Assessing Container Terminals’ Environmental Efficiency: The Modified Slack-Based Measure Model

Abstract

The classic Slack-Based Measure (SBM) model has been posited to be a favorable non-parametric tool to cope with undesirable output. Nevertheless, this model has two significant drawbacks that should be addressed in practice. Thus, this paper aims to revise the classic SBM model to estimate container terminals’ environmental efficiency with undesirable output. The originality of this article includes: (1) introducing the energy consumption method to calculate the quantity of CO₂ emitted by container terminal operators (CTOs), (2) adopting cluster analysis to identify homogeneous CTOs acting as Decision-Making Units (DMUs), and (3) introducing the modified SBM model to measure and analyze environmental efficiency for CTOs. Based on this research, the efficiency of the analyzed terminals and the management of the local port sector are improved.

1. Introduction

It has been argued that container ports (CPs) are the backbone of international business thanks to the increasing growth of trade globalization. According to UNCTAD [1], over 80% of commercialized cargo worldwide is transported by sea, illustrating that CPs are essential to the national economy and intermodal transportation system, especially in coastal countries such as Vietnam. Moreover, strategic actions to boost CP efficiency and performance are debatable. Besides, it has been postulated that CP functions are operated via container terminal (CT) activities, such as the temporary storage of containers [2], maintenance and repair [3], consolidation and deconsolidation of cargo, etc. Therefore, an increase in CT efficiency is a feasible policy for the development of CP performance and efficiency.

Another critical point that we should note is that CT operations create economic benefits (desirable outputs) for port cities, while releasing a hefty volume of harmful pollutants (i.e., particulate matter, CO₂, and industrial waste), which are seen as undesirable outputs faced by port governments. Evidently, estimating CT efficiency on the basis of only economic variables, such as profits and container throughputs, does not ensure the ranking precision for CTs. This statement is relatively consistent with the viewpoint of Martínez-Moya et al. [4], who argued that ignoring undesirable outputs in the evaluation of CT efficiency may provide deceptive results, and thus does not encourage CTOs to apply new technologies to solve environmental problems at ports. Therefore, it is more reasonable if the efficiency assessment includes both desirable and undesirable outputs, as suggested by Diakomihalis et al. [5], and Hsu et al. [6].

It is argued that the Data Envelopment Analysis (DEA) approach has been widely utilized to assess efficiency for maritime transportation systems, such as waterways, ports, and land-side connections. In particular, the classic SBM proposed by Tone (2004) is judged to be an advantageous approach for calculating the efficiency of DMUs in the presence of undesirable outputs. Nonetheless, this approach has two significant limitations. First, the classic SBM is based on the premise that undesirable outputs are easily replaceable, meaning that they can be reduced without affecting desirable outputs. This is not possible in most of real-world cases. It has been posited that undesirable outputs are secondary products derived from manufacturing processes and formed concurrently with manufacturing desirable outputs. As a result, reducing them will undoubtedly reduce desirable outputs to a certain proportion. This situation is defined as weak disposability [7]. Second, the classic SBM tends to enhance the efficiency ratings of DMUs as more outputs, whether desirable or undesirable, are added to the assessment model. DMU efficiency should be decreased when an undesirable output is added. To summarize, the classic SBM should be modified to assure output disposability and lower efficiency when undesirable outputs are considered.

Furthermore, CT operations in the context of underdeveloped and developing countries only concentrate on generating as many desirable outputs as possible, while undesirable outputs, viz., CO₂ emissions, are often neglected. As a result, data on undesirable outputs, for instance, CO₂ emissions, are unavailable. It is argued that this is one of the significant challenges in assessing efficiency scores for CT operations. So far, some methods have been developed to estimate the amount of CO₂ emitted by CTs at port regions, such as Terminal Processes [8,9], the convex mathematical programming model [10], the over-simplified fuel and energy consumption-based approach [11], and bottom–up methodology [12]. However, the aforementioned approaches necessitate the precise calculation of the levels of CO₂ generated by devices and equipment at CTs, thus weakening their practical use, particularly in complicated and multipurpose terminals. Accordingly, developing a new method for measuring the amounts of CO₂ emitted by CT operations is needed.

In an attempt to fill the research gap, this article aims at gauging the impact of undesirable outputs on container terminal efficiency using a modified SBM model. Theoretically, the proposed model has four applications. First, it enables SAs to establish the biggest amount of undesirable outputs that CTs can release into the environment. Secondly, it ensures that a specific CT’s efficiency measure will decline in the presence of undesirable outputs. Thirdly, the new model still produces slacks for input items, just like the classic SBM. At last, the proposed model allows the identification of return-to-scale characteristics for CTs (i.e., increased or decreased return to scale), which is pragmatically helpful in planning strategic actions to develop CT efficiency. In this research, CTOs doing business at the Cai Mep–Thi Vai ports located in the Vung Tau province of Vietnam (the VT case) were empirically surveyed to verify the suggested research model.

The article unfolds as follows: Section 2 will review the relevant literature in terms of port and terminal efficiency. Section 3 will present the research methods. Section 4 discusses the empirical findings. The final section is the conclusion.

2. Literature Review

By referring to the scope of the study, this current article focuses on reviewing previous research deploying undesirable outputs in efficiency assessment. In truth, little research has been conducted on environmental efficiency in the port sector.

It is argued that Chin and Low [13] were the first scientists to use undesirable outputs (i.e., NOx, SO₂, CO₂, and particulate matter) to evaluate port efficiency by the SBM model, with the empirical case being container seaports in East Asia. It was found that efficiency measures are appreciably affected by environmental factors. Particularly, if only economic outputs are included in the evaluation model, Singapore ports performed the best while Manila ports (Philippines) were the worst. Nonetheless, the rankings of Singapore and Manila ports changed to sixth and fifth positions, respectively, once undesirable outputs were considered. Moreover, undesirable outputs reduced the optimum shipping capacity of seaports. Haralambides and Gujar [14] deployed CO₂ emissions as an undesirable output to evaluate the efficiency of dry ports located in the North Capital Region of India. It was illustrated that environmental effects are vital in analyzing the performance and efficiency of port systems. Nguyen et al. [15] also have the same opinion.

Lee et al. [16] evaluated the biological efficiency scores of 11 port cities in North East Asia and the U.S. using the conventional SBM approach when NOx, SO₂, and CO₂ emissions were treated as undesirable outputs. It was found that Singapore is a highly environmentally efficient port city, while the port cities of Jeddah and Tianjin are relatively less ecologically efficient. To become fully efficient, inefficient DMUs should reduce NOx, SO₂, and CO₂ emissions with an average of 743 tons, 435 tons, and 66,086,545 tons, respectively. Moreover, this research suggested a way to determine the social costs and the opportunity costs of treating air pollutant emissions in inefficient port cities. Using the traditional SBM approach, Na et al. [17] divided Chinese seaports into three main clusters: the Bohai Bay Rim, the Yangtze River Delta, the Pearl River Delta, and South East Coastal. In addition, the empirical findings revealed that the overall environmental efficiency of Chinese seaports is relatively low, implying room for improvement.

Sun et al. [18] assessed the performance of China’s ports under significant environmental concerns based on the Directional Distance Function. It was found that the performance of China’s ports is considerably influenced by the assets, the port’s geographical location, and berth quantity. Further, large-scale and small-scale port enterprises were argued to perform better than medium-sized ones. To improve port performance, some strategies were suggested in this study, such as stimulating the development of both the economy and industry, cooperating with other ports to reduce unnecessary competition, and improving port outputs through rational marketing. Thanks to the two-stage SBM-DEA model, Chen and Lam [19] estimated the efficiency scores of port–city interactions, with CO₂ being the undesirable output. This research also identified benchmarks for other port cities by referring to the best performing ones.

Tsao and Thanh [20] introduced a multi-objective mixed robust possibilistic flexible programming (MOMRPFP) approach to optimize the design of the container port–dry port network (DCPDPN). The empirical results showed that the proposed method reduced about 1.14% of the total operating costs of DCPDPN while improving the efficiency of the computational time for large-sized instances. Hsu and Huynh [21] also stated that multi-objective programming could effectively solve the DCPDPN problem when economic and environmental aspects were considered simultaneously; thus, it contributes valuable practical applications in port management.

Tovar and Wall [22] evaluated the environmental efficiency of 28 Spanish port authorities observed in 2016 using the Directional Distance Function with undesirable outputs (i.e., CO₂ emissions). The study found evidence of substantial inefficient behavior, with large differences across PAs. Additionally, suppose all PAs are environmentally efficient in providing their services. In that case, CO₂ emissions could be reduced by up to 63% of their actual observed levels and good outputs could be increased by roughly 56% of the existing levels. On top of that, some solutions were suggested to abate CO₂ emissions, including financial support for clean technologies, the supply of alternative fuels and on-shore power supply (OPS), and reductions in port dues for agents adopting environmentally friendly practices. Hsu et al. [23] also have similar recommendations.

Castellano et al. [24] examined the efficiency of seaport Environmental Management Systems (EMS) in Italy. The novel idea in this research was to use two multi-dimensional factors for efficiency evaluation, including Sustainability and Eco-friendly Practices (SEPs) as the input and National-level Environmental Scores (NESs) as the output. The findings highly recommended that policymakers assist PAs in achieving sustainable development goals (SDGs) by applying a system of rewards for efficient seaports and punishments for inefficient ones. Some prior studies also suggest similar methods, for instance, Nguyen, Ngo, Huynh, Quoc and Hoang [15] and Hsu and Huynh [21].

Kong and Liu [25] adopted the Directional Distance Function approach to measure the sustainable efficiency of nine port cities from the perspective of external influence and internal interaction. The results postulated that Hong Kong has the best sustainable efficiency while Xiamen has the worst. Seaports are also recommended to improve production efficiency while ensuring sustainable development by forecasting container demand and making long-term port expansion plans based on such a market. Taleb et al. [26] determined the environmental efficiency of 19 container ports in South Korea using the super SBM approach. The results showed that undesirable outputs (i.e., CO₂ emissions) should be reduced to improve seaport environmental efficiency. This finding is consistent with that of Hsu et al. [27]. Tovar and Wall [28] estimated the ecological efficiency of 37 seaports in Spain, considering the total costs of externalities as undesirable output. The empirical results argued that Spanish ports are highly environmentally inefficient. More particularly, over half of the assessed seaports were unproductive. Besides, efficient ports were ranked using a super-efficiency version of the model with external costs per capita. Thanks to that, seaports were identified, which appeared to be referenced for best practice.

Jo and Chang [29] measured the environmental efficiency of nine Korean ports during 2019–2021, employing the SBM-DEA model with the sub-sampling technique. The proposed model showed that the efficiency of nine Korean ports decreased slightly from 2019 to 2021, probably because of the impact of COVID-19, which lowered international trade and port throughput. Djordjević et al. [30] carried out an environmental efficiency assessment of Dublin Port using the two-stage non-radial DEA model. The empirical results demonstrated that ecological efficiency measures improved significantly without adversely affecting the throughput growth of the port. This was primarily due to enhancing cargo handling technologies and adopting environmental management standards, such as the Sustainable Energy Authority of Ireland (SEAI). In theory, the proposed research model is argued to be an appropriate optimization method to evaluate port efficiency considering the economic and environmental factors of ports.

To sum up, many prior studies have figured out port efficiency by adopting the SBM approach in the presence of undesirable outputs. Yet, their main limitation is considering undesirable outputs and desirable outputs independently, thus neglecting the weak disposability of the production systems. This is a research gap that will be addressed in the current article.

3. Research Methods

3.1. The Estimation of CO₂ Emission at CTs

As noted earlier, some approaches have been developed to calculate the amounts of CO₂ emitted by the production systems. Nonetheless, these methods require numerous devices and equipment to capture CO₂ released from vehicles. Accordingly, they are inapplicable, especially in developing and underdeveloped countries. To overcome this challenge, this paper developed a new method to calculate the amounts of CO₂ emitted by container terminals. To this end, CO₂ emissions are computed by the formula:

$$c_a=\frac{(\sum _{t=1}^T{M}_t\ast N_T)}{1000};t=\mathrm{1,2},...,T$$

(1)

where:

C_a represents the tonnes of CO₂ emission of the ath container terminal (a = 1, 2, …, A).

M_t is the quantity of the tth energy power type (t = 1, 2, …, T) used by the ith CT, for example, crude oil, gasoline, electricity, etc.

N_t is the air emission coefficient of the tth energy source (See

Table 1. The emission factor of CO₂ according to the type of fuel.

The Type of Fuel	Units	Emission Factor	Source
Electricity	kg CO2/Kwh	0.8458	Wang et al. [31], Heidari et al. [32], Dong et al. [33]
Gasoline	kg CO2/L	2.8102	Kang et al. [34], Lin and Du [35]
Crude oil	kg CO2/L	3.1398	Saidi and Hammami [36], Lin and Du [35]
Coke	kg CO2/kg	2.9081	Wang et al. [37], Saidi and Hammami [36]
Diesel	kg CO2/L	3.765	Ali et al. [38], Liu et al. [39]
Coal	kg CO2/kg	1.8915	Yu et al. [40], Liu, Fan, Wu and Wei [39], Dong, Sun, Hochman, Zeng, Li and Jiang [33]
Natural gas	kg/m3	2.2097	Xu et al. [41], Dong, Sun, Hochman, Zeng, Li and Jiang [33]

Note: Emission factor is the average value from the different sources.

).

As a typical example, this research shed light on how to apply Formula (1) to compute the level of CO₂ emissions for CTO.1, the full name of which is the Vietnam International Container Terminals Corporation (VICTC for short). According to official financial records provided by VICTC, the types of energy source used for terminal operations comprise diesel, electricity, and gasoline, with corresponding volumes of 3,124,098 L, 2,589,012 kWh, and 1,308,004 L, respectively. Using Formula (1), the amount of CO₂ discharged by this company can be computed as:

C_CTO.1 = (3,124,098 ∗ 3.765 + 2,589,012 ∗ 0.8458 + 1,308,004 ∗ 2.8102)/1000 = 17,628 (tons)

The CO₂ emissions of the remaining CTOs can be estimated in a similar way, and the results are shown in the seventh column of

Table 2. CTO inputs and outputs for the VT case.

DMUs	x1	x2	x3	x4	y	cu	${\mathit{c}}_{\mathit{u}}^{\mathit{*}}$	cu/y	${\mathit{c}}_{\mathit{u}}-{\mathit{c}}_{\mathit{u}}^{\mathit{*}}$
CTO.1	970	143,000	4	13	609,388	17,628	4322	0.0289	13,306
CTO.2	540	528,000	4	17	815,599	17,912	5784	0.0220	12,128
CTO.3	1650	1,155,000	22	66	6,443,851	45,697	45,697	0.0071	0
CTO.4	330	22,000	3	17	815,599	17,067	5784	0.0209	11,283
CTO.5	606	172,700	7	11	213,637	5212	1515	0.0244	3697
CTO.6	540	330,000	6	17	1,129,524	18,912	8010	0.0167	10,902
CTO.7	801	843,179	11	24	2,307,036	17,108	16,360	0.0074	748
CTO.8	898	95,905	2	10	300,134	12,982	2128	0.0433	10,854
CTO.9	746	109,824	8	30	631,916	18,801	4481	0.0298	14,320
CTO.10	270	110,000	3	7	28,993	1223	206	0.0422	1017
CTO.11	385	187,000	3	3	30,260	584	215	0.0193	369
CTO.12	594	440,000	9	22	348,406	12,903	2471	0.0370	10,432

(termed c).

3.2. The Modified SBM Model

Assume that we have the sample of n DMUs exploiting m input items to produce p₁ desirable outputs and p₂ undesirable outputs. For the jth DMU (j = 1, 2, …, n), its vectors of inputs, desirable outputs, and undesirable outputs are defined by x_j, y_j, and c_j.

The classic SBM model for the 0th DMU under the constant returns to scale (CRS) is expressed in Model (2) below:

$$\begin{gathered} \left[SBM\right]{\theta }_0^{\ast }\left(C\right)=min\frac{1-\frac{1}{I}\sum _{i=1}^I\frac{S_{i0}^{-}}{x_{i0}}}{1+\frac{1}{D+U}\left(\sum _{d=1}^D\frac{S_{d0}^{+}}{x_{d0}}+\sum _{u=1}^U\frac{S_{u0}^{-}}{c_{u0}}\right)} \\ {x}_{i0}=\sum _{j=1}^n{x}_{ij}\ast {\lambda }_j+S_{i0}^{-} \\ {y}_{d0}=\sum _{j=1}^n{y}_{dj}\ast {\lambda }_j-S_{d0}^{+} \\ {c}_{u0}=\sum _{j=1}^n{c}_{uj}\ast {\lambda }_j+S_{u0}^{-} \\ {S}_{i0}^{-},S_{d0}^{+},S_{u0}^{-}\ge 0 \\ i=\mathrm{1,2},...,I;j=\mathrm{1,2},...,n;d=\mathrm{1,2},...,D;u=\mathrm{1,2},...,U. \end{gathered}$$

(2)

where:

$S_{i0}^{-}:$ the slack coefficient of the ith input item for the 0th DMU;

$S_{u0}^{-}$: the slack coefficient of the uth undesirable output item for the 0th DMU;

$S_{d0}^{+}$: the slack coefficient of the dth desirable output item for the 0th DMU;

i: the index of input items (i = 1, 2,…, I);

I: the number of inputs;

U: the number of undesirable outputs;

u: the index of undesirable outputs, u = (1, 2,…, U);

D: the number of undesirable outputs;

d: the index of desirable outputs, d = (1, 2,…, D).

The subscript “0” represents a DMU, whose efficiency score is being calculated in the current model.

It is important to note that the desirable output (y_d) and the undesirable one (c_u) in Model (2) are totally independent because they are assumed to be strongly disposable, as already mentioned. Therefore, Model (2) should be revised to consider the dependency between the desirable and undesirable outputs. Moreover, the overall master plan for the development of Vietnam’s seaport system in the 2021–2030 period, with a vision toward 2050, plans to minimize dirty industrial pollutants (i.e., particulate matter, carbon monoxide, ozone, sulfur dioxide, etc.) at port regions [42]. Accordingly, it is safe to argue that the biggest volume of undesirable outputs that firms should generate can be determined by reference to a firm attaining the smallest ratio of undesirable outputs to the desirable ones. Thus, it is reasonable to assign $c_{uj}^{*}(j=\mathrm{1,2},...,n)$ as the biggest undesirable output, which a particular firm is allowed to generate during manufacturing:

$$c_{uj}^{*}=\omega \ast c_{uj}$$

(3)

where $\omega$ is a potential coefficient reflecting the smallest ratio of the undesirable outputs to the desirable ones for a specific firm. And $c_{uj}$ is the (true) quantity of its undesirable output. Remember that $c_u^{\ast }$ is the maximum volume of the undesirable output authorized to discharge; thus, it is also the slack for the undesirable output. As a result, the efficiency of the original DMUs (x, y_d, c_u) is determined based on the PPS of the optimal DMUs (x, y_d, $c_u^{\ast }$). Consequently, Model (2) is modified by:

$$\begin{gathered} \left[SBM\right]{\theta }_0^{*}\left(C\right)=min\frac{1-\frac{1}{I}\sum _{i=1}^I\frac{S_{i0}^{-}}{x_{i0}}}{1+\frac{1}{D+U}\left(\sum _{d=1}^D\frac{S_{d0}^{+}}{x_{d0}}+\sum _{u=1}^U\frac{S_{u0}^{-}}{c_{u0}}\right)} \\ {x}_{i0}=\sum _{j=1}^n{x}_{ij}\ast {\lambda }_j+S_{i0}^{-} \\ {y}_{d0}=\sum _{j=1}^n{y}_{dj}\ast {\lambda }_j-S_{d0}^{+} \\ {c}_{u0}=\sum _{j=1}^n{c}_{uj}^{*}\ast {\lambda }_j+S_{u0}^{-} \\ {S}_{i0}^{-},S_{d0}^{+},S_{u0}^{-}\ge 0 \\ i=\mathrm{1,2},...,I;j=\mathrm{1,2},...,n;d=\mathrm{1,2},...,D;u=\mathrm{1,2},...,U. \end{gathered}$$

(4)

Bear in mind that the efficiency score in Model (4) is estimated under the assumption of CRS. Yet, in the case of VRS efficiency, the constraint $\sum _{j=1}^n{\lambda }_j=1$ will be added in Model (4). This is expressed symbolically as follows:

$$\begin{gathered} \left[SBM\right]{\theta }_0^{*}\left(V\right)=min\frac{1-\frac{1}{I}\sum _{i=1}^I\frac{S_{i0}^{-}}{x_{i0}}}{1+\frac{1}{D+U}\left(\sum _{d=1}^D\frac{S_{d0}^{+}}{x_{d0}}+\sum _{u=1}^U\frac{S_{u0}^{-}}{c_{u0}}\right)} \\ {x}_{i0}=\sum _{j=1}^n{x}_{ij}\ast {\lambda }_j+S_{i0}^{-} \\ {y}_{d0}=\sum _{j=1}^n{y}_{dj}\ast {\lambda }_j-S_{d0}^{+} \\ {c}_{u0}=\sum _{j=1}^n{c}_{uj}^{*}\ast {\lambda }_j+S_{u0}^{-} \\ \sum _{j=1}^n{\lambda }_j=1 \\ {S}_{i0}^{-},S_{d0}^{+},S_{u0}^{-}\ge 0 \\ i=\mathrm{1,2},...,I;j=\mathrm{1,2},...,n;d=\mathrm{1,2},...,D;u=\mathrm{1,2},...,U. \end{gathered}$$

(5)

As a result, the scale efficiency for DMUs can be calculated by Formula (6):

$$\theta \ast \left(S\right)=\frac{\theta \ast \left(C\right)}{\theta \ast \left(V\right)}$$

(6)

In principle, $\theta \ast \left(S\right)=1$ illustrates optimal DMU operations. Conversely, $\theta \ast \left(S\right)<1$ reflects IRS or DRS for DMU operations. However, the classic SBM model cannot figure out whether DMUs are IRS or DRS. To fill this literature gap, the three-step approach developed by Färe et al. [43] is deployed to verify returns to scale for DMUs. The first step of this approach is to estimate $\theta \ast \left(C\right)$ and $\theta \ast \left(V\right)$ using Models (4) and (5), respectively. Once the efficiency value $\theta \ast \left(S\right)<1$, we need to go through the non-linear program below:

$$\begin{gathered} \left[SBM\right]{\theta }_0^{*}\left(I\right)=min\frac{1-\frac{1}{I}\sum _{i=1}^I\frac{S_{i0}^{-}}{x_{i0}}}{1+\frac{1}{D+U}\left(\sum _{d=1}^D\frac{S_{d0}^{+}}{x_{d0}}+\sum _{u=1}^U\frac{S_{u0}^{-}}{c_{u0}}\right)} \\ {x}_{i0}=\sum _{j=1}^n{x}_{ij}\ast {\lambda }_j+S_{i0}^{-} \\ {y}_{d0}=\sum _{j=1}^n{y}_{dj}\ast {\lambda }_j-S_{d0}^{+} \\ {c}_{u0}=\sum _{j=1}^n{c}_{uj}^{*}\ast {\lambda }_j+S_{u0}^{-} \\ \sum _{j=1}^n{\lambda }_j\le 1 \\ {S}_{i0}^{-},S_{d0}^{+},S_{u0}^{-}\ge 0 \\ i=\mathrm{1,2},...,I;j=\mathrm{1,2},...,n;d=\mathrm{1,2},...,D;u=\mathrm{1,2},...,U. \end{gathered}$$

(7)

It is instructed that if the values $\theta \ast \left(I\right)<1$ and $\theta \ast \left(V\right)=\theta \ast \left(I\right)$, then DMUs will follow the IRS characteristics. If the values $\theta \ast \left(I\right)<1$ and $\theta \ast \left(V\right)>\theta \ast \left(I\right)$, DMUs shall be DRS [43].

It should be noted that Models (2), (4), (5), and (7) are non-linear programs, thereby increasing the computational complexity of the optimization model and the computational time required to solve it, especially in the case of many DMUs involved. Thence, they will be transformed into linearized programs by the mathematical algorithms of Charnes and Cooper [44].

3.3. Selecting DMUs

The current article aims at assessing CT environmental efficiency using the modified SBM model with the VT case as an empirical study. As of 2022, there were 16 container terminal operators operating in the VT case, the location of which is shown in Figure 1. It is argued that homogeneity should be satisfied in the efficiency assessment by DEA to guarantee that the benchmarks are applicable for inefficient DMUs [45,46]. To select homogeneous DMUs for the DEA model, Hansen and Jaumard [47] recommended using cluster analysis via three key steps, as follows:

Step 1 is to elect possible criteria for the cluster analysis. Via site investigation and terminal executive interviews, the article determined 14 necessary criteria for selecting homogeneous DMUs, comprising business rivals, information management, workplace culture, regulations and guidelines, technical progress, incentive schemes, quality control, the taxation system, business hazards, objective customers, freight prices, the production process, delivery performance, and marketing policies.

Step 2 is to gather data for the criteria in Step 1 using the five-point Likert scale. From October to December 2022, we succeeded in surveying 37 terminal executives of 16 CTOs in the VT case. The individual survey data were then averaged for further cluster analysis.

Step 3 is to carry out cluster analysis to determine homogeneous DMUs. Thanks to Rstudio with package “factoextra,” the cluster analysis with the silhouette technique determined two optimal groups of clusters from 16 CTOs, as exhibited in Figure 2. More particularly, such 16 CTOs were classified into two homogeneous groups. Group 1 included 4 CTOs, while Group 2 comprised 12 CTOs (Figure 3). Ultimately, this article chose the 12 CTOs as DMUs for efficiency assessment, as shown in the first field of Table 2.

3.4. Identifying Factors for the DEA Model

It has been posited that the robustness of the efficiency rating primarily relies on the selection of factors for the DEA model [4,5]. Based on the operating features of container terminals and consultation with CTO executives, the current study used six requisite factors to satisfy that the total of DMUs was equal to or greater than the number of factors. As shown in the first row of Table 2, input items included the berth length (x₁, m), the container yard area (x₂, m²), the number of ship-to-shore (STS) gantry cranes (x₃), and the number of yard gantry cranes (x₄), while output factors included container throughput (y, TEU) and CO₂ emissions (c, tonne).

3.5. Collecting Data

After figuring out 12 DMUs from 16 CTOs, as well as their corresponding input and output factors, the present research gathered data on factors from the Vung Tau seaport authority. Collected data were double-checked from the Vietnam Maritime Administration’s annual report if necessary. Consequently, the official database for the proposed model is presented in Table 2. It is worth noting that the quantities of CO₂ emitted by CTOs were calculated, as shown in Section 3.1.

3.6. Isotonicity Check

It is argued that the data’s isotonicity is one of the critical assumptions in the envelopment model of DEA [48,49]. To this end, the study adopted the Pearson correlation coefficient to check isotonicity.

Table 3. Pearson correlation coefficient between inputs and outputs.

	x1	x2	x3	x4
y	0.824	0.867	0.913	0.928
c	0.832	0.716	0.793	0.925

clearly demonstrates a significant positive correlation between inputs and outputs at the level α = 0.01, implying that if inputs increase, the outputs shall step up accordingly. Stated differently, the isotonicity feature for the VT case was verified.

4. Results and Discussion

4.1. CRS Efficiency

To deploy the modified SBM model in measuring efficiency ratings for CTOs, the first step was to find out the maximum quantity of CO₂ (c*) that DMUs should be allowed to generate. From the sample of the VT case, it was posited that CTO.3 obtained the smallest ratio of undesirable output (i.e., CO₂) to the desirable one. Thence, the optimal quantity of CO₂ emissions (c*) for the remaining CTOs was computed based on such ratio. Employing Formula (3), the optimal volume of CO₂ authorized to discharge is shown in the third-to-last field of Table 2.

Moreover, Figure 4 presents a specific example of the proportionate relationship between undesirable and desirable outputs, with the diagonal line disclosing the optimal undesirable output for DMUs. Specifically, the undesirable output (i.e., CO₂ emissions) proportionately varied with the change in the desirable output (i.e., container throughput) throughout the diagonal line. In other words, this idea satisfied the weak disposability assumption for manufacturing [50,51]. In addition, the blue and red points in Figure 4 exhibited the actual level of CO₂ emissions and the optimal one corresponding to container throughput, respectively. As a result, the slack of the undesirable output (i.e., CO₂ emissions) for DMUs was the distance between the red and blue points. For instance, the slack of undesirable output for CTO.12 was equal to 10,432 (12,903−2471). In the meantime, CTO.3 achieved a minimal ratio of CO₂ emissions; thus, its slack was zero. To sum up, the slack of the CO₂ emission for CTOs is shown in the last column of Table 2.

Table 4. CRS efficiency and slack coefficients.

DMUs	$\mathit{\theta }\mathit{\ast }\left(\mathit{C}\right)$	Slack Coefficients
		x1	x2	x3	x4	y	c
CTO.1	0.346	723	126,562	2	0	0	13,306
CTO.2	0.346	331	381,812	1	9	0	12,128
CTO.3	1.000	0	0	0	0	0	0
CTO.4	0.752	0	0	0	0	0	11,283
CTO.5	0.114	551	134,408	6	9	0	3697
CTO.6	0.480	251	127,543	2	5	0	10,902
CTO.7	0.716	210	429,664	3	0	0	748
CTO.8	0.246	777	87,809	1	4	0	10,854
CTO.9	0.222	490	92,779	6	17	0	14,320
CTO.10	0.027	263	104,803	3	7	0	1017
CTO.11	0.035	377	181,576	3	3	0	369
CTO.12	0.104	505	377,551	8	18	0	10,432

presents CRS-efficiency scores for DMUs under the heading of $\theta \ast \left(C\right)$ estimated by Model 4. It is evident that the efficiency of DMUs is low, with an average score of 0.357. Moreover, just one DMU (i.e., CTO.3) was efficient overall.

4.2. Slack Analysis

As noted earlier, inefficient CTOs might become efficient overall by eliminating both inputs and undesirable outputs without decreasing desirable outputs. Under this circumstance, the slack coefficients in the SBM model are helpful in doing so. In theory, the optimal value for the inefficient DMU₀ might be figured out by Formula (8):

$$\begin{gathered} {\widehat{x}}_0=x_0-s_i^{-*} \\ {\widehat{c}}_{u0}=c_{u0}-s_u^{-*} \\ {\widehat{y}}_{d0}=y_{d0}+s_d^{+*} \end{gathered}$$

(8)

Taking CTO.12 as an example, from the slack coefficients shown in column 3~8 of Table 4, by virtue of Equation (8), its optimal value was computed and exhibited in

Table 5. Optimal values of factors for CTO.12.

	Slacks	Original Values	Optimal Values	% Change
x1	505	594	89	−85
x2	377,551	440,000	62,449	−86
x3	8	9	1	−87
x4	18	22	4	−84
y	0	348,406	348,406	0
c	10,432	12,903	2471	−81

.

4.3. Return-to-Scale Efficiency

Besides overall efficiency, the suggested modified SBM model allows to assess return-to-scale efficiency for DMUs, which is helpful in offering long-term investment measures. Thanks to Model (5), VRS efficiency for CTOs in the VT case was determined and displayed in the third field of

Table 6. Types of efficiency of DMUs for the VT case.

DMUs	$\mathit{\theta }\mathit{\ast }\mathbf{\left(}\mathit{C}\mathbf{\right)}$	$\mathit{\theta }\mathit{\ast }\mathbf{\left(}\mathit{V}\mathbf{\right)}$	$\mathit{\theta }\mathit{\ast }\mathbf{\left(}\mathit{S}\mathbf{\right)}$	RTS
CTO.1	0.346	0.491	0.705	Decrease
CTO.2	0.346	0.449	0.770	Decrease
CTO.3	1	1	1	Constant
CTO.4	0.752	0.752	1	Constant
CTO.5	0.114	0.355	0.320	Increase
CTO.6	0.480	0.659	0.729	Increase
CTO.7	0.716	0.979	0.732	Decrease
CTO.8	0.246	0.705	0.349	Increase
CTO.9	0.222	0.266	0.837	Decrease
CTO.10	0.027	0.706	0.038	Decrease
CTO.11	0.035	0.760	0.047	Decrease
CTO.12	0.104	0.220	0.475	Increase

. It is posited that the technical efficiency of DMUs is low, with an average score of 0.612. In particular, only CTO.3 was technically efficient, illustrating that this DMU optimized the mix of input items to maintain manufacturing targets. Conversely, 83% of DMUs in the sample were not technically efficient. Accordingly, the determination of IRS or DRS is of paramount importance for DMUs to improve their operation and become efficient.

The fourth column of Table 6 displays the scale efficiency for CTOs employing Formula (6). The results showed that CTO.3 and CTO.4 attained scale efficiency, meaning that their RTS characteristic was constant. This suggests that changing the combination of manufacturing input components is unnecessary because of their optimized operating performance. Meanwhile, the ten remaining DMUs did not obtain scale efficiency because of IRS or DRS.

4.4. Discussion

As exhibited in Table 4, CRS efficiency of DMUs was generally low. In other words, the immense majority of DMUs in the VT case were inefficient because of inefficiencies in using input factors to generate outputs. More precisely, these DMUs deployed too many input factors and produced excessive undesirable output (i.e., CO₂). According to the DEA theory, such inputs and undesirable output have to be alleviated so that DMUs become fully efficient. In addition, Hsu et al. [52] explained poor resource allocation as a reason of CRS inefficiency. Stated differently, input resources that are allocated to production activities that do not generate sufficient returns can result in suboptimal output levels.

Moreover, it is worth noting that the slack coefficients from the proposed model provide the seaport authority with three applications: the estimation of the social costs and opportunity costs to cope with CO₂ emissions. First, the social costs caused by an additional ton of CO₂ emissions was estimated at $21–$28 per tonnes of CO₂ in 2010 by a U.S. government working group [53]. Accordingly, CTO.12 has to annually invest $219,077 to $292,103 to cut down its excessive amount of CO₂. In other words, the seaport authority needs to pay $1,870,186–$2,493,582 to abate the amount of CO₂ for the VT case. Secondly, environmentally friendly policies designed to mitigate CO₂ will reduce the desirable outputs. And the financial losses related to the reduction in the desirable output are defined as the opportunity cost [3]. Moreover, Lee, Yeo and Thai [16] suggested an approach to evaluate the opportunity cost to eliminate the quantities of CO₂ at port regions, as follows: $(1-\theta \ast )\times revenue.$ Going back to CTO.12 as an example, according to the 2022 official announcement, its total revenue reached $13,734,783. Accordingly, CTO.12 shall bear the opportunity cost of $8,712,278 to transform from the traditional production process to green manufacturing.

Based on the guidance of Färe, Grosskopf and Lovell [43], the proposed research model determines whether DMUs are IRS or DRS so that they can change the investment scale to obtain the optimized operating performance. The final column of Table 6 points out that six out of twelve CTOs were characterized as DRS, implying that all production variables increased by a certain percentage would result in a less-than-proportional increase in output. Accordingly, the suggested managerial action for these DMUs is to decrease their production scale. In addition, four of twelve CTOs were IRS, meaning that the output increased in a greater proportion than the increase in input. Therefore, these four DMUs are recommended to operate at a larger scale to boost operating performance and scale efficiency.

5. Conclusions

5.1. Conclusions

The current paper aims to evaluate the environmental efficiency of CTs in the presence of undesirable outputs. In doing so, the modified SBM model is developed in this research work to measure the efficiency scores for CTOs in Vietnam. Although classic SBM is still widely used today, its significant shortcomings should be taken into account in practice. For that reason, the modified SBM model in this research not only contributes a methodological reference to the relevant literature but also provides practical application for terminal executives and SAs to enhance terminal efficiency and protect the natural environment. Theoretically, the suggested efficiency assessment method guarantees that DMU efficiency will drop when undesirable outputs are considered. Also, the undesirable outputs proportionately vary with the change in desirable outputs, satisfying the criteria of weak disposability for the manufacturing process. Practically, the modified SBM supports terminal executives in identifying RTS aspects of terminal operations, for instance, IRS, CRS, and DRS, for long-term development strategies. Furthermore, the modified SBM can aid SAs in developing legislative guidelines for producing undesirable outputs as well as punishments for firms generating excessively undesirable outputs.

5.2. Policy Recommendation

First, the availability of undesirable outputs is arguably a challenge for the adoption of the SBM model in figuring out CT efficiency. Thence, Formula (1) can assist SAs and terminal executives in determining the amounts of CO₂ generated by CTs. It is argued that this method can also be implemented in calculating air emissions for equipment and devices used at CTs, for instance, yard trucks, straddle carriers, and reach stackers. Secondly, with reference to Formula (3), SAs can set up the biggest undesirable output that a particular CT is allowed to generate during manufacturing. Based on this threshold, some reward and punishment system can be proposed to reduce air emissions at port areas. Next, thanks to slack variables, inefficient DMUs should scale their input factors down to improve efficiency scores. Lastly, RTS aspects of terminal operations (i.e., IRS, CRS, and DRS) can provide a sign for terminal managers in putting forward strategic actions to develop CTs.

5.3. Research Limitation

This article’s limitations are as follows. First, the research merely investigates CTs’ operations as a “black box,” neglecting the internal linkage of CTs. Accordingly, the impact of divisional-specific inefficiencies on CTs’ environmental efficiency might not be determined. It is highly recommended that future research should evaluate the efficiency of CTs with multi-stage operations. Secondly, the SBM model has three main applications in estimating DMUs’ efficiency rating, including input-orientation, output-orientation, and non-orientation. Yet, this research just deployed the non-orientation approach to assess environmental efficiency for CTOs. Thus, it is highly recommended that future studies use three SBM model applications for better policies.