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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

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.

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 data-driven 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 multi-modal transport networks aiming at minimizing the average travel time of travelers. Wang et al.²⁰ examined the continuous network design problem with different 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.”

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 Port 2, and finally, they are delivered to City 2 by trucks. We use A representing the network and use $A_{s}$ , $A_{t}$ , and $A_{l}$ representing the sets of waterway links, transit links, and highway links, respectively. Then, $A = A_{s} \cup A_{t} \cup A_{l}$ .

Figure 1.

Method to represent the waterway and highway mixed network.

The impedance functions of different links are defined as follows:

1. For links other than transit ones

\begin{matrix} T (x_{a}) = β_{1} \cdot (g_{a} + α t_{a}) - M \cdot Min (0, c_{a}^{2} - x_{a}^{2}), \\ \forall a \in A_{s} \cup A_{l} \end{matrix}

(1)

This type of links includes waterway and highway links. Here, $g_{a}$ is the unit transport cost on link a, $t_{a}$ is the transport time on link a, $β_{1}$ is the congestion coefficient on link a, $α$ is the value of time, M is a big enough positive integer, $c_{a}$ is the capacity of link a, and $x_{a}$ 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 $(x_{a} \leq c_{a})$ , it will be 0. Otherwise $(x_{a} > c_{a})$ , 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 $β_{1}$ .

2. For transit links

T (x_{a}) = β_{2} \cdot (q_{a} + α t_{a}), \forall a \in A_{t}

(2)

here, $t_{a} = t_{a}^{wait} + t_{a}^{handle}$ is the transit time of freight on link a, $t_{a}^{wait}$ is the waiting time on link a, $t_{a}^{handle}$ is the handling time on link a, $β_{2}$ is a coefficient concerning port congestion, and $q_{a}$ is the unit transit cost on link a.

The bi-level programming model

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

\begin{matrix} min Z = λ \cdot t_{1} \cdot f_{1} (y_{1}) + λ \cdot t_{2} \cdot f_{2} (y_{2}) \\ + \sum_{a \in A} T (x_{a}) \cdot x_{a} + γ \cdot \sum_{a \in A} x_{a} \cdot E_{a} \end{matrix}

(3)

s . t . t_{1} + t_{2} = 1

(4)

f_{1} (y_{1}) \leq B

(5)

f_{2} (y_{2}) \leq B

(6)

t_{1}, t_{2} \in {0, 1}

(7)

here, $λ$ is the annual depreciation of the invested assets, $t_{1}$ is a 0–1 variable, if ship-lock is expanded $t_{1} = 1$ , otherwise $t_{1} = 0$ ; $t_{2}$ is a 0–1 variable, if pass-dam highway is constructed $t_{2} = 1$ , otherwise $t_{2} = 0$ ; $y_{1}$ is the expansion scale of the ship-lock; $y_{2}$ is the construction scale of the pass-dam highway; $f (y)$ is a function to calculate the investment, which is related to construction scale; $T (x_{a})$ is the unit-generalized transport cost on link a; $E_{a}$ is the CO₂ emission factor on link a; and $γ$ 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

Min z = \sum_{a \in A} \int_{0}^{x_{a}} T (x) dx

(8)

s . t . \sum_{k} f_{k}^{rs} = q_{rs}, \forall r \in R, \forall s \in S

(9)

f_{k}^{rs} \geq 0 \forall k \in W, \forall r \in R, \forall s \in S

(10)

x_{a} = \sum_{r} \sum_{s} \sum_{k} f_{k}^{rs} δ_{a, k}^{rs} \forall k \in W, \forall r \in R, \forall s \in S

(11)

here, $f_{k}^{rs}$ is the container traffic on path k between origin r and destination s; $δ_{a, k}^{rs}$ is a 0–1 variable, if link a is in path k then $δ_{a, k}^{rs} = 1$ , otherwise $δ_{a, k}^{rs} = 0$ ; A is the set of links; R is the set of origins; S is the set of destinations; $W_{rs}$ is the set of paths between r and s; and $q_{rs}$ 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

E = \sum_{a} x_{a} \cdot E_{a} \forall a \in A

(12)

{\begin{matrix} E_{a} = E_{truck} = T E_{truck} \times W_{truck} \times D_{a} \\ T E_{truck} = G \times F \end{matrix}, \forall a \in A_{l} \cup A_{t}

(13)

{\begin{matrix} E_{a} = E_{ship} = \frac{\sum \sum C_{ij} \times C F_{j}}{Q \cdot ρ} \\ C_{ij} = T_{i} \times F C_{j} \end{matrix}, \forall a \in A_{s}

(14)

here, E is the total CO₂ emissions of the traffic on the network; equation (13) is used to calculate the emission factor $(E_{a})$ on highway links, where $D_{a}$ is the length of link a; $W_{truck}$ is the weight of the container; $T E_{truck}$ 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 $(E_{a})$ on waterway links, where $C_{ij}$ 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; $ρ$ is the ship load ratio; $T_{i}$ is the time span of the ship in mode i; $F C_{j}$ is the consuming rate of fuel j; and $C F_{j}$ 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	ISO8217, RMA	0.86	3.15
Heavy fuel	ISO8218, RME	0.85	3.11

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 $T_{a}^{0} = T_{a} (0)$ , $\forall a$ , do all-or-nothing assignment to get link traffic as ${x_{a}^{1}}$ and set $n = 1$ .

Step 2. Update impedance of each link as $T_{a}^{n} = T_{a} (x_{a}^{n})$ .

Step 3. Find the direction of next iteration. With the updated ${t_{a}^{n}} \forall a$ , do another time of all-or-nothing assignment to get attached traffic volume ${y_{a}^{n}}$ .

Step 4. Step size determination. Use dichotomization to find $λ$ that meets the condition of $\sum_{a} (y_{a}^{n} - x_{a}^{n}) T_{a} [x_{a}^{n} + λ (y_{a}^{n} - x_{a}^{n})] = 0$

Step 5. Calculate the new start for next iteration $x_{a}^{n + 1} = x_{a}^{n} + λ (y_{a}^{n} - x_{a}^{n})$ .

Step 6. Judge whether the calculation can be terminated. If $\sqrt{\sum_{a} {(x_{a}^{n + 1} - x_{a}^{n})}^{2}} / \sum_{a} x_{a}^{n} < ε$ , then stop calculation and output ${x_{a}^{n + 1}}$ ; Otherwise, set $n = n + 1$ and go to Step 2.

Particle swarm optimization

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

V_{i}^{k + 1} = V_{i}^{k} + c_{1} r_{1} (P_{i} - X_{i}^{k}) + c_{2} r_{2} (P_{g} - X_{i}^{k})

(15)

X_{i}^{k + 1} = X_{i}^{k} + V_{i}^{k + 1}

(16)

here, i is the serial number of particle, k is the number of iteration, $V_{i}$ is the velocity vector of particle i, $X_{i}$ is the position vector of particle i, and $c_{1}$ and $c_{2}$ are the learning factors, and it is usually considered $c_{1} = c_{2} = 2$ . $P_{i}$ is the best position vector that particle i ever reached, $P_{g}$ is the best position vector that the swarm ever reached, and $r_{1}$ and $r_{2}$ 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 $P_{c}$ and the maximum of iterations $k_{max}$ . Use the objective function as the fitness function. Initialize the swarm with random solutions. Update $P_{i}$ and $P_{g}$ .

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 $P_{i}$ and $P_{g}$ , and set $k = k + 1$ .

Step 4. Judgment of termination. If $k < k_{max}$ , go to Step 2, otherwise go to Step 4.

Step 5. Output the best solution.

Numerical analysis

Needed data

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.

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.

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.

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.

Table 2.

Transport distance of waterway between ports (unit: km).

Port		1	2	3	4	5	6	7	8	9	10	11	12	13
1	Chongqing	0	576	581	670	860	1031	1204	1313	1448	1614	1750	1944	2087
2	Zigui	576	0	5	94	284	455	628	737	873	1038	1174	1368	1511
3	Yichang	581	5	0	89	279	450	623	732	868	1033	1169	1363	1506
4	Jingzhou	670	94	89	0	190	360	533	643	778	943	1080	1274	1416
5	Yueyang	860	284	279	190	0	171	343	453	588	754	890	1084	1226
6	Wuhan	1031	455	450	360	171	0	173	282	418	583	719	913	1056
7	Huangshi	1204	628	623	533	343	173	0	109	245	410	547	740	883
8	Jiujiang	1313	737	732	643	453	282	109	0	135	301	437	631	774
9	Anqing	1448	873	868	778	588	418	245	135	0	165	302	496	638
10	Wuhu	1614	1038	1033	943	754	583	410	301	165	0	136	330	473
11	Nanjing	1750	1174	1169	1080	890	719	547	437	302	136	0	194	336
12	Zhangjiagang	1944	1368	1363	1274	1084	913	740	631	496	330	194	0	143
13	Shanghai	2087	1511	1506	1416	1226	1056	883	774	638	473	336	143	0

Table 3.

Charges at ports.

Port	1	2	3	4	5	6	7	8	9	10	11	12	13
Port charges (Yuan/TEU)	200	200	200	200	200	200	200	200	200	200	200	200	200
Efficiency (TEU/h)	160	120	120	120	140	160	120	140	140	140	190	180	180
Reloading costs (Yuan/TEU)	100	100	100	100	100	100	100	100	100	100	100	100	100

TEU: twenty-foot equivalent unit.

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.

Table 4.

Specification of the ship.

Attributes	Value	Attributes	Value
Length overall	107 m	Container capacity	325
Beam	17.2 m	Loading capacity	4750 t
Depth	5.2 m	Operating speed	15 km/h
Design draft	4.0 m	Heavy fuel consumption	5 t/day
Design speed	17.5 km/h	Light fuel consumption	4 t/day

Analysis of results

Based on the capacities of the ship-lock and the pass-dam 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.

Figure 2.

Traffic flows of containers in the Yangtze River Basin.

Figure 3.

CO₂ emitted from container transportation.

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 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-and-broke 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 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 $P_{c} = 30$ and $k_{max} = 50$ to solve the model to get the results as shown in Table 5.

Table 5.

Solutions under the four scenarios (million Yuan).

Scenario	Scheme	Construction cost	Transport cost	Environmental cost	Value of the objective function
1	Do nothing	–	3577.26	7825.10	11,402.36
2	Expansion by 20%	40	4087.84	8961.78	13,089.62
2	Do nothing	−	4114.91	8999.77	13,114.68
3	Expansion by 40%	80	4872.18	10,809.19	15,761.37
3	Do nothing	−	4899.13	10,903.22	15,814.35
4	Expansion by 60%	120	6020.50	13,401.65	19,542.15
4	Do nothing	−	6088.57	13,526.33	19,614.90

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 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.

Figure 4.

Construction costs and induced benefits of lock expansion.

Figure 5.

Costs and benefits caused by pass-dam highway construction.

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 −4.25 million Yuan. As a result, the annual net benefit is −57.20 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 ship-lock 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. 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:

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.

Footnotes

Academic Editor: Gang Chen

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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Optimization of transport network in the Basin of Yangtze River with minimization of environmental emission and transport/investment costs

Abstract

Keywords

Introduction

Model development

Network construction

The bi-level programming model

The upper model

The lower model

CO2 emission calculation

Solution algorithm

Frank–Wolfe algorithm

Particle swarm optimization

The process of solution algorithm

Numerical analysis

Needed data

OD flows

Transport distance and cost on roadways

Transport distance and cost of waterway

Ship specifications

Analysis of results

Conclusion

Footnotes

Declaration of conflicting interests

Funding

References

CO₂ emission calculation