship-lock, Three Gorges Dam, pass-dam transport, multi-mode network
Date received: 10 April 2016; accepted: 1 July 2016
Academic Editor: Gang Chen
Introduction
The economic and social growth in the Basin of
Yangtze River leads to enormous logistics and traffic
demands. The volumes of the induced passenger and
freight traffic have increased continually during last
20 years. Currently, the regional freight traffic is about
40% of the national total. The average annual waterborne freights are over 1.5 billion tons and the container throughputs of the ports along the main channel
of the River are over 8 million twenty-foot equivalent
units (TEUs). It can be predicted that the transport
demands will grow further as the strategy of development of the economic belt along Yangtze River is put
into effect soundly, which puts forward higher requirements to the highway and waterway transport systems
along the River.
Although the River channel has provided a satisfied
transport service for the development of the economic
belt, the transport capacity of the ship-locks at Three
Gorges Dam has become the bottleneck of the shipping. Due to the traffic increment, the ships have to
wait longer and longer to pass the dam lock due to the
capacity constraints. The average waiting time is about
30 h, sometimes even up to 3–10 days.
Transportation Management College, Dalian Maritime University, Dalian,
China
Corresponding author:
Zhongzhen Yang, Transportation Management College, Dalian Maritime
University, Dalian 116026, China.
Email: [email protected]
Creative Commons CC-BY: This article is distributed under the terms of the Creative Commons Attribution 3.0 License
(http://www.creativecommons.org/licenses/by/3.0/) which permits any use, reproduction and distribution of the work without
further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sagepub.com/en-us/nam/
open-access-at-sage).
2
Some solutions are put forth to solve the bottleneck
problem, such as (1) lockage scheduling optimization
to raise the efficiency, (2) expansion of the ship-locks,
and (3) construction of pass-dam highway to shift a
part of cargos from waterway to highway. The last one
is a newly proposed idea. In this way, some cargos
transported by ship originally will be unloaded from
the ships at the port on the upstream of the Dam and
loaded on trucks passing the Dam through dedicated
highway to the destinations. As a result, the number of
ships reaching to the Dam will decrease and cargoes
both on ships and trucks may reach the destinations
with less time.
For lockage scheduling, some literatures studied
how to maximize the lock area utilization1 and minimize the waiting time.2 Dai and Schonfeld3 developed
a numerical method for estimating delays on congested waterways. Wang et al.4 established a novel
operation cost model of the scheduling problem of the
lockage at Three Gorges Dam and applied a datadriven approach to solve the problem. Pang and Wu5
constructed an optimization model for jointly scheduling the double-line ship-lock based on the nonlinear
goal programming. Bugarski et al.6 presented the
development of a decision support system (DSS) to
manage the ship-locks. Two criteria, which reflect the
interests of both shippers and lock owner, are presented and used in parallel with the fuzzy DSS. Yuan
et al.7 established a lockage scheduling model based
on the requirement of scheduling procedure in Three
Gorges Dam system and proposed chaotic embedded
particle swarm algorithm to solve the problem.
Optimization of the lockage scheduling8 can hardly
work in case that the ship-locks are in the saturation
due to the heavy traffic demand.
The expansion of the ship-locks or the construction
of pass-dam highway can be seen as a continuous network design problem.9 The objective of a continuous
network design problem is usually to minimize the sum
of the total travel times and investment costs.10–15 Yao
et al.16 presented a robust optimization model taking
into account the stochastic travel time to satisfy the
demand of passengers and provide reliable transit service. Chiou17 presented a conjugate sub-gradient projection method to efficiently solve the continuous
network design problem with global convergence.
Wang et al.18 proposed a combined model by joining
link-based credit charge and capacity improvement.
They discussed urban road network improvement
problem from both supply and demands sides. Yu
et al.19 proposed a bi-level programming model to solve
the design problem for bus lane distribution in multimodal transport networks aiming at minimizing the
average travel time of travelers. Wang et al.20 examined
the continuous network design problem with different
Advances in Mechanical Engineering
value of time for multiple user classes. In our study, the
objective consists of three parts, namely, minimization
of total freight transport costs, minimization of the cost
for the ship-lock expansion and dedicated highway
construction, and minimization of the cost to compensate the emitted CO2. The CO2 emission is a key performance index for transport network because massive
manpower and resources are needed to treat the pollution. Carbon emissions can be used to examine whether
the network design is environmentally friendly.
In most countries, vehicles have become the most
important source of pollution.21,22 Feng and
Timmermans23 formulated a policy decision support
tool that allows decision makers to identify maximum
mobility levels under environmental capacity constraints. Some literatures considered the CO2 emissions
when optimizing the network. Yang et al.24 proposed a
novel carbon tax–constrained city logistics network
planning model with rational hypotheses, parameter
design, and deployment of low-carbon resources.
Chaabane et al.25 introduced a framework to evaluate
the trade-offs between economic and environmental
objectives under various cost and operating strategies.
Bouchery and Fransoo26 studied the dynamics of intermodal transport solutions in the context of hinterland
networks in terms of cost, CO2 emissions, and modal
shift. Janic27 proposed a model for calculating the full
costs of an intermodal and road network. The cost
included the impact of the network on society and the
environment. Craig et al.28 calculated the CO2 emission
intensity of intermodal transport in the United States,
based on a data set of more than 400,000 intermodal
shipments. Zhang et al.29 wanted to include the environmental cost in optimally designing an intermodal
network.
By now, few literatures have quantificationally analyzed the congestion problem at the Three Gorges Dam
from the perspective of CO2 emission. In this article, to
find out which costs less and is environmentally
friendly, ship-lock expansion or pass-dam highway
construction, we use the three costs to compare the two
disputable methods.
This article is structured as follows. In section
‘‘Model development,’’ topology relationship between
waterway and highway is established. Meanwhile, the
links’ traffic attributes in the network are determined.
Then, a bi-level programming model considering transport cost, construction cost, and CO2 emission is proposed. In section ‘‘Solution algorithm,’’ to solve the
model, the particle swarm optimization is introduced.
In section ‘‘Numerical analysis,’’ the model is applied
to the Yangtze River Economic Belt. The result shows
that ship-lock expansion would be the optimal solution
in long term. Conclusions and some discussions are
stated in section ‘‘Conclusion.’’
Shi et al.
Model development
By analyzing the path selection behaviors of cargos on
a multi-mode network, we can know the cargo flows
and traffic attributes on links. Then, externalities such
as environmental load induced by freight transport can
be calculated, which may be used to evaluate the network schemes and transport operations. The problem
of continuous network design is a bi-level programming
problem. The upper level hopes to make an efficient
transport system through infrastructure construction.
The lower level wants to choose a path that can make
them reach the destination with the least cost and time.
In order to establish the bi-level model, a transport network consisting of different traffic models should be
built first.
Network construction
The container liner lines on the River and the highways
in the same corridor constitute the container transport
network. Containers in the region could be transported
from origins to destinations by the waterway and highway intermodal network. To analyze the path selection
behaviors, we propose a method to mathematically represent the intermodal network, namely, establishment
of topological relation between waterway and highway
and determination of the traffic attributes of the corresponding links.
The main work for building network is to separate a
port city into two nodes which represent the origin and
transit nodes, respectively, and then to use the method
shown in Figure 1 to construct the multi-mode network. In Figure 1, the upper side shows the abstracted
path, where containers are moved from City 1 to City
2. The lower side shows the details of the path, where
containers are moved from City 1 to Port 1 by highway
first and then are loaded on ships and transported to
3
Port 2, and finally, they are delivered to City 2 by
trucks. We use A representing the network and use As ,
At , and Al representing the sets of waterway links, transit links, and highway links, respectively. Then,
A = As [ At [ Al .
The impedance functions of different links are
defined as follows:
1. For links other than transit ones
T(xa ) = b1 (ga + ata ) M Min(0, c2a x2a ),
8a 2 As [ Al
ð1Þ
This type of links includes waterway and highway
links. Here, ga is the unit transport cost on link a, ta is
the transport time on link a, b1 is the congestion coefficient on link a, a is the value of time, M is a big enough
positive integer, ca is the capacity of link a, and xa is the
traffic volume on link a.
Equation (1) shows the impedance function of links
of waterway or highway, which is related to monetary
cost and time cost. The second item in the right side
means the capacity limitation of the dam lock; when
the demand is smaller than the capacity (xa ca ), it will
be 0. Otherwise (xa .ca ), it will may be a large enough
number. It ensures the carried cargos cannot be greater
than the capacity. It is assumed that the unit transport
cost depends on the ratio of the traffic volume to the
capacity, which is represented by b1 .
2. For transit links
T (xa ) = b2 (qa + ata ),
8a 2 At
ð2Þ
here, ta = tawait + tahandle is the transit time of freight on
link a, tawait is the waiting time on link a, tahandle is the
Figure 1. Method to represent the waterway and highway mixed network.
4
Advances in Mechanical Engineering
Xð
xa
handling time on link a, b2 is a coefficient concerning
port congestion, and qa is the unit transit cost on link a.
Min z =
a2A
The bi-level programming model
s:t:
There are two parts in the bi-level programming model.
The upper model aims to find a solution of network
scheme that minimizes the total cost, including transport cost, construction cost, and environmental cost of
CO2 emissions. The lower level model is used to assign
the container cargoes onto the network.
The upper model. The costs to be minimized for the network construction and transport operation consist of
three parts, namely, time and monetary costs for transporting all cargoes from origins to destinations, investment cost for expansion of ship-lock and construction
of pass-dam highway, and money used to treat the CO2
emitted from trucks or ships. The formulas of the upper
model are as follows
min Z = l t1 f1 (y1 ) + l t2 f2 (y2 )
X
X
T (xa ) xa + g xa Ea
+
a2A
s:t:
ð3Þ
a2A
t1 + t2 = 1
ð4Þ
X
ð8Þ
T (x)dx
0
fkrs = qrs , 8r 2 R, 8s 2 S
ð9Þ
k
fkrs 0 8k 2 W , 8r 2 R, 8s 2 S
XXX
fkrs drs
xa =
a, k 8k 2 W , 8r 2 R, 8s 2 S
r
s
ð10Þ
ð11Þ
k
here, fkrs is the container traffic on path k between origin r and destination s; drs
a, k is a 0–1 variable, if link a is
=
1,
otherwise
drs
in path k then drs
a, k
a, k = 0; A is the set
of links; R is the set of origins; S is the set of destinations; Wrs is the set of paths between r and s; and qrs is
the container origin–destination (OD) traffic.
CO2 emission calculation. Almost all motor vehicles are
driven by fossil fuels, thus the emission of motor vehicle
traffic is equal to the consumed fuel multiplied by the
emission factor.30 The CO2 emission factor primarily
depends on the carbon content of the fuel. The model
for calculating the CO2 emitted by the traffic on the network is as follows
X
E=
xa Ea 8a 2 A
ð12Þ
a
f1 ( y1 ) B
ð5Þ
f2 ( y2 ) B
ð6Þ
t1 , t2 2 f0, 1g
ð7Þ
here, l is the annual depreciation of the invested assets,
t1 is a 0–1 variable, if ship-lock is expanded t1 = 1, otherwise t1 = 0; t2 is a 0–1 variable, if pass-dam highway
is constructed t2 = 1, otherwise t2 = 0; y1 is the expansion scale of the ship-lock; y2 is the construction scale
of the pass-dam highway; f (y) is a function to calculate
the investment, which is related to construction scale;
T (xa ) is the unit-generalized transport cost on link a; Ea
is the CO2 emission factor on link a; and g is a cost
ratio of CO2 treatment. Equation (4) means that the
ship-lock expansion and construction of pass-dam highway cannot be done simultaneously; equations (5) and
(6) are investment constraints which mean that construction cost cannot exceed the investment budget B.
The lower model. The user equilibrium traffic assignment
model based on the multi-mode network is as follows
Ea = Etruck = TEtruck 3 Wtruck 3 Da
, 8a 2 Al [ At ð13Þ
TEtruck = G 3 F
(
PP
Cij 3 CFj
Ea = Eship =
, 8a 2 As
Qr
Cij = Ti 3 FCj
ð14Þ
here, E is the total CO2 emissions of the traffic on the
network; equation (13) is used to calculate the emission
factor (Ea ) on highway links, where Da is the length of
link a; Wtruck is the weight of the container; TEtruck is the
emitted CO2 for transporting 1-t cargo for a kilometer;
G is the fuel consumption for transporting 1-t cargo for
a kilometer; and F is the CO2 emission factor.
Equation (14) is used to calculate the emission factor
(Ea ) on waterway links, where Cij is the consumption of
fuel j when the ship is in operation mode i (namely,
navigating mode and berthing one); Q is the rated container capacity; r is the ship load ratio; Ti is the time
span of the ship in mode i; FCj is the consuming rate of
fuel j; and CFj is the un-spatial transfer factor of fuel j,
some of which based on the fuel types are shown in
Table 1.
Table 1. Transfer factors (CF) of some types of fuels.
Fuel type
ISO specification
Carbon content (kg/kg)
CF (kg/kg)
Light fuel
Heavy fuel
ISO8217, RMA
ISO8218, RME
0.86
0.85
3.15
3.11
Shi et al.
5
Xik + 1 = Xik + Vik + 1
Solution algorithm
To solve the bi-level programming model, we use two
algorithms: the Frank–Wolfe algorithm for the lower
model and the particle swarm optimization (PSO) for
the upper model.
Frank–Wolfe algorithm
The Frank–Wolfe algorithm is an iterative first-order
optimization algorithm for the constrained convex optimization problem. The method was originally proposed
by Marguerite Frank and Philip Wolfe.31 In each round
of iteration, the algorithm considers a linear approximation of the objective function and moves slightly
toward a minimizer of this linear function. Its main
steps are as follows:
Step 1. Initialization. For Ta0 = Ta (0), 8a, do allor-nothing assignment to get link traffic as fx1a g
and set n = 1.
Step 2. Update impedance of each link as
Tan = Ta (xna ).
Step 3. Find the direction of next iteration. With
the updated ftan g8a, do another time of all-ornothing assignment to get attached traffic volume fyna g.
Step 4. Step size determination. Use dichotomization
the condition of
P n to nfind nl that n meets
n
a (ya xa )Ta ½xa + l(ya xa ) = 0
Step 5. Calculate the new start for next iteration
xna + 1 = xna + l(yna xna ).
Step 6. Judge whether the calculation can be terqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi P
P n+1
n
n )2 =
minated. If
(x
x
a
a a
a xa \e, then
stop calculation and output fxna + 1 g; Otherwise,
set n = n + 1 and go to Step 2.
ð16Þ
here, i is the serial number of particle, k is the number
of iteration, Vi is the velocity vector of particle i, Xi is
the position vector of particle i, and c1 and c2 are the
learning factors, and it is usually considered
c1 = c2 = 2. Pi is the best position vector that particle i
ever reached, Pg is the best position vector that the
swarm ever reached, and r1 and r2 are independent two
random numbers between [0, 1].
The process of solution algorithm
In this article, a position vector of particle represents a
solution to the problem. A solution represents the scale
of ship-lock expansion or pass-dam highway construction. The general structure of solution algorithm is as
follows:
Step 1. Determine the population size Pc and the
maximum of iterations kmax . Use the objective
function as the fitness function. Initialize the
swarm with random solutions. Update Pi and
Pg .
Step 2. Calculate new velocity for each particle
by equation (15). Calculate the new position for
each particle by equation (16).
Step 3. According to the new position, use F-W
algorithm to calculate the container flows of
each particle. Calculate the fitness value for all
particles based on container flows. Update Pi
and Pg , and set k = k + 1.
Step 4. Judgment of termination. If k\kmax , go
to Step 2, otherwise go to Step 4.
Step 5. Output the best solution.
Numerical analysis
Particle swarm optimization
Needed data
PSO is an evolutionary algorithm based on iteration. It
is originally attributed to Kennedy and Eberhart.32 A
basic variant of the PSO algorithm works by having a
population (called a swarm) of candidate solutions
(called particles). These particles are moved around in
the search space according to a few simple formulas.
The movements of the particles are guided by their own
best known position in the search space as well as the
entire swarm’s best known position. When improved
positions are being discovered, these will then come to
guide the movements of the swarm. The process is
repeated, and thus, it is hoped that a satisfied solution
will eventually be found. The velocity vector and position vector of particles are updated as follows
Vik + 1 = Vik + c1 r1 (Pi Xik ) + c2 r2 (Pg Xik )
ð15Þ
In total, 13 major ports (Shanghai, Zhangjiagang,
Nanjing, Wuhu, Anqing, Jiujiang, Huangshi, Wuhan,
Yueyang, Jingzhou, Yichang, Zigui, and Chongqing)
on the Yangtze River are chosen as the port nodes
for container waterway transport. And 28 inland
cities (Anqing, Changde, Chengdu, Chuzhou, Ezhou,
Guiyang, Hangzhou, Hefei, Huzhou, Huangshi,
Jingmen, Jingzhou, Jingdezhen, Jiujiang, Nanchang,
Nanchong, Nanjing, Shanghai, Wuxi, Wuhu, Wuhan,
Xiaogan, Yangzhou, Yichang, Yueyang, Zhangjiagang,
Changsha, and Chongqing) in the Yangtze River Basin
are chosen as the city nodes. They are also the origins/
destinations of the being transported containers. The
data needed for the calculation include container OD
flows, highway network, shipping network, freight
rates, port charges, and ships’ specification.
6
Advances in Mechanical Engineering
Table 2. Transport distance of waterway between ports (unit: km).
Port
1
2
3
4
5
6
7
8
9
10
11
12
13
0
576
581
670
860
1031
1204
1313
1448
1614
1750
1944
2087
576
0
5
94
284
455
628
737
873
1038
1174
1368
1511
581
5
0
89
279
450
623
732
868
1033
1169
1363
1506
670
94
89
0
190
360
533
643
778
943
1080
1274
1416
860
284
279
190
0
171
343
453
588
754
890
1084
1226
1031
455
450
360
171
0
173
282
418
583
719
913
1056
1204
628
623
533
343
173
0
109
245
410
547
740
883
1313
737
732
643
453
282
109
0
135
301
437
631
774
1448
873
868
778
588
418
245
135
0
165
302
496
638
1614
1038
1033
943
754
583
410
301
165
0
136
330
473
1750
1174
1169
1080
890
719
547
437
302
136
0
194
336
1944
1368
1363
1274
1084
913
740
631
496
330
194
0
143
2087
1511
1506
1416
1226
1056
883
774
638
473
336
143
0
Port
1
2
3
4
5
6
7
8
9
10
11
12
13
Port charges (Yuan/TEU)
Efficiency (TEU/h)
Reloading costs (Yuan/TEU)
200
160
100
200
120
100
200
120
100
200
120
100
200
140
100
200
160
100
200
120
100
200
140
100
200
140
100
200
140
100
200
190
100
200
180
100
200
180
100
1
2
3
4
5
6
7
8
9
10
11
12
13
Chongqing
Zigui
Yichang
Jingzhou
Yueyang
Wuhan
Huangshi
Jiujiang
Anqing
Wuhu
Nanjing
Zhangjiagang
Shanghai
Table 3. Charges at ports.
TEU: twenty-foot equivalent unit.
Table 4. Specification of the ship.
Attributes
Value
Attributes
Value
Length overall
Beam
Depth
Design draft
Design speed
107 m
17.2 m
5.2 m
4.0 m
17.5 km/h
Container capacity
Loading capacity
Operating speed
Heavy fuel consumption
Light fuel consumption
325
4750 t
15 km/h
5 t/day
4 t/day
OD flows. It is hard to get accurate container OD flows
directly. Moreover, due to its minor role, we use average growth coefficient model to estimate the OD flows
between the 28 cities based on the container throughput
of the 13 ports on the Yangtze River.
Ship specifications. In recent years, with the waterway
deepening of the Yangtze River, the maximum ship that
can go through has become bigger. It is supposed that
container ships with capacity of 325 TEU are used. The
specifications are shown in Table 4.
Transport distance and cost on roadways. First, we digitize
the highway network and then calculate the shortest
path and transport distance between two nodes.
Finally, we get the transport cost matrix of the 28
cities.
Analysis of results
Transport distance and cost of waterway. With the similar
method, we get distance matrix of the 13 ports
(Table 2). Shipping costs between ports can be calculated based on the distance and unit freight cost.
Meanwhile, the collected port charges and reloading
costs at each port are shown in Table 3.
Based on the capacities of the ship-lock and the passdam highway, the model is solved to obtain the link
flows on the multi-mode network, which are shown in
Figure 2, and the corresponding carbon emissions are
shown in Figure 3.
It can be seen from Figure 2 that total container
flows in the Yangtze River Basin are 3.8 million
TEUs, in which container turnover of the waterway
is 800 million TEU-km, while container turnover of
the highway is 700 million TEU-km. The containers
between the upper and middle reaches of the River
Shi et al.
7
Figure 2. Traffic flows of containers in the Yangtze River Basin.
Figure 3. CO2 emitted from container transportation.
are 275,000 TEUs, in which 250,000 containers are
transported by waterway, accounting for 91% of the
total. It can be said that the River is the core transport corridor for the upper and middle reaches. In
the lower reaches, such as Wuhu-Zhangjiagang, more
than 400,000 TEUs are transported by waterway,
while no highway link will carry more than
100,000 TEUs in the corresponding region. The
multi-mode network can be regarded as a hub-andbroke one, mainly based on waterway and with highway as the supplementary. The ship-lock link is
represented by waterway link from Yichang port to
Zigui port. The containers on the waterway link at
the upper stream of the ship-lock are 250,000 TEUs
and the containers on the waterway link at the lower
stream of ship-lock are 280,000 TEUs, while the containers on the ship-lock link are 200,000 TEUs only.
It means that about 20% of the containers choose
other paths instead of waterway to go over the Three
Gorges Dam.
Comparing Figures 2 and 3, it can be seen that the
CO2 emitted from transport is directly related to traffic
8
Advances in Mechanical Engineering
Table 5. Solutions under the four scenarios (million Yuan).
Scenario
Scheme
Construction cost
Transport cost
Environmental cost
Value of the objective
function
1
2
Do nothing
Expansion by 20%
Do nothing
Expansion by 40%
Do nothing
Expansion by 60%
Do nothing
–
40
–
80
–
120
–
3577.26
4087.84
4114.91
4872.18
4899.13
6020.50
6088.57
7825.10
8961.78
8999.77
10,809.19
10,903.22
13,401.65
13,526.33
11,402.36
13,089.62
13,114.68
15,761.37
15,814.35
19,542.15
19,614.90
3
4
volume and moving distance. The larger the traffic volume, the more the CO2 will be emitted. The longer the
container is transported, the more the CO2 will be
emitted. Emission from waterway transport is much
less than that from highway. For example, the traffic
on link from Chongqing port to Zigui port is
250,000 TEUs and the distance is 576 km. The traffic
on link from Chongqing to Chengdu is 190,000 TEUs
and the distance is 283 km. Although the former link
has more traffic and is longer, the CO2 emissions are
19,000 t, only 39% of the latter. It can be seen that
transporting containers by trucks generates about six
times more CO2 than that by ships.
In order to find the best solution to the network
design problem, we solve the model under several scenarios of traffic increments. Considering that infrastructure construction should be able to work many
years and traffic increments would be large, we set four
scenarios, namely, (1) without increment, (2) increase
by 15%, (3) increase by 30%, and (4) increase by 50%.
We set Pc = 30 and kmax = 50 to solve the model to get
the results as shown in Table 5.
For Scenario 1, the optimum solution is ‘‘Do
Nothing,’’ and the transport and environmental costs
are 3577.26 and 7825.10 million Yuan, respectively. For
Scenario 2, the corresponding costs of the ‘‘Do
Nothing’’ and the ‘‘Expansion by 20% (optimum solution)’’ are 4114.91/8999.77 and 4087.84/8961.78 million
Yuan, respectively. Although 40 million Yuan is spent
for the expansion, the ‘‘Value of the Objective
Function’’ is 25.06 million Yuan less. It means under
the optimum solution, the net profit of the investment
of the 40 million Yuan is 25.06 million Yuan.
Similarly, in Scenario 3, the net profit of the optimum solution is 52.98 million Yuan. And in Scenario
4, the net profit of the investment of the 120 million
Yuan is 72.75 million Yuan. It can be seen that as the
traffic increases, the ship-lock should be expanded, and
the construction of pass-dam highway is never the solution. We take Scenario 3 as an example to analyze the
reasons. For Scenario 3, the costs and benefits of the
four expansion schemes of the ship-lock are shown in
Figure 4, and the costs and benefits of the four
Figure 4. Construction costs and induced benefits of lock
expansion.
construction schemes of the pass-dam highway are
shown in Figure 5, where the benefit means the saved
transport cost or environmental cost, while the construction cost is considered as the negative benefit.
From Figure 4, it can be seen that both environmental and transport benefit increase due to ship-lock
expansion, and the total benefit goes up until the point
of extending the ship-lock by 40%. After that, the saved
costs cannot offset the construction cost. Thus, extending the ship-lock by 40% is the optimum solution for
Scenario 3. In the optimum solution, the expansion will
cost 80 million Yuan and may save 38.95 and 94.03 million Yuan for transport and environmental costs,
respectively, in 1 year. The total annual benefit is
52.98 million Yuan. Although the net benefit decreases
after the point of extending the ship-lock by 40%, it
remains positive as long as the ship-lock is extended.
The reason is that expansion of ship-lock enlarges
waterway’s capacity and makes more container traffic
shift from highway to waterway, which is much cheaper
and environment friendly.
In Figure 5, the net benefit keeps going down due to
the construction of the pass-dam highway. Taking the
point of increasing the capacity of the pass-dam highway by 40% as an example, we can see that the construction cost is 64 million Yuan and can save
11.05 million Yuan for container transport in 1 year.
However, environment benefit is 24.25 million Yuan.
Shi et al.
9
The objective of the model is to minimize the total
costs, which include the infrastructure construction
cost, transport cost, and environmental cost induced
by container transport. To solve the bi-level model,
we design a particle swarm algorithm. According to
the calculated results, some findings are as follows:
1.
Figure 5. Costs and benefits caused by pass-dam highway
construction.
As a result, the annual net benefit is 257.20 million
Yuan. It can be seen that construction of pass-dam
highway can save the transport cost because the
expended highway may attract container traffic from
waterway to alleviate the congestion. However, environmental cost will increase because more containers
will be transported by highway. As a result, the net
benefit is never positive. It is found that the annual net
benefit may decrease 15 million Yuan due to the 10%
increment in highway capacity.
The reasons in other scenarios are similar. In
Scenario 2, the optimum solution is to expand the shiplock by 20%. Construction of pass-dam highway needs
investment and cannot bring enough transport and environmental benefits. Therefore, the net benefit of building pass-dam highway is negative. In Scenario 4, the
traffic demand is increased by 50%, and the optimum
solution is to expand the ship-lock by 60%. The result
indicates that larger ship-lock can generate more benefits when the traffic demand increases. However, in
Scenario 1, the optimum solution is ‘‘Do Nothing.’’
Although expanding ship-lock can also decrease the
transport cost and environmental cost, the benefits are
less than the investment due to the small traffic demand.
To sum up, it can be seen that expansion of ship-lock
can not only reduce transport cost but also reduce environment cost. Meanwhile, the expansion may meet the
needs well in the future. Construction of pass-dam highway can alleviate the congestion but generates much
more environmental load, thus it is not an environment
friendly solution.
Conclusion
We dealt with the bottleneck problem of the transport
capacity of the ship-lock at the Three Gorges Dam. To
find the optimal solution based on the general idea of
solving the problem by expanding the ship-lock
capacity or constructing pass-dam highway, we built
a bi-level programming model, where the upper model
optimizes the expansion or construction scheme,
while the lower model finds users for the travel paths.
2.
3.
The Yangtze River waterway has advantages in
saving transport cost and reducing environmental load. It is worth to expand the ship-lock at
the Three Gorges Dam.
Pass-dam transport can alleviate the traffic congestion at the Three Gorges Dam in short term.
However, development of pass-dam transport
will increase the mode share of highway to lead
more environmental load.
Developing waterway transport by expanding
the ship-lock can not only solve the traffic congestion problem but also reduce carbon emissions from container transport. Moreover, the
transport cost can also be reduced because of
the increase in the mode share of the waterway
transport.
Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with
respect to the research, authorship, and/or publication of this
article.
Funding
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this
article: This research is supported by the Fundamental
Research Funds for the Central Universities (Grant No.
3132016303).
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