# Flexible Optimization of International Shipping Routes considering Carbon Emission Cost

Authors: Yao Yu; Jincheng Tu; Kun Shi; Mei Liu; Jihong Chen
Journal: Mathematical Problems in Engineering
 (2021)

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## Abstract

Carbon emissions cost is a potential effective measure to restrict hydrocarbon pollution in the international shipping trade. The minimization of the total cost is pursued by ship operators, whereas voyage cost is increasingly involving the replacement of clean fuel and changing the cost of the shipping route. A flexible optimization method focusing on maximizing the total profit is developed in terms of sailing speed optimization and single port skips integrate carbon emission influence. An actual ocean shipping route from Shanghai to Rotterdam is applied to validate the effectiveness of the proposed models. The results have shown that the shipping route profit is volatile along with the sailing speed and the number of port calls. However, the profit will be maximized when applying the single port skip and will slow down the sailing speed at the same time. The demand of planned skip port can be supported by a short line container. A system composed of ocean container liner and short line container can improve the profit by 4.05% and reduce the carbon emission by 19.70%. Furthermore, sensitive results show that the profit is less affected by the changing of the carbon emission cost. A small size container has enough ability to solve the short transportation demand in adjacent ports and convert extraberthing cost into profit. These findings can provide reliable support for the shipping route decision process considering future carbon emission costs.


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## Body

## 1. Introduction

Shipping plays an important role in international logistics, but while bringing huge economic benefits, it is also causing environmental pollutants. Ships consume a lot of fossil fuel and produce a great number of air pollutant emissions during transportation, which may cause a negative impact on the environment [1, 2]. As a result of the rapid development of the shipping industry, the carbon emission from ship transportation has grown by an average of 0.3% every year, accounting for about 2.8% of the world [3]. Massive greenhouse gases are the main cause of global warming [4]. According to the greenhouse gas emission report of the Fourth International Maritime Organization (IMO), the carbon intensity of international maritime transportation decreased by about 11% from 2012 to 2018, but the annual emission of greenhouse gas increased from 977 million tons to 1076 million tons. It is estimated that by 2050, with the continuous growth of shipping demand, carbon dioxide emissions will increase by about 50% compared with 2018 and 90–130% compared with 2008. [5].Moreover, charging carbon emission such as carbon tax policy is a future powerful emission-reduction policy that takes into account the cost of shipping. The so-called carbon tax is levied primarily on carbon emissions from fossil fuels. According to the “bottom-up” estimation method of ship emission, fossil fuels consumptions are directly proportional to ship emissions [6]. A lot of fuel consumption will produce more air pollutants. Based on the statistics of the 2018 Fuel Market Analysis Report, the total emissions demand of oil fuel in China was about 19.45 million tons, an increase of 1.7 million tons, or 9.85% year on year [7]. Therefore, imposing the extra carbon charing on the large amount of fuel consumed can achieve the goal of controlling fuel consumption by increasing operating costs, thereby mitigating pollutant emissions. Ship speeds also have important impacts on carbon emissions and transport costs. Lindstad et al. [8] pointed out that reducing the speed can effectively decrease the ship pollutant emissions. According to the data released by the OOCL shipping company, the port of Los Angeles heading for a voyage to Kaohsiung has a 6% drop in speed and a 30% drop in fuel costs. Since there exist positive correlations between carbon emissions and fuel consumption, speed reduction not only optimizes the amount of fuel consumption but also reduces carbon emissions. Therefore, potential carbon emission cost and the measure of the reduction of ship speed are equally important for the reduction of ship emissions.In recent years, a large number of researches mainly focus on the optimization of the sailing speed, demand-based port selection, and planning without considering carbon emission. In the study of speed optimization, the influence of ship mechanical structure and external factors on ship speed reduction should be considered synthetically. Some researchers [9, 10] analyzed the main engine fuel consumption and route time changes at different speeds, and the results showed that fuel consumption accounted for about 20%–40% of the total navigation cost and constructed a functional relationship between fuel consumption and navigation speed, as shown in equation (1). Moreover, reducing the sailing speed of the ship can decrease running costs. Some researchers [11, 12] have studied the effect on the cost of ship transportation after the ship has slowed down. Studies pointed out that the cost of carbon emission decreases with the decrease in speed, but the transportation restriction cost increases gradually.Considering the liner transportation and ship scheduling under emission control influence, Prpicorsic et al. [13] and Simonsen et al. [14] introduced ship carbon emission costs to plan low carbon transportation routes. De et al. [15] quantified the expression of carbon emission, and a mixed-integer linear model considering the demand of different linked ports is proposed to calculate the optimal speed. Dulebenets [16] evaluated whether vessel speed reduction can be a potentially cost-effective carbon mitigation option for ships calling on US ports. The results showed that the shipping profit closely depending on how the fleet responds to a speed reduction mandate. Corbett et al. [17] indicated that the carbon tax value might cause significant changes in the design of vessel schedules in referring to the environmental improvement issues, i.e., decreasing the vessel sailing speed to reduce fuel consumption and carbon dioxide emissions. Reducing speed and fuel consumption is equivalent to improving energy efficiency, but the increase in flight time leads to a decrease of industry profit [18, 19]. Abioye et al. and Sheng et al. [20, 21] considered ECA (Emission Control Area) policy to adjust the speed and route and increase the profit. In order to reduce the cost of carbon emissions, some researchers [19, 22] reconfigure the transportation network. These studies [16, 23, 24] also analyzed the applicability of the liner subshipment and the selecting optimal route design considering carbon cost. It is shown that the proposed MNL mixed-integer linear model is suitable for the liner fleet deployment, but the flexible countermeasures brought by the model under the reduced speed navigation are not considered, such as the selection of the link ports and then plan to skip.In summary, the current research mainly focuses on the effect of ship speed and ship route planning on emission reduction. There are few kinds of research on flexible route planning, such as skipping port combined with carbon emission cost aiming to increase shipping profit. Therefore, this study proposes an optimization method for the integration of speed design and flexible port selection. Taking the profit maximization of transport ships as the goal, the numerical verification and sensitivity analysis are carried out considering the cost of the carbon emission.


## 2. Analysis of Influencing Factors

### 2.1. Impact of Liner Speed on Cost and Route

Voyage speed has an important impact on the liner cycle and transport costs. The relationship between fuel consumption and speed can be expressed in the following equation:(1)Q=k∗vn,where Q is the daily fuel consumption of the ship (unit: per ton/day); kpresents the ship function coefficient, which is related to the ship’s condition, deadweight, and the navigation environment; v is the ship speed (unit: knot). Åström et al. [19] indicate that in ocean-going container liner transportation, the value of n is 3. Fagerholt et al. [28] show that the fuel consumption per time unit increases to a power of three with speed. In addition, Bialystocki et al. [11] also point out that the relationship among voyage L (unit: nautical miles), time t (unit: hour), and speed v (unit: knot), as shown in the following equation:(2)t=Lv.According to equations (1) and (2), the vessel’s fuel consumption per nautical mile per hour is Qdis and the expression formula is shown below:(3)Qdis=k∗v224.In general, the sailing route can be adjusted according to the capacity when speed decreases. However, if we take port arrival time windows into account, there are two ways to solve the negative effects caused by the decrease in speed. First of all, we can increase the number of shipping routes, i.e., reduce the liner shipping interval. The second option is to selectively reject some relatively small port calls. In addition, liner at a lower speed can often increase the probability of punctuality to the port; i.e., when liner encountered unexpected circumstances, a port time extension can be increased to compensate for the loss of time. The quantization of flexibility is also related to the speed reduction ratio.


### 2.2. Impact of Carbon Emission Costs on Liner Route Optimization

The carbon emission cost levied on fossil fuel based on their carbon content or carbon emission, thus achieving the purpose of controlling carbon emissions from shipping by means of increasing the cost of shipping. Currently, the United States, Australia, Japan, and other economically developed countries and regions such as the European Union have issued relevant carbon emission policies. The carbon emission cost model is shown as follows:(4)C=Qco2×D,where C represents the carbon emission cost (unit: USD); Qco2 is the carbon emission (unit ton); Dis the carbon emission cost rate (unit: USD/ton). For the determination of carbon emissions, De et al. [15] propose that the composition of carbon emissions is equal to the product of fuel consumption and carbon emission factors based on existing research. Among them, the carbon emission factor is a measure of the ability of fuel consumption to convert to carbon dioxide, and the carbon emission factor under heavy oil is picked as 3.021 [16], that is,(5)Qco2=Qo×3.021,where Qo represent the fuel consumption (unit: tons). According to equation (3), the cost of carbon emissions can be summarized as follows:(6)C=D∗3.021∗disij∗k∗v224,where disij is the distance between port i and port j (unit nautical mile);The promulgation of potential carbon emission policies has a great impact on the total profits of liner routes. Apart from the improvement of the ship's own power structure, due to the easy payment of more carbon emission cost under high-speed navigation, some liners will choose to reduce the speed to achieve the purpose of reducing the cost of the voyage. However, speed reduction will lead to the change of the departure schedule, and the route must be reallocated or increase the number of ships and other means.


## 2.1. Impact of Liner Speed on Cost and Route

Voyage speed has an important impact on the liner cycle and transport costs. The relationship between fuel consumption and speed can be expressed in the following equation:(1)Q=k∗vn,where Q is the daily fuel consumption of the ship (unit: per ton/day); kpresents the ship function coefficient, which is related to the ship’s condition, deadweight, and the navigation environment; v is the ship speed (unit: knot). Åström et al. [19] indicate that in ocean-going container liner transportation, the value of n is 3. Fagerholt et al. [28] show that the fuel consumption per time unit increases to a power of three with speed. In addition, Bialystocki et al. [11] also point out that the relationship among voyage L (unit: nautical miles), time t (unit: hour), and speed v (unit: knot), as shown in the following equation:(2)t=Lv.According to equations (1) and (2), the vessel’s fuel consumption per nautical mile per hour is Qdis and the expression formula is shown below:(3)Qdis=k∗v224.In general, the sailing route can be adjusted according to the capacity when speed decreases. However, if we take port arrival time windows into account, there are two ways to solve the negative effects caused by the decrease in speed. First of all, we can increase the number of shipping routes, i.e., reduce the liner shipping interval. The second option is to selectively reject some relatively small port calls. In addition, liner at a lower speed can often increase the probability of punctuality to the port; i.e., when liner encountered unexpected circumstances, a port time extension can be increased to compensate for the loss of time. The quantization of flexibility is also related to the speed reduction ratio.


## 2.2. Impact of Carbon Emission Costs on Liner Route Optimization

The carbon emission cost levied on fossil fuel based on their carbon content or carbon emission, thus achieving the purpose of controlling carbon emissions from shipping by means of increasing the cost of shipping. Currently, the United States, Australia, Japan, and other economically developed countries and regions such as the European Union have issued relevant carbon emission policies. The carbon emission cost model is shown as follows:(4)C=Qco2×D,where C represents the carbon emission cost (unit: USD); Qco2 is the carbon emission (unit ton); Dis the carbon emission cost rate (unit: USD/ton). For the determination of carbon emissions, De et al. [15] propose that the composition of carbon emissions is equal to the product of fuel consumption and carbon emission factors based on existing research. Among them, the carbon emission factor is a measure of the ability of fuel consumption to convert to carbon dioxide, and the carbon emission factor under heavy oil is picked as 3.021 [16], that is,(5)Qco2=Qo×3.021,where Qo represent the fuel consumption (unit: tons). According to equation (3), the cost of carbon emissions can be summarized as follows:(6)C=D∗3.021∗disij∗k∗v224,where disij is the distance between port i and port j (unit nautical mile);The promulgation of potential carbon emission policies has a great impact on the total profits of liner routes. Apart from the improvement of the ship's own power structure, due to the easy payment of more carbon emission cost under high-speed navigation, some liners will choose to reduce the speed to achieve the purpose of reducing the cost of the voyage. However, speed reduction will lead to the change of the departure schedule, and the route must be reallocated or increase the number of ships and other means.


## 3. Construction of Flexible Optimization Model

### 3.1. Assumptions

In this study, considering the optimization of liner speed and the redistribution of linked ports, the following assumptions are made for the proposed flexible optimization model:(1)
Port cargo demand, interport distance, and freight between ports are known under voyage trip.(2)
Port fees are known; the speed of loading and unloading is identical through the whole shipping.(3)
The times of pilotage are the same and known when the ship calls at each port.(4)
The weather conditions and shipping route circumstances in each section are the same.(5)
Only consider using heavy oil. Its voyage cost and carbon emission cost rate are known and do not vary with the ship's sailing time.(6)
With the original departure port and the port at the farthest part of the route as the terminal ports, the ship may not choose to call at any port except the terminal port.The voyage costs mainly include fuel charges, potential carbon emission cost charges, port charges, loading and unloading charges, berthing charges for ships in the course of loading and unloading, and penalty charges in case of the port skip. To ensure the on-time arrival of the ship in the next cycle when the ship is sailing at a slower speed, only the method of port skipping can be adopted, and the losses caused by the port dumping are also included in the cost.Ship company cost in the proposed model includes fuel cost, carbon emission cost, port operation fee, container handling cost, ship berthing cost, and port skip penalty cost. The revenue of ship transportation mainly comes from freight; we take the product of freight between loading and unloading as the revenue of ship transportation.In this study, we sum the cost of all sections of a certain route as the total cost of the route, and the sum of the revenue of all sections as the total revenue of the route. A mixed nonlinear programming model with the maximum difference between total revenue and cost as the objective function is established. Table1 declares the variables for the model.Table 1
Variable declaration.
SymbolSymbol meaningPTotal profit on routes excluding operating and capital costs (USD)nNumber of ports in routesEFuel price ($/ ton)i,jPorti and port jdisijThe distance from porti to port j (nautical mile)vThe speed at which ships sail on the course (knot)uijWhether there is a container transport between portiand portjXijWhether there is an actual route between portsiandjkShip functional coefficientTPort surcharge such as terminal chargefzStandard container handling charges (USD/TEU)θPenalty coefficient for port skip, between 0 and 1volijContainer volume from porti to portjdeijActual demand for container transport between porti to portjfijStandard container unit freight at porti to portj (USD/TEU)DCarbon emission cost (USD/TEU)tyPilotage time of container ships in ports and other time consumption other than loading and unloading time (h)vzContainer handling speed (TEU/h)fsThe cost of a ship at anchor (USD/TEU)twThe maximum time that the shipping company specifies at which the ship will travel on that route (hour)capMaximum liner loadfuiAuxiliary coefficient


### 3.2. Modeling

According to the above assumptions and conditions, the total profit objective function of the route can be represented as follows:(7)max:P=∑∑uij∗volij∗fij−2∗fz−∑∑,Xij∗E+3.17∗D∗disij∗k∗v224+T,−∑∑1−uij∗θ∗deij∗fij,−2∗∑∑uij∗volijvz∗fs24,where ∑∑uij∗volij∗fij−2∗fz is the total freight revenue for removal of loading and unloading charges; ∑∑Xij∗E+3.17∗D∗disij∗k∗v2/24+T refers to the cost of fuel, carbon emission cost, and port fees during transportation; ∑∑1−uij∗θ∗deij∗fij is the penalty for port skip; and 2∗∑∑uij∗volij/vz∗fs/24 is the ship berthing cost in port.The decision variables are constrained as shown in the following equation:(8)S.t.vmin≤v≤vmax,vis round number,Xij=10,i,j=1,2,3,…,n,0≤volij≤deij,i,j=1,2,3,…,n,Xij=0,i=j.The intermediate variable constraint is shown in the following equation:(9)S.t.uij=∑j=inxij∗∑i=1jxij0<j<i≤n,∑j=1ixij∗∑i=jnxij0<i<j≤n,i,jare round numbers.The time constraints are shown in the following equation:(10)S.t.∑∑Xij∗disijv+2∗∑∑uij∗volijvz+∑∑Xij∗ty<tw.The onward route capacity constraints are shown in the following equation:(11)S.t.∑i=11∑j=2nuij∗volij≤cap,∑i=12∑j=3nuij∗volij≤cap,∑i=1n−1∑j=nnuij∗volij≤cap.The return route capacity constraints are shown in the following equation:(12)S.t.∑i=nn∑j=1n−1uij∗volij≤cap,∑i=n−1n∑j=1n−2uij∗volij≤cap,∑i=n−3n∑j=1n−3uij∗volij≤cap,∑i=2n∑j=11uij∗volij≤cap,n>3.The capacity constraints can be presented in Figure1. When the ship starts from port 1, the load can be recorded as vol12 (Containers between 1 and 2 ports) and the sum of containers of vol13 and vol14. When the ship arrives at port 2, unload the corresponding container vol12 and load the container of vol23 and vol24.Figure 1
Schematic diagram of capacity constraints.Route constraints are as follows:(13)S.t.∑∑i∗fui−j∗fuj∗Xij+n∗fun−1∗fu1=0,∑∑i∗fui−j∗fuj∗Xij−n∗fun+1∗fu1=0,1≤i<j≤n.Each segment of the journey and return is regarded as a vector, and the characteristics of each other can be eliminated by adding the first and last parts of the vector. Therefore the segment of the journey and return is always composed of routes, thus ensuring the effectiveness of the routes.


## 3.1. Assumptions

In this study, considering the optimization of liner speed and the redistribution of linked ports, the following assumptions are made for the proposed flexible optimization model:(1)
Port cargo demand, interport distance, and freight between ports are known under voyage trip.(2)
Port fees are known; the speed of loading and unloading is identical through the whole shipping.(3)
The times of pilotage are the same and known when the ship calls at each port.(4)
The weather conditions and shipping route circumstances in each section are the same.(5)
Only consider using heavy oil. Its voyage cost and carbon emission cost rate are known and do not vary with the ship's sailing time.(6)
With the original departure port and the port at the farthest part of the route as the terminal ports, the ship may not choose to call at any port except the terminal port.The voyage costs mainly include fuel charges, potential carbon emission cost charges, port charges, loading and unloading charges, berthing charges for ships in the course of loading and unloading, and penalty charges in case of the port skip. To ensure the on-time arrival of the ship in the next cycle when the ship is sailing at a slower speed, only the method of port skipping can be adopted, and the losses caused by the port dumping are also included in the cost.Ship company cost in the proposed model includes fuel cost, carbon emission cost, port operation fee, container handling cost, ship berthing cost, and port skip penalty cost. The revenue of ship transportation mainly comes from freight; we take the product of freight between loading and unloading as the revenue of ship transportation.In this study, we sum the cost of all sections of a certain route as the total cost of the route, and the sum of the revenue of all sections as the total revenue of the route. A mixed nonlinear programming model with the maximum difference between total revenue and cost as the objective function is established. Table1 declares the variables for the model.Table 1
Variable declaration.
SymbolSymbol meaningPTotal profit on routes excluding operating and capital costs (USD)nNumber of ports in routesEFuel price ($/ ton)i,jPorti and port jdisijThe distance from porti to port j (nautical mile)vThe speed at which ships sail on the course (knot)uijWhether there is a container transport between portiand portjXijWhether there is an actual route between portsiandjkShip functional coefficientTPort surcharge such as terminal chargefzStandard container handling charges (USD/TEU)θPenalty coefficient for port skip, between 0 and 1volijContainer volume from porti to portjdeijActual demand for container transport between porti to portjfijStandard container unit freight at porti to portj (USD/TEU)DCarbon emission cost (USD/TEU)tyPilotage time of container ships in ports and other time consumption other than loading and unloading time (h)vzContainer handling speed (TEU/h)fsThe cost of a ship at anchor (USD/TEU)twThe maximum time that the shipping company specifies at which the ship will travel on that route (hour)capMaximum liner loadfuiAuxiliary coefficient


## 3.2. Modeling

According to the above assumptions and conditions, the total profit objective function of the route can be represented as follows:(7)max:P=∑∑uij∗volij∗fij−2∗fz−∑∑,Xij∗E+3.17∗D∗disij∗k∗v224+T,−∑∑1−uij∗θ∗deij∗fij,−2∗∑∑uij∗volijvz∗fs24,where ∑∑uij∗volij∗fij−2∗fz is the total freight revenue for removal of loading and unloading charges; ∑∑Xij∗E+3.17∗D∗disij∗k∗v2/24+T refers to the cost of fuel, carbon emission cost, and port fees during transportation; ∑∑1−uij∗θ∗deij∗fij is the penalty for port skip; and 2∗∑∑uij∗volij/vz∗fs/24 is the ship berthing cost in port.The decision variables are constrained as shown in the following equation:(8)S.t.vmin≤v≤vmax,vis round number,Xij=10,i,j=1,2,3,…,n,0≤volij≤deij,i,j=1,2,3,…,n,Xij=0,i=j.The intermediate variable constraint is shown in the following equation:(9)S.t.uij=∑j=inxij∗∑i=1jxij0<j<i≤n,∑j=1ixij∗∑i=jnxij0<i<j≤n,i,jare round numbers.The time constraints are shown in the following equation:(10)S.t.∑∑Xij∗disijv+2∗∑∑uij∗volijvz+∑∑Xij∗ty<tw.The onward route capacity constraints are shown in the following equation:(11)S.t.∑i=11∑j=2nuij∗volij≤cap,∑i=12∑j=3nuij∗volij≤cap,∑i=1n−1∑j=nnuij∗volij≤cap.The return route capacity constraints are shown in the following equation:(12)S.t.∑i=nn∑j=1n−1uij∗volij≤cap,∑i=n−1n∑j=1n−2uij∗volij≤cap,∑i=n−3n∑j=1n−3uij∗volij≤cap,∑i=2n∑j=11uij∗volij≤cap,n>3.The capacity constraints can be presented in Figure1. When the ship starts from port 1, the load can be recorded as vol12 (Containers between 1 and 2 ports) and the sum of containers of vol13 and vol14. When the ship arrives at port 2, unload the corresponding container vol12 and load the container of vol23 and vol24.Figure 1
Schematic diagram of capacity constraints.Route constraints are as follows:(13)S.t.∑∑i∗fui−j∗fuj∗Xij+n∗fun−1∗fu1=0,∑∑i∗fui−j∗fuj∗Xij−n∗fun+1∗fu1=0,1≤i<j≤n.Each segment of the journey and return is regarded as a vector, and the characteristics of each other can be eliminated by adding the first and last parts of the vector. Therefore the segment of the journey and return is always composed of routes, thus ensuring the effectiveness of the routes.


## 4. Example Analysis

### 4.1. Description of Parameters

To evaluate the applicability of the proposed models and the efficiency of the port skip strategy, we adopt a real trading route case from Asia to Europe provided by OOCL. This route involved eight ports as shown in Figure2. There is the ship operated on the route derived from eight ports: Shanghai, Ningbo, Yantian, Singapore, Dubai, Antwerp, Rotterdam, and Hamburg. We use the proposed models to select the optimal voyages between two ports and optimal route profit on the whole route design. We assume the ship firstly departs from Shanghai and finally back to Shanghai. The distance among individual ports is shown in Table 2.Figure 2
The shipping routes of eight ports.Table 2
The distance among individual ports (n miles).
Dis(i,j)ShanghaiNingboYantianSingaporeDubaiAntwerpRotterdamHamburgShanghai010979621485606104311044910740Ningbo109073920905549103731039210640Yantian7967390145449119736975410002Singapore21482090145403454827982978545Dubai56065549491134540618962076455Antwerp10431103739736827961890200710Rotterdam10449103929754829762072000480Hamburg107401064010002854564557104800We regard port as the original set ofn elements, while (port, port) as its derived set includes variables of shipping route segment and variables of cargo transport demand. The actual container liner parameters are shown in Table 3.Table 3
Ship parameters.
Ship parametersNumerical valueThe maximum deadweight of the ship (TEU)8000Minimum speed (knot)14Maximum speed (knot)27Container handling speed (Containers/h)120Ship function coefficientk0.0112Port fees, etc. (USD)21000Parking charges (USD/day)2500Carbon emission factors3.021Pilotage time and stay in the port except for handling time (h)4Container handling charges (USD/TEU)150The value range of the ship function coefficientk can be calculated by linear regression according to historic fuel cost and average speed. Here, let k = 0.0112 at 8000 TEU situation. Port fees and miscellaneous port charges, berthing charges, and handling charges are valued at $21,000, $2,500 per hour, and $150/TEU, respectively, according to China Port Association [25]. Pilotage time and stay in the port (excluding loading and unloading time) is 4 hours. Select the Shanghai Port-Hamburg Port route; the route related parameters are shown in Table 4.Table 4
Route parameters.
Route parametersNumerical valueTotal voyage time (hours)1510Port penalty factor0.5Heavy oil price (RMB/ton)500Carbon emission cost rate (USD/ton)30


### 4.2. Analysis of Results

The original section is Shanghai Port-Ningbo Port-Yantian Port-Singapore Port-Dubai Port-Antwerp Port-Rotterdam Port-Hamburg Port. The existence of the optimized segment is shown in Table5.Table 5
Results of segment optimization.
O/DShanghai portNingbo portYantian portSingapore portDubai portPort AntwerpRotterdam portPort HamburgShanghai port01000000Ningbo port10100000Yantian port01010000Singapore port00100100Dubai port00000000Port Antwerp00010010Rotterdam port00000101Port Hamburg00000010As presented in Table5, the optimized result is obtained by using LINGO 16.0. The optimized route is Shanghai Port-Ningbo Port-Yantian Port-Singapore Port-Antwerp Port-Rotterdam Port-Hamburg Port. The return route is Hamburg-Rotterdam-Antwerp-Dubai-Singapore-Yantian-Ningbo-Shanghai. Compared to the original route, the port of Dubai is not on the visiting list. The container transport optimization results are shown in Table 6.Table 6
Cargo transport optimization.
O/DShanghai portNingbo portYantian portSingapore portDubai portPort AntwerpRotterdam portPort HamburgShanghai port01201759700151285173Ningbo port1150809600110140112Yantian port24018008700125165137Singapore port810650000152273178Dubai port00000000Port Antwerp7205906403000080360Rotterdam port9807108605800900150Port Hamburg74059071058002301100The comparisons of original and optimized routes results are shown in Table7.Table 7
Comparison of original and optimized route data.
ParameterOriginal routeOptimization of rear routesVoyage profit (USD)94319799780768Speed of a ship (knot)2219Time of voyage (h)14961503Total shipments (TEU)1756616191Total sailing distance (nautical mile)2525022522Total fuel consumption (ton)57033794Carbon emission cost (USD)542355360809Number of linked ports87Profitability (USD/h)63056507As presented in Table7, the profit-making performance of the optimized route is significantly higher than that of the original route. The speed of the voyage decreased by 13.70%. The total freight volume decreased by 7.8%, and the total sailing distance decreased by 10.8%. The voyage profit increased by 3.70%. The voyage time was about equal to the original route time (only 7 hours). The total fuel consumption decreased by 33.48%. The carbon emission cost decreased by about 33.47%.According to the analysis of cost structure, the proportion of carbon emission cost decreased from 5.75% to 3.69%, and the proportion of fuel cost decreased from 30.23% to 19.40% under the simultaneous action of shipping at the same time.


## 4.1. Description of Parameters

To evaluate the applicability of the proposed models and the efficiency of the port skip strategy, we adopt a real trading route case from Asia to Europe provided by OOCL. This route involved eight ports as shown in Figure2. There is the ship operated on the route derived from eight ports: Shanghai, Ningbo, Yantian, Singapore, Dubai, Antwerp, Rotterdam, and Hamburg. We use the proposed models to select the optimal voyages between two ports and optimal route profit on the whole route design. We assume the ship firstly departs from Shanghai and finally back to Shanghai. The distance among individual ports is shown in Table 2.Figure 2
The shipping routes of eight ports.Table 2
The distance among individual ports (n miles).
Dis(i,j)ShanghaiNingboYantianSingaporeDubaiAntwerpRotterdamHamburgShanghai010979621485606104311044910740Ningbo109073920905549103731039210640Yantian7967390145449119736975410002Singapore21482090145403454827982978545Dubai56065549491134540618962076455Antwerp10431103739736827961890200710Rotterdam10449103929754829762072000480Hamburg107401064010002854564557104800We regard port as the original set ofn elements, while (port, port) as its derived set includes variables of shipping route segment and variables of cargo transport demand. The actual container liner parameters are shown in Table 3.Table 3
Ship parameters.
Ship parametersNumerical valueThe maximum deadweight of the ship (TEU)8000Minimum speed (knot)14Maximum speed (knot)27Container handling speed (Containers/h)120Ship function coefficientk0.0112Port fees, etc. (USD)21000Parking charges (USD/day)2500Carbon emission factors3.021Pilotage time and stay in the port except for handling time (h)4Container handling charges (USD/TEU)150The value range of the ship function coefficientk can be calculated by linear regression according to historic fuel cost and average speed. Here, let k = 0.0112 at 8000 TEU situation. Port fees and miscellaneous port charges, berthing charges, and handling charges are valued at $21,000, $2,500 per hour, and $150/TEU, respectively, according to China Port Association [25]. Pilotage time and stay in the port (excluding loading and unloading time) is 4 hours. Select the Shanghai Port-Hamburg Port route; the route related parameters are shown in Table 4.Table 4
Route parameters.
Route parametersNumerical valueTotal voyage time (hours)1510Port penalty factor0.5Heavy oil price (RMB/ton)500Carbon emission cost rate (USD/ton)30


## 4.2. Analysis of Results

The original section is Shanghai Port-Ningbo Port-Yantian Port-Singapore Port-Dubai Port-Antwerp Port-Rotterdam Port-Hamburg Port. The existence of the optimized segment is shown in Table5.Table 5
Results of segment optimization.
O/DShanghai portNingbo portYantian portSingapore portDubai portPort AntwerpRotterdam portPort HamburgShanghai port01000000Ningbo port10100000Yantian port01010000Singapore port00100100Dubai port00000000Port Antwerp00010010Rotterdam port00000101Port Hamburg00000010As presented in Table5, the optimized result is obtained by using LINGO 16.0. The optimized route is Shanghai Port-Ningbo Port-Yantian Port-Singapore Port-Antwerp Port-Rotterdam Port-Hamburg Port. The return route is Hamburg-Rotterdam-Antwerp-Dubai-Singapore-Yantian-Ningbo-Shanghai. Compared to the original route, the port of Dubai is not on the visiting list. The container transport optimization results are shown in Table 6.Table 6
Cargo transport optimization.
O/DShanghai portNingbo portYantian portSingapore portDubai portPort AntwerpRotterdam portPort HamburgShanghai port01201759700151285173Ningbo port1150809600110140112Yantian port24018008700125165137Singapore port810650000152273178Dubai port00000000Port Antwerp7205906403000080360Rotterdam port9807108605800900150Port Hamburg74059071058002301100The comparisons of original and optimized routes results are shown in Table7.Table 7
Comparison of original and optimized route data.
ParameterOriginal routeOptimization of rear routesVoyage profit (USD)94319799780768Speed of a ship (knot)2219Time of voyage (h)14961503Total shipments (TEU)1756616191Total sailing distance (nautical mile)2525022522Total fuel consumption (ton)57033794Carbon emission cost (USD)542355360809Number of linked ports87Profitability (USD/h)63056507As presented in Table7, the profit-making performance of the optimized route is significantly higher than that of the original route. The speed of the voyage decreased by 13.70%. The total freight volume decreased by 7.8%, and the total sailing distance decreased by 10.8%. The voyage profit increased by 3.70%. The voyage time was about equal to the original route time (only 7 hours). The total fuel consumption decreased by 33.48%. The carbon emission cost decreased by about 33.47%.According to the analysis of cost structure, the proportion of carbon emission cost decreased from 5.75% to 3.69%, and the proportion of fuel cost decreased from 30.23% to 19.40% under the simultaneous action of shipping at the same time.


## 5. Sensitivity Analysis

### 5.1. Impact of Changes in Carbon Emission Cost Rates on Voyage Profits

In this study, carbon emission cost is taken as an external uncertain factor that has an influence on the final profit of shipping companies. We assume all factors except carbon emission cost are not changing as the environmental variance and give a sensitivity analysis to test the performance of the total profit considering the carbon emission cost rateD, as written in the following equation:(14)dP=−3.021∗disa∗k∗v224∗dD,where disa represents the total nautical mileage of the planning route.From equation (14) and the optimized data calculation in the model example, it can be calculated as follows:(15)dP=−12027∗dD.Equation (15) implies that when the carbon emission cost changes in $1 per ton, the total profit of the route would reduce by $12,027. The sensitive results of shipping profit with the changing rate of carbon emission cost are shown in Figure 3.Figure 3
Chart of changes in shipping route profits with the carbon emission cost.Though the carbon emission cost has been regarded as a additional potential sailing cost, the actual impact on the shipping profit is relatively small (+1.23%∼−2.16%). For example, when the carbon emission cost increases by $5, the profit shrinks by about 0.6%.


### 5.2. Impact of Port Skip on Port Transport

Since one or more ports would be skipped aiming to maintain maximum profit of ship carriers, substitute vessels should be considered to handle the transportation demand of the planned skipped port or cargo owner. For example, the transportation demand of Dubai port cargo (includes loading and unloading) is 1375 TEU. The number of untransported containers is totally 3440TEU according to the statistics of other calling ports. A 1436 TEU alternative container ship is chosen based on the remaining transportation demand of Dubai port. The substitute container ship is designed to accomplish the loading/unloading tasks in Dubai port. The 1436 TEU substitute ship information is as Table8 shown.Table 8
1436 TEU container ship parameters.
Ship parametersNumerical valueThe maximum deadweight of the ship (TEU)1436Service speed (knot)18.5Container handling speed (containers/hour)120Ship function coefficientk0.0137Port fees, etc. (USD)21000Parking charges (USD/d)2500Carbon emission factors3.021Pilotage time and stay in the port except for handling time (h)4Container handling charges (USD/TEU)150Heavy oil prices (USD/ton)500Carbon emission cost rate (USD/ton)30As seen from equation (3), the Qdis per nautical mile consumption of the ship can be expressed as follows:(16)Qdis=0.0137∗v1.8924∗dis.The simulation results are shown in Table9. (17)P=R−CV−Co−Cc.where P represents the voyage net profit; R donates the voyage revenue; CV is the voyage cost; Co reflects the operating cost; CCmeans the capital cost.Table 9
1436 TEU ship route simulation results.
Model results parametersNumerical valueVoyage profit (USD)936839Speed of the ship (knot)13Total shipments (TEU)4815Total sailing distance (nautical miles)11325Travel time (hours)871Total fuel consumption (ton)824Number of linked ports8Profitability (USD/hour)622This study assumes that the 1456 TEU container ship cooperates with 8000 TEU formulated as a group and the 1456 short line container considering the economical speed with reference to the cost efficiency. For example, we set the short line container speed as 13 kn. The chartering fee of a 1436 TEU container ship includes the following: daily capital cost is $8,700; annual operating cost is $1480,000, and average daily consumption of light crude oil is 2 tons (here we assume the consumption of the light crude oil is fixed while at berthing). According to inquire the price onChina Maritime Services Network in April 2019, the light crude oil price was $650 per ton. So we can calculate the voyage crude oil cost as $76,646. Moreover, we calculated the emission cost of 1456 TEU is $74,675. Based on the above, the profit from Shanghai-Hamburg is $108,191 excluding emission cost, and the final profit is $33,516 after carbon emission cost deduction. Therefore, the proposed scheme is feasible with respect to the positive profit result of an additional 1436 TEU container ship, which could be accepted by a shipping company.In addition, it is worth noting that the simulation result implies that the smaller container ship has enough ability to solve the short transportation demand between adjacent ports and convert extra berthing cost into profit compare to a larger size of a container ship. Considering the profitability in terms of the voyage, a regional or branch container ship only costs $622 per hour compared to $6,507 an hour for 8,000 TEU ships even after route optimization. To sum up, the integration of ocean containers and short line supplement containers will have a significant improvement in the profit of the international shipping route.


## 5.1. Impact of Changes in Carbon Emission Cost Rates on Voyage Profits

In this study, carbon emission cost is taken as an external uncertain factor that has an influence on the final profit of shipping companies. We assume all factors except carbon emission cost are not changing as the environmental variance and give a sensitivity analysis to test the performance of the total profit considering the carbon emission cost rateD, as written in the following equation:(14)dP=−3.021∗disa∗k∗v224∗dD,where disa represents the total nautical mileage of the planning route.From equation (14) and the optimized data calculation in the model example, it can be calculated as follows:(15)dP=−12027∗dD.Equation (15) implies that when the carbon emission cost changes in $1 per ton, the total profit of the route would reduce by $12,027. The sensitive results of shipping profit with the changing rate of carbon emission cost are shown in Figure 3.Figure 3
Chart of changes in shipping route profits with the carbon emission cost.Though the carbon emission cost has been regarded as a additional potential sailing cost, the actual impact on the shipping profit is relatively small (+1.23%∼−2.16%). For example, when the carbon emission cost increases by $5, the profit shrinks by about 0.6%.


## 5.2. Impact of Port Skip on Port Transport

Since one or more ports would be skipped aiming to maintain maximum profit of ship carriers, substitute vessels should be considered to handle the transportation demand of the planned skipped port or cargo owner. For example, the transportation demand of Dubai port cargo (includes loading and unloading) is 1375 TEU. The number of untransported containers is totally 3440TEU according to the statistics of other calling ports. A 1436 TEU alternative container ship is chosen based on the remaining transportation demand of Dubai port. The substitute container ship is designed to accomplish the loading/unloading tasks in Dubai port. The 1436 TEU substitute ship information is as Table8 shown.Table 8
1436 TEU container ship parameters.
Ship parametersNumerical valueThe maximum deadweight of the ship (TEU)1436Service speed (knot)18.5Container handling speed (containers/hour)120Ship function coefficientk0.0137Port fees, etc. (USD)21000Parking charges (USD/d)2500Carbon emission factors3.021Pilotage time and stay in the port except for handling time (h)4Container handling charges (USD/TEU)150Heavy oil prices (USD/ton)500Carbon emission cost rate (USD/ton)30As seen from equation (3), the Qdis per nautical mile consumption of the ship can be expressed as follows:(16)Qdis=0.0137∗v1.8924∗dis.The simulation results are shown in Table9. (17)P=R−CV−Co−Cc.where P represents the voyage net profit; R donates the voyage revenue; CV is the voyage cost; Co reflects the operating cost; CCmeans the capital cost.Table 9
1436 TEU ship route simulation results.
Model results parametersNumerical valueVoyage profit (USD)936839Speed of the ship (knot)13Total shipments (TEU)4815Total sailing distance (nautical miles)11325Travel time (hours)871Total fuel consumption (ton)824Number of linked ports8Profitability (USD/hour)622This study assumes that the 1456 TEU container ship cooperates with 8000 TEU formulated as a group and the 1456 short line container considering the economical speed with reference to the cost efficiency. For example, we set the short line container speed as 13 kn. The chartering fee of a 1436 TEU container ship includes the following: daily capital cost is $8,700; annual operating cost is $1480,000, and average daily consumption of light crude oil is 2 tons (here we assume the consumption of the light crude oil is fixed while at berthing). According to inquire the price onChina Maritime Services Network in April 2019, the light crude oil price was $650 per ton. So we can calculate the voyage crude oil cost as $76,646. Moreover, we calculated the emission cost of 1456 TEU is $74,675. Based on the above, the profit from Shanghai-Hamburg is $108,191 excluding emission cost, and the final profit is $33,516 after carbon emission cost deduction. Therefore, the proposed scheme is feasible with respect to the positive profit result of an additional 1436 TEU container ship, which could be accepted by a shipping company.In addition, it is worth noting that the simulation result implies that the smaller container ship has enough ability to solve the short transportation demand between adjacent ports and convert extra berthing cost into profit compare to a larger size of a container ship. Considering the profitability in terms of the voyage, a regional or branch container ship only costs $622 per hour compared to $6,507 an hour for 8,000 TEU ships even after route optimization. To sum up, the integration of ocean containers and short line supplement containers will have a significant improvement in the profit of the international shipping route.


## 6. Conclusions

This study analyzes marine transportation profit maximization issues considering carbon emission costs based on the actual freight demand in the international shipping trade. A flexible route optimization method is proposed to improve the shipping profit and decrease the carbon emission costs based on scheduled voyage cycles. An actual case, including routes from Asia to Europe, is applied to validate the effectiveness of the proposed model considering sailing speed optimization and port skip strategies. Only considering the ocean ship, the results show that the flexible optimization model can increase the voyage profit by 3.7% and reduce the carbon emission cost by 33.47%. In the case of international shipping from Shanghai to Hamburg, the voyage distance has decreased by 10.8% and a 13.7% decline in sailing speed in this transportation. To compensate for the loss for the skipped port, a shortline container can be arranged to solve the demand of the one that is not calling.It is worth noting that the final voyage profit is increased by 4.05% and the carbon emission cost is reduced by 19.70%, which is better than that of the ocean container liner before optimization in the proposed whole system composed of two types of container ships. Finally, sensitivity analyses are performed to illustrate the impact of the different carbon emission cost rates on the voyage profit, revealing that the total profit would decrease/increase by 0.62% with a tiny increase/decrease by $5 per ton of carbon emission cost enrollment.However, the proposed method has some limitations including the timeliness of shortline containers and the external marine environment which need to be further discussed in the model. Therefore, the future research may focus on the following extensions: (1) integrated time windows to satisfy the on-time demand for each port; (2) consider the carbon emission regulations when vessel passing through ECA (Emission Control Areas); (3) adjust the port charge and port handling efficiency as dynamic parameters in the model; (4) conduct a multilevel analysis of internal factors (i.e., vessels mechanical conditions, manipulate response, etc.) and external factors (i.e., whether environmental or socioeconomic) to obtain the potential influence on voyage state with respect to the accordingly indirect emission control strategies, which have a significant impact on the final profit for shipping liner owners.



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*Source: 6678473-2021-02-10.xml*