A Comparative Analysis of Performance Efficiency for the Container Terminals in China and Korea

Abstract

In this study, the static and dynamic performance efficiencies of container terminals are analyzed and compared for the main container terminals in China and Korea. The static performance efficiency is calculated using the Super-SBM model based on slack variables at the micro-level. An analysis on the dynamic performance efficiency is conducted with the Malmquist index method. The factors of scale and technology of container terminals are mainly taken into account to explore the performance efficient improvement path of container ports. We obtained the following conclusions: (1) The container terminals in Korea show a similar performance efficiency level to the terminals in China, and their performance efficiency is an overall upward trend over the past five years. (2) The main reason for inefficiency in the container terminals in China and Korea is predominantly scale inefficiency. (3) Boosting the automation degree does not have a completely positive impact on the efficiency of the terminal. (4) In 2019–2023, the technical progress index of all container terminals in China and Korea showed a decreasing trend, leading to performance inefficiency of the container terminals.

1. Introduction

Container shipments have become the primary mode of global trade. As key facilities for transportation, container terminals are essential for social and economic development. The container terminal has been propelled towards greater automation and intelligence due to innovative technology. The competitiveness between different container terminals has become a symbol of port status, with more concentrated logistics turnover and traffic at the container terminals. The competitiveness of container terminals, therefore, is necessary to improve the development of shipping needs. The competitiveness improvement measures include fully utilizing resources, adjusting the scale, and designing the development path of terminals.

The ongoing expansion of the global economy and the growth of international trade have led to annual increases in container throughput at ports. In order to manage this increasing throughput and mitigate port congestion, higher container terminal operational efficiency at container terminals is vital [1]. Significant investment is required to balance the inputs and outputs. A strategic approach is needed to establish the resource allocation of such substantial investments.

In the past ten years, the water transportation economy in China has seen remarkable achievements [2]. The container ports in China, such as Shanghai Port, Ningbo Port, Guangzhou Port, Shenzhen Port and Tianjin Port, have been developed rapidly. A number of indicators, such as port cargo throughput, container throughput and the scale of infrastructure, have consistently ranked first globally.

As a developed country in East Asia, Korea hosts the Busan port, the fifth busiest container port globally and the largest transshipment hub in Northeast Asia. Currently, the Busan port has shipping connections with 500 major ports across 100 countries. With the implementation of the Korean “Super Smart Port” plan in 2023 and the openness of new routes to the Middle East and Southeast Asia, the Korean container shipping industry has seen consistent growth. In April 2024, the fully automated Terminal 7 project at the new port of Busan was officially opened. Under the general environment of global shipping development, there is always fierce competition among ports in Northeast Asia.

In terms of port conditions, geographic location, and even policy implications, the competition between Chinese and Korean ports is more realistic and intense [3]. Thus, an efficiency comparative analysis of the container terminals in China and Korea is conducted in this study, which is beneficial to the shipping trade between the two countries.

The container terminal efficiency is an important research topic in current port development. These studies are significant in prompting container terminals to embark on the rational resource allocation and efficient enhancements, further improving the terminal core competitiveness and regional economy. For instance, Li et al. [4] analyzed the efficiency of 25 container terminals of China in 2019 using a network DEA cross-efficiency model and demonstrated that the terminals’ production operations were efficient, but profit conversion and overall efficiency were quite low. Kim et al. [5] measured the efficiency of container terminals in Korea using the data envelopment analysis (DEA) method to provide a basis for the rationalization of national terminals. Mustafa et al. [6] compared the technical efficiency of container ports in Asia and the Middle East. Kutin et al. [7] analyzed the relative efficiency of 50 container ports and terminals in ASEAN; Yuen et al. [8] conducted a comparative analysis of ports in inland China, Hong Kong, and other Asian cities from a user’s point of view. Based on the perspective of port operating costs and energy consumption, Xu et al. [9] conducted a comparative analysis of different container terminal layouts. Paraskevas et al. [10] used a DEA-Tobit model to analyze the efficiency of the top 50 container terminals in the world during 2013–2017. Zheng et al. [11] used a DEA model to analyze the efficiency of container terminals in China and Korea, concluding that the efficiency level of Korean terminals was comparable to that of Chinese terminals. The technical efficiency of interconnected container terminals was assessed using stochastic frontier analysis (SFA) in [12], revealing that the most efficient terminal may not necessarily be the most productive one. The joined Efficiency of Tunisian Commercial Seaports was evaluated using the DEA approach in [13], proving that the decrease in efficiency is mainly due to the regression of technology.

However, research on the comparative efficiency of container terminals across countries or regions remains relatively scarce. Previous studies typically focus on either broader regional assessments or individual terminal analyses, lacking a comparative framework that integrates both static and dynamic efficiency measures. This study addresses this by utilizing the latest available data from 2019 to 2023, applying the Super-SBM model for static efficiency and the Malmquist-DEA model for dynamic efficiency. This approach not only captures the current state of terminal efficiencies but also tracks changes over time, providing a comprehensive view of how recent economic policies and operational strategies influence these crucial maritime hubs.

This research contributes novel insights to the field of maritime economics by offering a detailed comparative analysis of operational efficiencies, which is enhanced by the adoption of advanced efficiency modeling techniques. Furthermore, the findings offer actionable insights that can directly influence policy formulations and strategic planning in port management, ultimately aiming to enhance the economic impact and competitive edge of these critical trade hubs.

This paper consists of five sections. Section 2 presents a literature review. Section 3 describes the evaluation model, which allows for calculating the static and dynamic efficiency of container terminals. Section 4 provides a comparative analysis. Section 5 concludes this study.

2. Literature Review

As shown in

Table 1. Literature summary on terminal efficiency analysis.

Researcher	DMU (Quantity)	Input	Output	Model	Main Findings
Nong [15]	Vietnamese ports (22)	Funding Operating Costs Labor Port Area Quay Length Berth Depth	Sales Revenue Cargo throughput	DEA	Scale and management skills are the primary sources of efficiency; Vietnamese ports perform rather high management skills.
Wu et al. [16]	China Ports (11)	Labor Quay length Number of berths Total business assets	Standard container throughput PM emissions	DEA	The expected output of port cooperation would be reduced with the increase in PM emission standards.
Yen et al. [17]	World Smart Ports (20)	Port charges	Cargo throughput	DEA-Tobit	Pollution control from the environment has the largest positive impact on port efficiency.
Mustafa et al. [6]	Container ports in Asia and the Middle East (30)	Number of cranes Length of berths Number of berths Ventilation volume	Container throughput	DEA	The average efficiency in East Asia showed similar to that in South Asia and the Middle East.
Liu et al. [18]	Main container terminal in Guangzhou, Shenzhen and Hongkong in 2018–2019 (17)	Gross crane productivity Cranes intensity Berth depth Berth length	Container moves and Elapsed time	SBM-DEA and undesirable DEA	Yantian and Container Terminal 9 (South) in Shenzhen were the most efficient, followed by container terminals 6 and 7.
Wang et al. [19]	Vietnam Seaport Company (14)	Namely total assets Owner’s equity Liabilities Operating expense	Revenue Profit	DEA-Malmquist	Technology has been increasingly becoming a crucial factor in the competitiveness of seaport organizations.
Giacalone et al. [20]	Italian courts (54)	Judges employed Number of administrative Pending cases New cases filed	Cases Finished	Malmquist	The appliance of the DEA methodology and the Malmquist Index to assess judicial efficiency can produce useful results with important implications for the administration of justice.
Iyer et al. [21]	Container terminals in India (26)	Draft Quay length Yard area Quay cranes Yard equipment	Throughput	Malmquist	The relative efficiency of container terminals on the west coast of India has been found to be better than that of the east coast, with the scale of the terminal being the dominant factor influencing efficiency

, in previous studies, various methods have been employed to measure the port efficiency, including the stochastic frontier method (SFA) for parametric methods, the data envelopment analysis method (DEA model) for non-parametric methods, and the SBM model developed on the basis of the DEA model. The SFA, DEA, and SBM can analyze the static efficiency. By contrast, the DEA-Malmquist model can be used to conduct the dynamic efficiency analysis [14].

3. Methodology

3.1. Super-SBM Model

The SBM model is an expanded model based on the DEA model, which can accurately compute all slack variables [22]. The conventional radial DEA model allows whole input variables to scale down and output variables to scale up in the same proportion, but it is difficult for the department to achieve such an ideal state, as a problem of input redundancy or output deficiency is often inevitably generated. Thus, we need to introduce slack variables in an effort to coordinate this condition. The non-radial SBM model can address this problem, adequately reflecting the improvements in non-zero slack variables. Moreover, the traditional DEA model cannot explain the case that the efficiency of DMUs is 1 at the same time, meaning that it is not able to further rank the DMUs.

There is the super-efficiency DEA (Super-DEA) model proposed by [23], which can overcome the constraint that the measured efficiency cannot exceed 1 and has since evolved into the super-efficient SBM (Super-SBM) model. As a kind of Super-DEA model, the Super-SBM model combines the advantages of the Super-DEA model and SBM model. Consequently, a non-radial Super-SBM model was selected to calculate the efficiency of 25 container terminals in China and 6 terminals in Korea in 2023.

Suppose that the port system contains $n$ decision variables $DM{U}_k, \left(k=1, 2, \dots , n\right)$; each contains $m$ input index $x$, $s_1$ desirable output index $y$ and $s_2$ undesirable output index $y^{*}$. The corresponding matrices are, respectively, $\mathrm{X} =\left[x_1,x_2,x_3, \dots ,x_m\right], \mathrm{X}\in R^{m\times n}; Y=\left[y_1,y_2,y_{3 },\dots ,y_{s_1}\right],Y\in R^{s_1\times n};Y^{*}=\left[y_1^{*},y_2^{*},y_3^{*}\dots \dots y_{s_2}^{*}\right],Y^{*}\in R^{s_2\times n}$. We defined the production possibility set as:

$$\begin{array}{c}P\left(X,Y,Y^{*}\right)=\left\{(\left(X,Y,Y^{*}\right)|x_{ik} \ge X_{\omega },y_{rk}\le Y_{\omega },y_{lk}^{*}\ge Y_{\omega }^{*}\right\}\end{array}$$

(1)

In Formula (1), $R$ is the set of real numbers, $\mathsf{\omega }$ is the weight vector. When the sum of $\mathsf{\omega }$ is 1, it denotes constant return to scale (CRS); otherwise, it is a variable return to scale (VRS). $x_{ik}$, $y_{rk}$, $y_{lk}^{*}$, respectively, denote the $i\text{-}\mathrm{th}$ input variable, the $r\text{-}\mathrm{th}$ desirable output variable and the $l\text{-}\mathrm{th}$ undesirable output variable of the $k$ DMU. $X_{\omega }$, $Y_{\omega }$, $Y_{\omega }^{*}$ are the projection values of input, desirable output, and undesirable output on the production front. Considering that the variable return to scale of DMU is more practical, we cannot determine which stage the return to scale is in. As a result, the VRS hypothesis was chosen to assess the efficiency, and the basic SBM model is:

$$\begin{array}{c}\rho =min{\displaystyle \frac{1-\frac{1}{m}{{\displaystyle \sum }}_{i=1}^m\frac{S_i^{-}}{x_{i_0}}}{1+\frac{1}{s_1}\left({{\displaystyle \sum }}_{r=1}^{s_1}\frac{S_r^d}{y_{r_0}^d}\right)}}\end{array}$$

(2)

$$s.t.\left\{\begin{array}{c}{x}_0=X\lambda +S^{-}\\ y_0^d=Y^d\lambda -S^d\\ S^{-}\ge 0,S^d\ge 0, \lambda \ge 0, i=1,2,\dots \dots m; r=1,2,\dots \dots ,s_1\end{array}\right.$$

The objective function $\rho$ represents the efficiency of DMU, and $\lambda$ is the linear combination coefficient of DMU, $0 \le \rho \le 1$. After introducing the undesirable output, the SBM-DEA model is:

$$\begin{array}{c}\beta =min{\displaystyle \frac{1-\frac{1}{m}{{\displaystyle \sum }}_{i=1}^m\frac{S_i^{-}}{x_{i_0}}}{1+\frac{1}{s_1+s_2}\left({{\displaystyle \sum }}_{r=1}^{s_1}\frac{S_r^d}{y_{r_0}^d}+{{\displaystyle \sum }}_{l=1}^{s_2}\frac{S_l^{ud}}{y_{l_0}^{ud}}\right)}}\end{array}$$

(3)

$$s.t.\left\{\begin{array}{c}{\mathrm{x}}_0=X\lambda +{\mathrm{S}}^{-}\\ y_0^d=Y^d\lambda -S^d\\ y_0^{ud}=Y^{ud}\lambda +S^{ud}\\ {\mathrm{S}}^{-}\ge 0, {\mathrm{S}}^{\mathrm{d}}\ge 0, {\mathrm{S}}^{\mathrm{ud}}\ge 0, \lambda \ge 0, i=1,2,\dots \dots m;r=1,2,\dots \dots ,s_1;l=1,2,\dots \dots ,s_2\end{array}\right.$$

In Formula (3), $\beta$ is the efficiency data of a DMU, that is, port efficiency, $0 \le \beta \le 1$. $x_{io}$, $y_{r0}$, $y_{lo}$ denote the $i\text{-}\mathrm{th}$ input, r$\text{-}\mathrm{th}$ desirable output, and l$\text{-}\mathrm{th}$ undesirable output of a particular DMU. The vectors $S_i^{-}$, $S_r^d$, $S_l^{ud}$ represent the slack variables of the $i\text{-}\mathrm{th}$ input, $r\text{-}\mathrm{th}$ desirable output, and $l\text{-}\mathrm{th}$ undesirable output, respectively. $\omega$ is the weight vector. The vectors $S^d$ denote deficient desirable outputs; the vectors $S^{-}$ and $S^{ud}$ denote redundancy of inputs and undesirable outputs, respectively. When $S^{-}$ = $S^d$ = $S^{ud}$, DMU is efficient, that is $\beta =1$. If $\beta <1$, DMU is inefficient, which suggests that inputs and outputs need to be improved.

To further sort the efficient DMUs, the Super-SBM model needs to be employed. We supposed ${\mathrm{DMU}}_{\mathrm{k}}$($x_k$,$y_k^d$,$y_k^{ud}$) is efficient, so the Super-SBM model is formulated as follows:

$$\begin{array}{c}{\beta }_{SE}=min{\displaystyle \frac{1+\frac{1}{m}{{\displaystyle \sum }}_{i=1}^m\frac{S_i^{-}}{x_{i_k}}}{1-\frac{1}{s_1+s_2}\left({{\displaystyle \sum }}_{r=1}^{s_1}\frac{y_r^d}{y_{r_k}^d}+{{\displaystyle \sum }}_{l=1}^{s_2}\frac{y_l^{ud}}{y_{l_k}^{ud}}\right)}}\end{array}$$

(4)

$$s.t.\left\{\begin{array}{c}{x}_i^k\ge {\displaystyle {\displaystyle \sum }_{j=1,j\ne k}^n}{x}_{ij}{\lambda }_j-S_i^{-}\\ y_{rk}^d\le {\displaystyle {\displaystyle \sum }_{j=1,j\ne k}^n}{y}_{rj}^d+y_r^d\\ y_{lk}^{ud}\ge {\displaystyle {\displaystyle \sum }_{j=1,j\ne k}^n}{y}_{lj}^{ud}{\lambda }_j+y_l^{ud}\\ 1-{\displaystyle \frac{1}{s_1+s_2}}({\displaystyle {\displaystyle \sum }_{r=1}^{s_1}}{\displaystyle \frac{y^d}{y_{rk}^d}}+{\displaystyle {\displaystyle \sum }_{l=1}^{s_2}}{\displaystyle \frac{y_l^{ud}}{y_{lk}^{ud}}})>0\\ \lambda ,S^{-},S^{+}\ge 0\\ i=1,2,\dots \dots m;j=1,2,\dots ..,n\left(n\ne k\right);r=1,2,\dots ..,s_{1;}l=1,2,\dots \dots ,s_2\end{array}\right.$$

The efficiency value ${\beta }_{SE}$ of the Super-SBM model can be greater than 1, and the other variables have the same meaning as the above model.

3.2. Malmquist Index Model

In the DEA model, the efficiency value of DMU will change with the passage of time [24]. In order to estimate the dynamic efficiency of DMU across time, Caves, Christensen, and Diewert [25] applied the Malmquist index to measure the efficiency change in the production sector in 1982. The Malmquist index assumes that there are n DMUs, and each DMU obtains m outputs with s inputs in t period. $x_i^t={\left(x_{i1}^t,x_{i2}^t,\dots \dots ,x_{is}^t\right)}^T$ denotes the input index of the $i\text{-}$th DMU during the $t$ period, $y_i^t={\left(y_{i1}^t,y_{i2}^t,\dots \dots ,y_{im}^t\right)}^T$ denotes the output index of the $i\text{-}$th DMU in t period, and $x_i^t>0,y_i^t>0,t=1,2,\dots ..T$.

Assuming constant returns to scale, let the distance function of $\left(x^t,y^t\right)$ in $t$ period be $D_c^t\left(x^t,y^t\right)$, the distance function in $t+1$ period be $D_c^{t+1}\left(x^t,y^t\right)$, let the distance function of $\left(x^{t+1},y^{t+1}\right)$ in t period be $D_c^t\left(x^{t+1},y^{t+1}\right)$, and the distance function in $t+1$ period be $D_c^{t+1}\left(x^{t+1},y^{t+1}\right)$.

Under the technical conditions of period $t$, the change value of technical efficiency of the input and output index of DMU from period t to period $t+1$ is:

$$\begin{array}{c}{M}^t={\displaystyle \frac{D_c^t\left(x^{t+1},y^{t+1}\right)}{D_c^t\left(x^t,y^t\right)}}\end{array}$$

(5)

Under the technical conditions of period $t+1$, the change value of technical efficiency of the input and output index of DMU from period t to period $t+1$ is:

$$\begin{array}{c}{M}^{t+1}={\displaystyle \frac{D_c^{t+1}\left(x^{t+1},y^{t+1}\right)}{D_c^{t+1}\left(x^t,y^t\right)}}\end{array}$$

(6)

The productivity changes in each production index of DMU from period $t$ to period $t+1$ can be obtained by calculating the geometric average of the above two Malmquist indexes:

$$\begin{array}{c}M\left(x^t,y^t,x^{t+1},y^{t+1}\right)={\left(M^t\times M^{t+1}\right)}^{{\displaystyle \frac{1}{2}}}={\left[{\displaystyle \frac{D_c^t\left(x^{t+1},y^{t+1}\right)}{D_c^t\left(x^t,y^t\right)}}\times {\displaystyle \frac{D_c^{t+1}\left(x^{t+1},y^{t+1}\right)}{D_c^{t+1}\left(x^t,y^t\right)}}\right]}^{{\displaystyle \frac{1}{2}}}\end{array}$$

(7)

Malmquist index is used to measure the dynamic change index of input and output of DMU from period $t$ to period $t+1$, where $M$ is represented:

• If $M>1$, the Malmquist index shows an increasing trend from period $t$ to $t+1$, and the efficiency increases.
• If $M=1$, then the Malmquist index is constant from period $t$ to $t+1$, and the efficiency is constant.
• If $M<1$, then the Malmquist index decreases between period t and t + 1, and the efficiency decreases.

According to Fare et al. [14], the Malmquist index is divided into two parts. One is the change in technical efficiency, which is called the change index of technical efficiency and is represented by effch. The second is the movement of the efficiency front, which is called the Technological Progress Index and is represented by techch. The technical efficiency change index was decomposed into the pure technical efficiency change index and scale efficiency change index. The detailed decomposition of the index prompted Ray and Des li [26] to revise the Malmquist index:

$$M_{RD}\left(x^t,y^t,x^{t+1},y^{t+1}\right)={\displaystyle \frac{D_v^{t+1}\left(x^{t+1},y^{t+1}\right)}{D_v^t\left(x^t,y^t\right)}}\times {\left[{\displaystyle \frac{D_v^t\left(x^t,y^t\right)}{D_v^{t+1}\left(x^t,y^t\right)}}\times {\displaystyle \frac{D_v^t\left(x^{t+1},y^{t+1}\right)}{D_v^{t+1}\left(x^{t+1},y^{t+1}\right)}}\right]}^{{\displaystyle \frac{1}{2}}}\times {\left[{\displaystyle \frac{\frac{D_c^t\left(x^{t+1},y^{t+1}\right)}{D_v^t\left(x^{t+1},y^{t+1}\right)}}{\frac{D_c^t\left(x^t,y^t\right)}{D_v^t\left(x^t,y^t\right)}}}\times {\displaystyle \frac{\frac{D_c^{t+1}\left(x^{t+1},y^{t+1}\right)}{D_v^{t+1}\left(x^{t+1},y^{t+1}\right)}}{\frac{D_c^{t+1}\left(x^t,y^t\right)}{D_v^{t+1}\left(x^t,y^t\right)}}}\right]}^{{\displaystyle \frac{1}{2}}}$$

(8)

$M_{RD}$ denotes the modified RD model of Malmquist decomposition.

The technical efficiency change index (TEC) represents the catch-up degree of the research variable to the production front from $t$ period to $t+1$ period, that is, the change degree of technical efficiency of DMU during t to t + 1 period. When $TEC>1$, the technical efficiency increases; that is, the management and technology of the DMU are improved. When $TEC<1$, the technical efficiency decreases; that is, the management and technology of the DMU deteriorate. The Technology Progress Index (TC) represents the movement of the production front from t period to t + 1 period, that is, the degree of technological change in the DMU from t to t + 1 period. Similarly, when $TC>1$, the technology of DMU progresses; when $TC<1$, the technology of DMU declines. The symbols and abbreviations are explained as shown in

Table 2. Summary of the explanation of symbols and abbreviations.

Symbol	Explanation	Symbol	Explanation
$n$	Number of DMU	$\rho$	The efficiency of DMU of the basic SBM model
$m$	Number of input index	$\lambda$	The linear combination coefficient of DMU
$s_1$	Number of desirable output index	$\beta$	The efficiency data of DMU of the undesirable output-SBM model
$s_2$	Number of undesirable output index	$S^d$	The deficiency of desirable outputs
$x$	Input index	$S^{-}$	The redundancy of inputs
$y$	Desirable output index	$S^{ud}$	The redundancy of undesirable outputs
$y^{*}$	Undesirable output index	${\beta }_{SE}$	The efficiency value of the Super-SBM model
$X$	The matric of input index	$x_i^t$	$\mathrm{The} \mathrm{input} \mathrm{index} \mathrm{of} \mathrm{the} i\text{-}$$\mathrm{th} \mathrm{DMU} \mathrm{during} \mathrm{the} t$ period
$Y$	The matric of desirable output index	$y_i^t$	$\mathrm{The} \mathrm{output} \mathrm{index} \mathrm{of} \mathrm{the} i\text{-}$th DMU in t period
$Y^{*}$	The matric of undesirable output index	$D_c^t\left(x^t,y^t\right)$	$\mathrm{The} \mathrm{distance} \mathrm{function} \mathrm{of} \left(x^t,y^t\right)$ in t period
$R$	The set of real numbers	$D_c^{t+1}\left(x^t,y^t\right)$	$\mathrm{The} \mathrm{distance} \mathrm{function} \mathrm{of} \left(x^t,y^t\right)$$\mathrm{in} t+1$ period
$\omega$	The weight vector of variables	$D_c^t\left(x^{t+1},y^{t+1}\right)$	$\mathrm{The} \mathrm{distance} \mathrm{function} \mathrm{of} \left(x^{t+1},y^{t+1}\right)$ in t period
$x_{ik}$	$\mathrm{The} i\text{-}\mathrm{th}$$\mathrm{input} \mathrm{variable} \mathrm{of} \mathrm{the} k$ DMU	$D_c^{t+1}\left(x^{t+1},y^{t+1}\right)$	$\mathrm{The} \mathrm{distance} \mathrm{function} \mathrm{of} \left(x^{t+1},y^{t+1}\right)$$\mathrm{in} t+1$ period
$y_{rk}$	$\mathrm{The} r\text{-}\mathrm{th}$$\mathrm{desirable} \mathrm{output} \mathrm{variable} \mathrm{of} \mathrm{the} k$ DMU	$M^t$	$\mathrm{The} \mathrm{change} \mathrm{value} \mathrm{of} \mathrm{technical} \mathrm{efficiency} \mathrm{under} \mathrm{the} \mathrm{technical} \mathrm{conditions} \mathrm{of} \mathrm{period} t$
$y_{lk}^{*}$	$\mathrm{The} l\text{-}\mathrm{th}$$\mathrm{undesirable} \mathrm{output} \mathrm{variable} \mathrm{of} \mathrm{the} k$ DMU	$M^{t+1}$	$\mathrm{The} \mathrm{change} \mathrm{value} \mathrm{of} \mathrm{technical} \mathrm{efficiency} \mathrm{under} \mathrm{the} \mathrm{technical} \mathrm{conditions} \mathrm{of} \mathrm{period} t+1$
$X_{\omega }$	The projection values of input on the production front	$M_{RD}$	The modified RD model of Malmquist decomposition.
$Y_{\omega }$	The projection values of desirable output on the production front	TEC	Technical efficiency change index (The change degree of technical efficiency of DMU during t to t + 1 period.)
$Y_{\omega }^{*}$	The projection values of undesirable output on the production front	TC	Technology Progress Index (The degree of technological change in the DMU from t to t + 1 period)

.

4. Data and Analysis

4.1. Data

Considering the accuracy and timeliness of the data, 25 container terminals from 9 Chinese ports and 6 container terminals from Korean ports were selected, including Dalian, Rizhao, Tianjin, Shanghai, Ningbo, Xiamen, Guangzhou, Shenzhen, Guangxi, and Busan. The following factors are considered: (1) The decision-making units (DMUs) selected were all container terminals in coastal ports. (2) The terminals have been operated for five years at least and entered the stable operation stage. (3) The terminals have an average container throughput surpassing 3 million TEU during the last five years, which has a certain reference value. (4) The terminal’s container cargo operation is the main business of the company it belongs to. (5) Significant data can be obtained from the official website of the terminal company they belong to as well as the academic literature and port magazines. The number of DMUs finally selected is 31, as shown in

Table 3. Comparison of the number of research terminals.

Country (Quantity)	Port	Terminal	Subtotal
China (25)	Dalian	DCT	1
	Rizhao	RPCD	1
	Tianjin	TPCT, TOCT, TCT	3
	Shanghai	SECT, SGYCTB, SGZCTB, SMCT, SSICT, SGICT, SIPG	7
	Ningbo	MSICT, NBPORT, NBSCT, CMICT, NBCT	5
	Xiamen	IPC	1
	Guangzhou	GNICT, NICT, GOCT,	3
	Shenzhen	YICT, SCT, CCT	3
	Guangxi	BPCT	1
Korea (6)	Busan	PNIT, PNC, HJNC, HPNT, BNCT, BPT	6

, and the full names of the terminals are listed in Appendix A.

Through literature research, we noticed that most of the prior studies chose the number of berths and terminal length as input variables. Some scholars introduced net fixed assets and management costs as input indexes to embody the economic impact of indexes on DMUs. However, these variables only have a huge impact on the efficiency of terminals in small- and medium-sized coastal cities, where terminal operations are the main source of GDP growth, which would have limitations and weaken the accuracy of assessment results. Therefore, the variables that have the strongest correlation with the efficiency value of container terminals were selected [27]. These variables have different characteristics and functions, which are universally applied in container terminals of various types in coastal cities. The quay shoreline length, the yard area, the number of quay cranes, and the number of yard cranes are selected as input, and the container throughput is output. Throughput is a typical measurement of the efficiency of a port [28]. The quay shoreline length reflects the number of berthing ships and the quay cranes that can be carried by the front of the terminal. A long shoreline brings more docked ships and quay cranes, which can improve the loading and unloading quantity. The yard area can reflect the number of container cargo that can be accommodated in the storage area, further embodying the storage capacity of the terminal. The number of quay cranes and yard cranes can reflect the terminal turnover speed. Accordingly, the input index selected in this study can directly affect the terminal efficiency. The evaluation indexes are shown in

Table 4. Summary of input and output variables.

Input Variable	Output Variable
Terminal quay shoreline length	Container Throughput (TEU)
Yard Area
Number of Quay Cranes
Number of Yard Cranes

.

4.2. Analysis

4.2.1. Static Efficiency

The input variables have the most direct impact on the container efficiency. Minimizing the inputs, with controlling output variables, can improve the precision of assessment results. Moreover, the production management and operation technology in the terminal are significant to the efficiency values. In other words, the purely technical efficiency factors must be considered in the assessment model.

Based on actual states, we need to prohibit input and output variables from changing in the same proportion and direction. As a result, an input-oriented, non-radial, Super-SBM model was selected to calculate the static efficiency of 25 Chinese container terminals and 6 Korean terminals in 2023. Static efficiency refers to the ability of a port to maximize outputs from given inputs at a specific point in time, focusing on immediate operational effectiveness. We obtained the initial values under the variable return to scale (VRS) condition and analyzed the slack variable values for each terminal, as shown in

Table 5. Efficiency values of various research terminals in 2023.

City	Terminal	Efficiency
Dalian	DCT	0.7
Rizhao	RPCD	0.49
Tianjin	TPCT	0.34
	TOCT	0.44
	TCT	1.59
Shanghai	SECT	0.41
	SGYCTB	1.61
	SGZCTB	0.43
	SMCT	0.45
	SSICT	0.71
	SGICT	0.6
	SIPGSD	0.43
Ningbo	MSICT	1.26
	NBPORT	0.79
	NBSCT	0.35
	CMICT	0.26
	NBCT	0.45
Xiamen	IPC	0.21
Guangzhou	GNICT	0.46
	NICT	0.71
	GOCT	0.35
Shenzhen	YICT	1.3
	SCT	0.4
	CCT	0.41
Guangxi	BPCT	0.47
Busan	PNIT	1.01
	PNC	1.32
	HJNC	1.05
	HPNT	1.12
	BNCT	0.73
	BPT	0.75

. A summary of the input and output variables is provided in Appendix B.

Based on Table 4, the efficiency of different DMUs derived from the Super-SBM model has a large gap. In assessing efficiency values, values greater than 1 denote efficiency, whereas values between 0 and 1 indicate inefficiency [29]. The maximum value reaches 1.61 and the minimum value only 0.21, which obviously breaks the limit of the value being 1. Compared with the Super-DEA model, the selection problem about the dimensions of input and output variables was taken into account in the Super-SBM model, which can differentiate the inefficient DMU when the dimensions of input and output variables are not uniform [30]. We select the Super-SBM model due to its more obvious advantages and disadvantages between the values and then gauge the efficiency, compared with the Super-DEA model.

As shown in the results, in 2023, the efficiency values of Tianjin TCT terminal, Ningbo MSICT terminal, Shanghai SGYCTB terminal, and Shenzhen YICT terminal are 1.59, 1.26, 1.61, and 1.3, respectively. These four container terminals are at the forefront of efficiency. It shows that these four terminals achieved effective input and output scales in 2023, because their technology and management levels have been improved. The efficiency values of the other 21 terminals are in an entirely inefficient state, attributed to operation scale problems. Inefficient container terminals due to scale redundancy in China account for 67.7% of all research container terminals.

By contrast, Tianjin TPCT terminal, TOCT terminal, Ningbo NBPORT terminal, NBSCT terminal, CMICT terminal, Shanghai SIPGSD terminal, Guangzhou NICT terminal, Shenzhen YICT terminal, and CCT terminal have a high degree of automation. The efficiency of Tianjin TCT terminal and Shenzhen YICT terminal is 1.59 and 1.3, respectively, which are effective values, but the values of other terminals are inefficient. This may be affected by the limited working rate of terminal machinery. Moreover, the risk of damage to the handling machinery is inevitable, and it takes time to repair the equipment as well as the waiting time for goods to be turned around. As stated by Zhang [25], a good scheduling method can improve container handling efficiency with the limitations of existing equipment, thus reducing ship turn-around time. For this reason, not only the problems of scale and equipment need to be solved but, also, effective operation scheduling solutions should be explored.

It is worth noting that in the same port, the efficiency of Tianjin TCT terminal is 3 and 2 percentage points higher than the TPCT terminal and TOCT terminal, respectively. According to the survey, the automation degree of these three terminals has been enhanced rapidly in the last three years. Among them, the automation degree of berthing operation at the TPCT terminal is higher, and the traditional manual berthing operation is nearly replaced by the full-process mechanical operation controlled remotely by a computer system. The TOCT terminal has a high degree of automation in yard operation and a new breakthrough in yard crane automation technology. The TCT terminal has realized unmanned operation on the whole, but its degree of automation is lower than the TPCT terminal and TOCT terminal, resulting from a lower coverage rate of automation equipment. This explains that, although the terminal is at a low level of automation, its efficiency is actually higher. It once again confirms that in the development process of container terminals, promoting the automation step of terminals and reducing labor costs should be followed whilst not completely ignoring the advantages of manual operations.

Based on the efficiency ranking of various research terminals in 2023, Shanghai SGYCTB terminal ranked first. On the one hand, the terminal has achieved such achievements due to its gradually improved production management model and upgraded operation technology. On the other hand, the reason why the terminal has a large efficiency gap with other terminals may also originate from the problem of overloaded operations. The SGYCTB terminal handled 4.38 million TEU of cargo on only 860 m of dock shoreline and approximately 200,000 square meters of yard. It means that each meter of shoreline carries about 5000 TEU containers, and each square meter of yard stores about 22 TEU of cargo, which is quite a large treatment capacity compared to other terminals with the same container throughput. Consequently, the terminal controller needs to further improve the operation mode to speed up the cargo turnover, reducing the waiting time for berthing so as to improve the service level of the terminal. On the contrary, the efficiency of the IPC terminal in Xiamen has the minimum value, which may be due to the fact that the layout of IPC terminals is decentralized, unlike most terminal companies, leading to bias in data collection. For such a reason, the efficiency of IPC terminals in Xiamen needs to be further examined.

In 2023, the Busan port in Korea has four efficient terminals, which shows a good development trend. The output of the PNIT, PNC, HJNC, and HPNT terminals has increased effectively. Those four terminals are semi-automated terminals whose efficient results are due to the development of their automation technology. Particularly, the container throughput of the PNC terminal has been growing rapidly, which draws the conclusion that the PNC terminal can be expanded by increasing its investment appropriately in order to meet the market demand volume. Terminals where the inefficiency was analyzed were the BNCT terminal and BPT terminal. The BNCT terminal is the newest terminal developed by Busan Port, with a tremendous climbing space. BPT terminal belongs to the old port area, and its development priority has gradually shifted to new terminals, which explains the inefficient result. The scales of the two inefficient terminals are relatively redundant, but the amount of redundancy is in a reasonable range compared to the normal size of facilities and the amount of equipment. It is necessary for the two terminals to focus on increasing their outputs through improving the service level and management quality to gain more cargo for import and export.

The results of the slack values are presented in Figure 1 as a heat map, showing “Slack values” distributed across five concentric rings. Each ring represents a distinct operational metric from a port setting, arranged from the innermost to the outermost ring: ‘Berth Length’, ‘Yard Area’, ‘No. of QC’, ‘No. of TC’, and ‘Throughput’. The color intensity, ranging from dark blue through white to dark purple, indicates the magnitude of the values, with light colors denoting values close to zero. The slack-value-denoted output in Shenzhen YICT terminal is negative, while the slack-value-denoted inputs are all 0, showing that the terminal has a large output. The optimization of technology and the improvement of the service level in the terminal have brought about huge market competitiveness. As such, the scale of the terminal needs to be expanded appropriately, which would adapt to the growing demand for container throughput. Among inefficient terminals in China, Tianjin TPCT terminal, Tianjin TOCT terminal, Ningbo-Zhoushan NBSCT terminal, Ningbo CMICT terminal, Ningbo NBCT terminal, Shanghai SECT terminal, Shanghai SMCT terminal, Shanghai SGZCTB terminal, Shanghai SGICT (Yangshan III) terminal, Shanghai SIPGSD (Yangshan IV) terminal, Guangzhou GNICT terminal, Guangzhou GOCT terminal, Shenzhen Shekou SCT terminal, Shenzhen Chiwan CCT terminal, Rizhao RPCD terminal, and Guangxi BPCT terminal have a lower-than-average efficiency. The slack variables represent input and output, which are almost greater than 0, which suggests that there is redundancy in the scale of terminals. On the one hand, the terminals need to adjust the scale and improve the utilization rate of the terminal berth shoreline, yard, and handling equipment. On the other hand, the terminals should optimize the technology and service mode to improve market competitiveness. The slack values represented the output variables of Ningbo NBCT terminal, Shanghai SIPGSD terminal, and Shenzhen CCT terminal, with a value of 0, indicating that the output of these three terminals grows efficiently, and the ineffective scaling down of inputs leads to an inefficient result. The slack variables denoting the shoreline of Tianjin TOCT terminal, Ningbo-Zhoushan NBSCT terminal, and Shanghai SECT terminal are 0, showing that the inputs in the shoreline construction of these three terminals are effective, so that efficiency improvements need to be modified in other indicators.

However, the slack values denoting shoreline and the number of quay cranes in Xiamen IPC terminal are both the maximum values at the same index for all terminals. This suggests that there is a large amount of input redundancy of shore-side facilities in this terminal, which has become a major factor hindering improvements in the terminal’s efficiency. Apart from coordinating the shoreline scale and improving the utilization rate of facilities, the terminal needs to strive for more cargo sources through effective measures to speed up cargo handling and improve the competitiveness of the terminal.

Additionally, both slack values representing the shoreline length and the number of quay cranes for the Busan HPNT terminal are 0. It explains that there is no redundancy or deficiency in the shoreline facility inputs at this terminal, which is similar to the Tianjin TCT terminal, Ningbo MSICT terminal, and Shenzhen YICT terminal in China. Despite the tremendous difference in throughput with the MSICT terminal, the HPNT terminal shows a smaller gap in handling throughput in the shoreside area and even handles more per unit of quay cranes.

Table 6. Key productivity indicators of terminals.

City	Terminal	Quay Shoreline Throughput (TEU/m)	Yard Throughput (TEU/m2)	Unit Processing Number of QC (TEU/QC)	Unit Processing Number of TC (TEU/TC)
Tianjin	TCT	5959	14.22	685,285.42	265,271.77
Ningbo	MSICT	2498.58	22.49	188,892.62	62,135.73
Shenzhen	YICT	3528.92	6.24	161,437.78	54,019.57
Busan	HJNC	2536.78	4.01	232,538.42	66,439.55
	HPNT	2078.83	4.69	199,221.33	62,912
	PNC	2467.34	4.11	224,304.05	67,598.48

shows that the shoreline throughput of the MSICT terminal and HPNT terminal is 2499 TEU/m and 2079 TEU/m, respectively; the quay crane handling is 188,893 TEU/QC and 199,221 TEU/QC, respectively, values that are close to each other. But the container throughput of the two terminals is 9,444,631 TEU and 2,390,656 TEU, respectively, which are enormously different from each other. That would sufficiently embody the effective ratio of inputs and outputs in the HPNT terminal. The shoreline throughput and quay crane handling capacity in Tianjin TCT terminal are 5959 TEU/m and 685,285 TEU/QC, respectively, which are the maximum values in the same indicator, including all studied terminals, reflecting the worthy experience in the management model. The slack values representing the container throughput, yard area, and number of quay cranes at the PNC terminal are all negative, again confirming that the terminal’s output has increased massively. The PNC terminal needs to be adapted to the growth in throughput by swelling the inputs of quay cranes and yard cranes. It has to be mentioned that the efficiency value of PNC terminal is the largest in Busan Port, which is close to the YICT terminal in Shenzhen, China. Comparing the unit output between the two terminals shows that the PNC terminal has a higher throughput of quay cranes and yard cranes, while the YICT terminal has a higher output of shoreline and yard. This indicates that if the terminals in China and Korea are in a similar situation, the overall efficiency of Chinese terminals would be higher than that of Korean terminals. Particularly, Shenzhen YICT terminal is excellent in terms of facility inputs and operation management. Korean terminals have a larger handling capacity per unit of equipment than Chinese terminals, which may be attributed to the advancing technology. The throughput for each indicator of Busan HJNC terminal is at a high level in Busan ports, which is in similitude to Ningbo MSICT terminal. The efficiency of MSICT terminal and HJNC terminal is 1.26 and 1.05, respectively, with the former being higher than the latter. HJNC terminal has greater management than the MSICT terminal in shoreline throughput, quay crane handling, and yard crane handling. The slack values for each indicator of the BNCT terminal are all positive, but the input redundancy of the BNCT terminal is comparatively small, confirming that the inefficiency is mainly due to the lack of output.

4.2.2. Dynamic Efficiency

Based on previous related studies, the Malmquist index was adopted to conduct a dynamic analysis of the efficiency in research terminals during 2019–2023. Dynamic efficiency evaluates the rate at which a port improves its efficiency over time, accounting for technological advancements and operational improvements. A value greater than 1 indicates an improving efficiency trend, while a value less than 1 signifies a declining trend [31]. We used deap2.1 software to analyze the Malmquist index, and then the technical efficiency change index (effch), technical progress change index (techch), and total factor productivity change index (tfpch) of each terminal were obtained, as shown in

Table 7. Malmquist index analysis results of each research terminal during 2019–2023.

City	Terminal	effch	techch	tfpch
Dalian	DCT	0.935	0.932	0.871
Rizhao	RPCD	1.073	1.012	1.086
Tianjin	TPCT	1.09	1.012	1.103
	TOCT	1	1.005	1.005
	TCT	1	1.026	1.026
Shanghai	SECT	1.008	1.012	1.02
	SGYCTB	1.04	0.973	1.012
	SGZCTB	0.978	1.012	0.99
	SMCT	0.99	1.012	1.002
	SSICT	1.012	1	1.012
	SGICT	1.026	1.012	1.038
	SIPGSD	1.262	0.951	1.201
Ningbo	MSICT	1.253	0.945	1.184
	NBPORT	0.999	1.012	1.011
	NBSCT	0.988	1.007	0.995
	CMICT	0.981	1.012	0.993
	NBCT	1.121	0.975	1.093
Xiamen	IPC	1.003	1.015	1.017
Guangzhou	GNICT	0.992	1.012	1.004
	NICT	1.136	0.937	1.064
	GOCT	0.994	1.012	1.006
Shenzhen	YICT	1.006	1.012	1.018
	SCT	1.012	1.005	1.017
	CCT	1.147	0.946	1.084
Guangxi	BPCT	1.384	1.012	1.401
Average		1.052	0.994	1.046
Busan	PNIT	1.069	0.988	1.057
	PNC	1	0.973	0.973
	HJNC	1.019	0.982	1.001
	HPNT	1.019	1.006	1.025
	BNCT	1.060	0.983	1.042
	BPT	1.044	0.975	1.018
Average		1.035	0.984	1.019

.

From the results, during 2019–2023, the average values of the technical efficiency change index, technical progress change index, and total factor productivity change index in a Chinese terminal are 1.052, 0.994, and 1.046, respectively, showing the downward trend of the technical progress change index and the upward trend of the remaining indexes. In Table 4, we can observe that in the most recent five years, a drop in the technical progress index has become the main reason for the inefficiency of each terminal. The development of the terminal needs to be focused on technological innovation. However, in the last five years, the proportion of terminals with a descending technical efficiency change index reached 32% in China, which reflects the fact that the decline in total factor productivity was primarily influenced by a decline in technical efficiency. As a result, the production ratio of various elements has impacted factors, such as technology, management, and scale. Moreover, the average values of technical efficiency change, technical progress change, and total factor productivity change of Busan Port terminals in Korea during 2019–2023 are 1.035, 0.984, and 1.019, respectively, explaining that the inefficiency of the terminals in Busan is principally affected by the technical progress index decline over five years, which is similar to Chinese terminals.

In 2019–2023, the technical efficiency change index, technical progress change index, and total factor productivity change index of Tianjin TPCT terminal, Tianjin TOCT terminal, Tianjin TCT terminal, Shanghai SECT terminal, Shanghai SSICT terminal, Shanghai SGICT terminal, Shenzhen YICT terminal, Rizhao RZPCD terminal, and Xiamen IPC terminal are all greater than 1. This demonstrates that the development of these terminals over five years has shown an overall upward trend. The construction of Tianjin automation terminal promotes the technological innovation and production efficiency improvement of Tianjin TPCT terminal, Tianjin TOCT terminal, and Tianjin TCT terminal. With the completion of the main project of the North Port Area of Shanghai Yangshan Deep Water Port Area, the international competitiveness of Shanghai SSICT terminal and Shanghai SGICT terminal has been improved, increasing the technological development and output in the terminal. Shenzhen YICT terminal, with strong and continuous technological developments, is also a major automated container terminal in South China. With the promotion of national policies and effective management of enterprises, the information and intelligent technologies are effectively applied to the terminal work, which results in the enhancement of overall technical efficiency and production efficiency. Under the guidance of the party’s policy, Rizhao RZPCD terminal has shown prodigious development potential as the integrated operation of containers and the resource allocation adjustment have improved the technical efficiency, total factor productivity, and technical change rate of the RZPCD terminal over five years.

It is worth observing that the total factor productivity change value of Busan terminal nearly shows an upward trend, except PNC terminal in 2019–2023. PNC terminal can make further efforts to improve its technology. In addition, HPNT terminal shows an upward trend in technical efficiency change value, technical progress change value, and total factor productivity change value, which shows that this terminal has improved in output efficiency, technical quality, and scale management. This is similar to Tianjin TPCT terminal, Tianjin TOCT terminal, Tianjin TCT terminal, Shanghai SECT terminal, Shanghai SSICT terminal, Shanghai SGICT terminal, Shenzhen YICT terminal, and Rizhao RZPCD terminal in China.

The efficiency of Shanghai SIPGSD terminal, Shenzhen CCT terminal, and Guangxi BPCT terminal showed a steady upward trend during 2019–2023. The efficiency of these three terminals increased annually due to the effective total factor productivity and technical efficiency, which demonstrates that the production efficiency and technical utilization rate of the terminals were raised annually. However, the technical progress change index of the terminal was only effective in 2020–2021. Taking the latest year, 2023, for example, the change rates of technical progress of Shanghai SIPGSD terminal, Shenzhen CCT terminal, and Guangxi BPCT terminal are 0.98, 0.97, and 0.97, respectively, which reflects the fact that these terminals need to be further advanced in technological innovation. The ascending efficiency of Shanghai SIPGSD terminal reflects that the fourth phase of Shanghai Yangshan Deep Water Port project has achieved rapid development, showing continuous technological progress and resource optimization in this terminal. The rising efficiency of Shenzhen CCT terminal originates from the investment of advanced technologies and the cooperation between neighboring terminals. With the automation process of maritime and railway combined transport in Qinzhou Free Trade Zone, Guangxi BPCT terminal realizes an efficiency improvement, and the technical efficiency change index, technical progress change index, and total factor productivity change index of the terminal are 1.384, 1.012, and 1.401, respectively, which are the highest values of all terminals. This illustrates that in the last five years, BPCT terminal has grown in terms of technological progress, management development, resource utilization, and production efficiency, which has an overpowering development potential. DCT terminal in Dalian is the only one in which the changes of technical efficiency, technical progress, and total factor productivity have all shown a downward trend over five years. As a consequence, this port needs to be improved in management, technology, and scale adjustment, especially focusing on technology innovation and the service level after reversing the relatively backward situation of a hinterland economy in order to win more supplies.

5. Conclusions

In this study, the efficiency of container terminals in China and Korea was compared. A non-radial Super-SBM model was chosen to measure the efficiency of container terminals. The slack variables were introduced in the Super-SBM model, which can not only solve the problem of redundant inputs or deficient outputs but can also further rank all effective DMUs to give an exact result. Based on the assessment results, we can draw the conclusion that the terminals in Korea show a similar level to terminals in China. They have shown an overall upward trend in efficiency changes over five years. In order to improve the efficiency of terminals, it is necessary for policy makers to enhance the scale adjustment, management services, and technological innovations so as to realize highly efficient automated development in terminals [32].

The main conclusions are listed as follows:

The reason for the inefficiency of Chinese and Korean terminals is predominantly due to scale inefficiency. Specifically, the container terminals in China need to be ameliorated in management modes so as to improve the suitability between facilities and cargo. In Korea, the container terminals have a relatively small amount of scale redundancy, of which the efficiency can be raised by increasing output.

Although the automated operation of the terminal can improve the service level of cargo treatment, simplify the process, and reduce the labor cost, boosting the automation degree is not a completely positive impact on the efficiency of the terminal. In other words, the traditional manual work cannot be thoroughly replaced by intelligent and automated machinery.

Shanghai SGYCTB terminal has the problem of overloaded operation, which means the maximum efficiency of this terminal is not optimistic. This container terminal is in urgent need of improving the handling speed of cargo and, thereupon, accelerating the circulation of ships and cargoes through expanding the scale, optimizing the resource allocation, advancing technological innovation, and perfecting the management mode.

When the terminals in China and Korea are at the same level of development, the efficiency of Chinese terminals is higher than Korean terminals, especially the Shenzhen YICT terminal, which shows prominent performance. Nevertheless, the unit handling capacity of Korean terminals is larger than that of Chinese terminals. For example, the turnover efficiency of the HPNT terminal, HJNC terminal, and PNC terminal is higher. On the one hand, this outcome results from the gradual evolution of terminal technology in Korea. On the other hand, 60% of Korean ports are transshipment ports. The character of transfer service in Busan Terminal has reduced the waiting time for ships in port, which results in a higher turnover rate of the terminal. Further, 80% of ports in China are import and export ports. The terminals in China gain more outputs due to the operation mode of import and export, which elucidates high efficiency in Chinese terminals compared with Korean terminals.

In 2019–2023, the proportion of terminals with a falling technical efficiency change index in China reached 32%, explaining that the degeneration in the Malmquist index of terminals is primarily affected by the decline in the rate of technical efficiency change. Furthermore, the technical progress index of both terminals in China and Korea shows a decreasing trend in the last five years, reflecting that the decline in the technical progress index mainly impacts the inefficiency of terminals. For example, in 2022–2023, the proportion of inefficient terminals due to a technological recession in China reached 60%, implying that the terminals should be focused on technological advancements in the future.

In future research, we will expand methodological approaches by integrating parametric testing with the non-parametric Super-SBM model to enhance inferential robustness. Geographic expansion to additional Northeast Asian ports will deepen our understanding of regional efficiency trends. Further, integrating non-expected outputs will align with initiatives towards greener ports. Combining the Super-SBM with stochastic frontier methods could reduce noise from random and environmental factors, while employing dynamic network models may offer insights into the operational interdependencies within container terminals, highlighting the impact of both internal structures and external environments on efficiency.