1. Introduction
Transportation is the backbone of the world’s economy and has a close relationship with international trade [
1,
2,
3,
4,
5]. Given the substantial impacts of the COVID-19 pandemic on the transportation industry [
6], shipping still plays a crucial role in the global economy, transporting more than 80% of the world’s cargo [
7]. Due to the significance of maritime transportation, numerous academic studies have been conducted on management problems in this industry [
8,
9,
10,
11]. According to the investigation and prediction of United Nations Conference on Trade and Development (UNCTD) [
7], the maritime industry’s environmental impact cannot be overlooked, and there are plenty of studies focusing on the sustainability aspect of shipping transportation [
12,
13,
14]. The shipping industry can produce numerous sulfur dioxide emissions that pollute the air and water, leading to health problems for people residing near ports and coastal areas, and have significant negative impacts on the oceans and marine ecosystems [
15].
In response, the International Maritime Organization (IMO) has developed and implemented several regulations, particularly the regulation of emission control areas (ECAs). ECAs refer to sea areas in which stricter controls are used to minimize shipping emissions, such as sulfur oxides and nitrogen oxides. The sulfur ECA (SECA), as one ECA, focuses on limiting sulfur oxide emissions. Since 1 January 2015, ships have been subject to a more stringent upper limit of 0.1% for sulfur content within SECAs [
16]. Starting from 1 January 2020, another regulation involves limiting the sulfur content used on board outside the SECAs. It regulates that globally marine fuels with a sulfur content of more than 0.5% by mass cannot be adopted on board unless the exhaust gases are properly processed. These regulations regarding marine fuel sulfur content are compulsory unless technical measures with equivalent emission reduction effects are adopted.
As marine fuel prices vary significantly with sulfur content, regulations of the sulfur content limit considerably impact bunker costs, which make up over 60% of the total operating costs and 35% of the total freight rate of a shipping company [
7,
17,
18,
19,
20]. Therefore, shipping companies have been actively seeking countermeasures to control operating costs while obeying stringent regulations.
The first group of methods is operation-based, such as slow steaming [
21], fuel efficiency enhancements [
22], and shipping route optimization considering emission reduction regulations [
23]. While these operation-based methods have proven helpful in certain scenarios, their effectiveness in reducing emissions is limited. As more stringent regulations come into effect, excessive adjustments to operational plans for emission reduction purposes potentially impact service levels or freight revenue. For instance, reducing emissions through slow steaming may result in longer voyage times, leading to increased operating costs and potential delays.
In contrast, technique-based methods offer more comprehensive solutions. One option is to employ exhaust gas treatment methods prior to emission, which includes internal engine modifications and scrubbers. In recent years, emerging technologies have also been explored to reduce shipping emissions. For example, renewable energy sources, represented by wind and solar power, have been investigated as a promising solution to the emission problem [
24,
25]. Combined with battery systems [
26] and fuel cells [
27], these renewable energy sources can provide clean and stable power for ships. These technique-based methods hold great promise in significantly reducing shipping emissions while promoting sustainable and environmentally friendly practices in the maritime industry.
However, implementing these advanced technologies has been challenging due to several factors. One major obstacle is the lack of supporting infrastructure, which limits their operational range [
28]. Moreover, for existing vessels, significant modifications are required to adapt to these new technologies, resulting in high installation costs and a complex retrofitting process. These factors pose significant challenges to the widespread adoption of new technologies in the shipping industry.
Of all the emission control methods mentioned above, scrubbers are extensively applied due to their mature technology and relatively convenient installation [
29]. Scrubbers can help remove sulfur oxides and particulate matter from gases, allowing ships to use high-sulfur fuels while complying with sulfur emission regulations [
30]. Although the initial installation costs may be high, the ongoing maintenance costs of scrubber systems are generally lower than those associated with alternative compliance options. As scrubber technology continues to improve, more and more ship owners and operators will likely choose to install these systems to improve their environmental performance and maintain their competitiveness in the industry. These advantages make scrubbers [
29,
30] an attractive option for ship owners attending to reduce sulfur emissions without switching to more expensive cleaner fuels or investing intensively in new technologies [
31,
32,
33]. However, the existing literature has not considered the variable costs associated with the use of scrubber systems, nor has it considered the characteristics of different scrubber systems, including differences in variable costs and usage restrictions. Therefore, in this study, we originally proposed a nonlinear model to address these issues. Specifically, an optimization model was developed to formulate the problem. Then, numerical experiments based on data collected from existing studies and official reports were carried out to validate the proposed model and capture managerial insights. The main academic contribution of this study can be summarized as follows.
Firstly, the installation and utilization of fleet scrubbers in liner shipping were investigated, considering SECAs and fuel switching. Secondly, an integer nonlinear programming model was initially developed to formulate the problem. The characteristics of different types of scrubbers and the variable costs of using them were integrated into the proposed model. Considering SECAs and open-scrubber-prohibited areas (OSPA) simultaneously enables companies to make more informed decisions regarding compliance with these emission regulations. Additionally, various numerical experiments and sensitivity analyses were conducted to validate the effectiveness and robustness of the proposed model. Finally, some managerial insights gained from this study are provided to assist shipping companies in reducing costs, improving environmental performance, and maintaining competitiveness in the shipping industry.
The following sections begin by reviewing related works to underscore the academic contributions of this study. Subsequently, in
Section 3, a mathematical model is formulated to demonstrate the optimization problem investigated. Then, explanations regarding how to use the proposed model to enhance shipping efficiency while considering emission constraints are provided. Abundant numerical experiments and sensitivity analysis are demonstrated in
Section 4 to validate the effectiveness and robustness of the proposed model.
Section 5 gives the overall conclusion and directions for further research.
3. Problem Description and Model Formulation
This section includes background information on the proposed model, the definition of the shipping management problem, and the development of a scrubber-based scheduling method.
3.1. Background Information
The shipping company currently faces the challenge of operating one shipping route while complying with increasingly strict emission regulations, including the sulfur content limits of marine fuels used in and out of SECAs. Given the regulation, the shipping company decides to install scrubbers on the fleet deployed, which consists of a set of container ships, denoted by . All deployed ships sail at a predetermined speed, and the fuel consumption rates of ship while sailing and berthing are denoted by and . Currently, there are two types of scrubbers available: closed scrubbers and open scrubbers. For the same ship, closed scrubbers have a higher fixed installation and more variable costs than open scrubbers, namely , , and . In practice, open scrubbers emit liquid exhaust while operating, which can lead to ocean acidification and pose health problems for people residing near ports or coastal areas. Therefore, some ports set OSPAs to forbid the use of open scrubbers in the vicinity to control pollution. The main characteristics of open and closed scrubbers are summarized as follows.
Open scrubber, which involves using seawater to wash out sulfur dioxide from the exhaust gases. Disadvantages: it can cause seawater pollution, so some ports prohibit the use of open scrubbers while berthed or sailing near the port. Advantages: lower installation cost and lower variable cost during usage (pollutes seawater but not the atmosphere).
Closed scrubber, which involves reacting sodium bicarbonate with sulfur dioxide in the ship’s exhaust gases. Disadvantages: higher installation cost and higher variable cost during usage. Advantages: the solid by-products generated can be offloaded at the port without causing pollution; therefore, there is no restriction on the application area from competent authorities.
Combining the regulation of SECAs and OSPAs, the set of regulation scenarios along the shipping route
includes four situations: no emission regulation, being within a SECA, being within an OSPA, and being within both an OSPA and a SECA.
Figure 1 shows an example of a liner shipping route with three ports of call. The blue double line represents the SECA, and the orange circle represents the OSPA. Specifically, a SECA refers to specific coastal areas with a more stringent upper limit of 0.1% for marine fuel sulfur content. On the other hand, OSPAs are designated zones around ports where the use of open scrubbers is restricted. In the real world, there may be an overlap between these two areas.
To complete a closed loop along the route, a deployed container ship needs to sail nm and berth hours under regulation scenario . According to the regulation details, a set of marine fuels, denoted by , with different sulfur contents and fuel prices can be used while a ship is operated along part of the route. Considering the current sulfur content regulations on marine fuel used onboard, three types of fuels are included, which have the sulfur content of 0.1%, 0.5%, and 3.5%, respectively.
With the objective to minimize the total operational costs, the shipping company has to decide whether to install a scrubber on ship and which kind of scrubber to install, denoted by . Additionally, given the variable cost of using scrubbers and the price disparity between different fuel types, the shipping company also makes a scrubber usage plan, denoted by , and marine fuel choices, denoted by , under different emission regulation scenarios.
According to the regulations set by the IMO, the sulfur content in marine fuel should not exceed 0.5%. In SECAs, the sulfur content of the fuel used should not exceed 0.1%. However, when utilizing a scrubber, fuel with a sulfur content of 3.5% can be used and still not violate the sulfur content regulation. It is important to note that LSFOs with lower sulfur content generally come at a higher price. Based on this information,
Table 1 illustrates the permitted fuels for different scrubber installations in various areas. Additionally, considering that the scrubber installation cost is a one-time investment at the beginning of the scrubber usage, an upper bound of the total scrubber installation costs for the whole fleet is set, denoted by
.
3.2. Model Formulation
3.2.1. Notations Used to Formulate the Problem
Before the mathematical model,
Table 2 and
Table 3 display the notations that are used to construct the proposed model to solve the proposed scrubber management problem.
3.2.2. Formula for the Scrubber-Based Shipping Management Problem
The objective function is to minimize the operational cost, which is calculated as the sum of the fixed installation costs of scrubbers (considering the average costs over their lifespan), the variable costs associated with using scrubbers (such as sodium bicarbonate and additional fuel consumption), and bunker costs. For the convenience of expression, the planning period is set at
weeks. Then, the objective function can be expressed as:
The objective function needs to satisfy the following constraints. First, as shown in constraint (2), each ship in the fleet can be equipped with either a closed scrubber, an open scrubber, or no scrubber, and only one of them can be chosen.
Next, as shown in constraint (3), due to the one-time investment required for scrubber installation costs, the shipping company sets an upper limit of
on the total expenditure for scrubber installations to ensure smooth cash flow management.
Additionally, constraints (4) and (5) state that scrubbers can be used only when they are installed.
Finally, constraints (6) and (7) imply that for each ship j in scenario r, it is mandatory to utilize at least one type of fuel during sailing and berthing operations.
In the first scenario (r = 1), when the ships are out of the SECA and OSPA, the satisfaction of constraints (8)–(13) is required. Constraints (8) and (9) demonstrate that without installing a scrubber, fuel with a sulfur content exceeding 0.5% cannot be used. Constraints (10)–(13) show that by installing an open/closed scrubber but not using them, the sulfur content of the fuel must also be limited to 0.5% or less. However, when an open/closed scrubber is used, the choice of fuel becomes unrestricted.
In the second scenario (r = 2), when the ships are within a SECA and out of an OSPA, the satisfaction of constraints (14)–(25) is required. Constraints (14)–(17) stipulate that fuel containing more than 0.1% sulfur cannot be utilized when no scrubber is installed. Constraints (18)–(25), moreover, indicate that when an open/closed scrubber is installed but not utilized, the sulfur content of the fuel must also be restricted to 0.1% or lower. Nonetheless, the utilization of an open/closed scrubber allows for unrestricted fuel selection in this scenario.
In the third scenario (r = 3), compliance with constraints (26)–(31) is essential within the restricted area of open scrubber operation. Constraints (26)–(29) show that without a closed scrubber, fuel containing over 0.5% sulfur cannot be adopted. Constraints (30) and (31) indicate that when a closed scrubber is installed but not utilized, the sulfur content of the fuel must also be restricted to 0.5% or lower. However, when a closed scrubber is installed and actively utilized, there are no limitations on fuel selection.
In the fourth scenario (r = 4), when operating within the prohibited area for open scrubbers and the SECAs, it is necessary to satisfy constraints (32)–(43). Constraints (32)–(39) state that in the absence of an installed scrubber, only fuel with a sulfur content not exceeding 0.1% can be utilized. Constraints (40)–(43) indicate that when a closed scrubber is installed but not utilized, the sulfur content of the fuel must also be restricted to 0.1% or lower. However, when a closed scrubber is installed and actively utilized, there are no restrictions on fuel usage.
Constraint (44) represents a range of values for each variable, with all variables being binary and restricted to values of either 0 or 1.
The originally proposed model [M1] is an integer nonlinear programming model, which contains nonlinear constraints that can be linearized in a standard method. For detailed information about the linearization of [M1], please see
Appendix A.
5. Conclusions and Future Work
Sustainable development and emission problems have been listed among the top priorities of the maritime industry. To achieve the emission reduction targets, the IMO has discussed and promoted various regulations on ship operations. One of the most far-reaching policies is the restriction on the sulfur content of marine fuels, leading to a significant rise in bunker costs. Shipping companies have multiple approaches to control the total operating costs, including operational and technical methods. Scrubbers are an effective method that can purify exhaust gases before emitting them, obeying regulations without reducing service quality.
This study initially considers the OSPAs and operating costs of onboard scrubbers, and investigates the scrubber installation and utilization of a container ship fleet with emission regulations and marine fuel-switching operations. A mixed-integer nonlinear programming model was developed to describe the problem and identify the optimal installation and utilization plan of scrubbers that minimized the total operational costs. Numerical experiments were conducted to validate the originally proposed model.
A comparison between the results obtained under the scenarios including and excluding the adoption of scrubbers shows the effectiveness of scrubbers in cost reduction and the necessity of this study. Sensitive analyses regarding the sailing speed, SECAs, and OSPAs demonstrate that the proposed model significantly reduces total operational costs under multiple scenarios. It is also revealed that conducting the scrubber installation work over several years can obtain a better scrubber installation plan without incurring extra financial pressures.
Given the limitations of this study, there are two directions that future research regarding this topic can follow. First, take the time required to consider scrubber installation work. Second, the combination of various emission reduction technologies can be investigated, for example, sailing speed optimization and engine modification.