Flexible Optimization of International Shipping Routes considering Carbon Emission Cost

Carbon emissions cost is a potential effective measure to restrict hydrocarbon pollution in the international shipping trade. (e 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 proposedmodels.(e 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.(e 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. (ese findings can provide reliable support for the shipping route decision process considering future carbon emission costs.


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. e 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]. erefore, 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. erefore, 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, demandbased 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 mixedinteger 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. e 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. ese 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. ere are few kinds of research on flexible route planning, such as skipping port combined with carbon emission cost aiming to increase shipping profit. erefore, 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.

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. e relationship between fuel consumption and speed can be expressed in the following equation: where Q is the daily fuel consumption of the ship (unit: per ton/day); k presents 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: According to equations (1) and (2), the vessel's fuel consumption per nautical mile per hour is Q dis and the expression formula is shown below: 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. e 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. e quantization of flexibility is also related to the speed reduction ratio.

Impact of Carbon Emission Costs on Liner Route
Optimization.
e 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.
e carbon emission cost model is shown as follows: where C represents the carbon emission cost (unit: USD); Q co 2 is the carbon emission (unit ton); D is 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, where Q o represent the fuel consumption (unit: tons). According to equation (3), the cost of carbon emissions can be summarized as follows: where dis ij is the distance between port i and port j (unit nautical mile); e 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.

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. (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.
e 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. e 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. Table 1 declares the variables for the model.

3.2.
Modeling. According to the above assumptions and conditions, the total profit objective function of the route can be represented as follows: where is the total freight revenue for removal of loading and unloading charges; refers to the cost of fuel, carbon emission cost, and port fees during transportation; is the penalty for port skip; and (2 * u ij * vol ij /vz) * fs/24 is the ship berthing cost in port.
e decision variables are constrained as shown in the following equation: e time constraints are shown in the following equation: e onward route capacity constraints are shown in the following equation: e return route capacity constraints are shown in the following equation: e capacity constraints can be presented in Figure 1. When the ship starts from port 1, the load can be recorded as vol 12 (Containers between 1 and 2 ports) and the sum of containers of vol 13 and vol 14 . When the ship arrives at port 2, unload the corresponding container vol 12 and load the container of vol 23 and vol 24 .
Route constraints are as follows: Port i and port j dis ij e distance from port i to port j (nautical mile) v e speed at which ships sail on the course (knot) u ij Whether there is a container transport between port i and port j X ij Whether there is an actual route between ports i and j k Ship functional coefficient T Port surcharge such as terminal charge fz Standard container handling charges (USD/TEU) θ Penalty coefficient for port skip, between 0 and 1 vol ij Container volume from port i to portj de ij Actual demand for container transport between port i to portj 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. erefore the segment of the journey and return is always composed of routes, thus ensuring the effectiveness of the routes.

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. is route involved eight ports as shown in Figure 2. ere 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. e distance among individual ports is shown in Table 2.
We regard port as the original set of n elements, while (port, port) as its derived set includes variables of shipping route segment and variables of cargo transport demand. e actual container liner parameters are shown in Table 3. e value range of the ship function coefficient k 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.

Analysis of Results.
e original section is Shanghai Port-Ningbo Port-Yantian Port-Singapore Port-Dubai Port-Antwerp Port-Rotterdam Port-Hamburg Port. e existence of the optimized segment is shown in Table 5.
As presented in Table 5, the optimized result is obtained by using LINGO 16.0. e optimized route is Shanghai Port-Ningbo Port-Yantian Port-Singapore Port-Antwerp Port-Rotterdam Port-Hamburg Port. e 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. e container transport optimization results are shown in Table 6. e comparisons of original and optimized routes results are shown in Table 7.
As presented in Table 7, the profit-making performance of the optimized route is significantly higher than that of the original route. e speed of the voyage decreased by 13.70%. e total freight volume decreased by 7.8%, and the total sailing distance decreased by 10.8%. e voyage profit increased by 3.70%. e voyage time was about equal to the original route time (only 7 hours). e total fuel consumption decreased by 33.48%. e 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.

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 rate D, as written in the following equation: where dis a 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: 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. e sensitive results of shipping profit with the changing rate of carbon emission cost are shown in Figure 3.
ough 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%.

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  Mathematical Problems in Engineering 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. e 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. e substitute container ship is designed to accomplish the loading/unloading tasks in Dubai port.
e 1436 TEU substitute ship information is as Table 8 shown.
As seen from equation (3), the Q dis per nautical mile consumption of the ship can be expressed as follows: e simulation results are shown in Table 9.
where P represents the voyage net profit; R donates the voyage revenue; C V is the voyage cost; Co reflects the operating cost; CCmeans the capital cost.
is 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. e 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 on China 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. erefore, 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.

Conclusions
is 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. erefore, 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.

Data Availability
e data used to support the findings of this study are included within the article. Disclosure e authors are solely responsible for all the views and analyses in this paper.

Conflicts of Interest
e authors declare no conflicts of interest in their research.