Integrating the Additive Seasonal Model and Super-SBM Model to Compute the Efficiency of Port Logistics Companies in Vietnam

Abstract

The growing trade process is pushing the importing and exporting ratio of products at ports in Vietnam. The total amount of goods is determined by analyzing the effectiveness of products that are delivered at ports. Thus, this research presents a whole performance picture of the port logistics operation process at two airports and six seaport logistics companies in Vietnam to describe exchanging products by utilizing additive trend methods to formulate the efficiency and rank them from previous periods to future terms. Based on the prediction analysis, the best accuracy result is calculated by the additive Holt Winters method when the mean absolute percentage error (MAPE) indicators remain at the standard level, and its average qualification is also the lowest. Combining the actual and prediction values, the ranking of all ports accordingly by year during the past, current, and future time periods from 2011–2022 is obtained after calculating the final efficiency via the super-SBM model. The empirical result of the current and estimated efficiency denotes that Da Nang port logistics is always selected as the best port logistics company and maintained the first ranking with consistently high scores on the basis of the performance qualification. The empirical analysis result proposes the status quo of port logistics companies in Vietnam from the past to future to describe the amount of exchanging goods.

1. Introduction

Growing international trade requires a larger amount of products to be delivered to places all over the world. Further, the affected globalization and competitive economics are a supported foundation [1], which leads to establishing and expanding logistics servers all over the world. Professional transportation ensures that a high-quality service is provided with the criteria of safety, cost reduction, and speed [2]. In the transportation process, the port logistics company is defined as a key element to smoothly implement and control transferring goods and information at the ports in question [3]. The main services of port logistics such as environmental technologies, processes and quality improvement, monitoring and upgrading, communication and cooperation, and active participation [4], are necessary to execute the successful delivery of goods. The activities of importing and exporting products are controlled by port information systems [5]. As shown in Figure 1, the operation process is managed by the port logistics company. When a shipping container is transferred from the supplier to the warehouse at the port, customs will begin to execute their procedures step-by-step. After receiving a container, the clearance process starts by establishing a profile and then checks the image of the container and materials. It is delivered to the customer if it has been cleared; it is held and sent back to the supplier if customs detects errors.

Vietnam is a developing country with a high speed of exchanging products; after joining the World Trade Organization (WTO), Vietnam was given new opportunities to take part in the global market [7].

Table 1. Vietnam’s Logistics Performance Index.

Year	LPI Rank	LPI Score	Customs	Infrastructure	International Shipments	Logistics Quality/Competence
2016	64	2.98	2.75	2.7	3.12	2.88
2014	48	3.15	2.81	3.11	3.22	3.09
2012	53	3	2.65	2.68	3.14	2.68
2010	53	2.96	2.68	2.56	3.04	2.89
2007	53	2.89	2.89	2.5	3	2.8

Source: The World Bank [8].

shows the past logistics status quo in Vietnam over the period of 2007–2016 [8]. The World Bank revealed Vietnam’s position among 160 countries by employing the logistics performance index (LPI); Vietnam ranked 53rd from 2007 to 2012 and increased to 48th in 2014, but decreased to 64th in 2016. The database of the international shipments showed a continuous increase from 3.00 to 3.22 during the 2007–2014 period; however, this figure decreased to 3.12 in 2016.

For that reason, with the purpose of evaluating the operation performance and ranking of port logistics companies from past to future terms, this research project proposes recognizing the efficiency of the exchanged process of products in Vietnam’s airport and seaport logistics companies by combining additive trend methods and the super-SBM model. The study applies additive trend methods for predicting the future time of airport and seaport logistics companies in Vietnam during the 2018–2022 term because Tableau integrates a prediction tool with time-series and formulating indicators such as gamma, beta, MAPE, and so on, in order to obtain accurate results. Then, for calculating their performance and determining their ranking, super-SBM in DEA helps to determine the probability of reaching the maximum efficiency [9] and ranking methodology for different performances [10]. Hence, super-SBM is utilized to escalate the efficiency of each year separately in order to seek out their position every year. The empirical analysis process provides full particular acknowledgment of airport and seaport logistics companies in Vietnam.

The paper is organised as follows: Section 1 introduces common transportation and the current status logistics in Vietnam, in addition to major characteristics of the additive trend method and super-SBM model; Section 2 is a literature review of port logistics and common background application of Tableau and its additive trend model and super-SBM model; Section 3 provides the research approach and the study’s methodology; Section 4 analyzes the empirical results; and Section 5 summarizes the empirical results and makes suggestions for future research.

2. Literature Review

Port Logistics is terminology used to point out an enterprise that specializes in checking and approving customs clearance procedures, as well as managing loading and unloading containers at importing and exporting points [11,12]. With the central activity roles of information transmission and the physical movement of products to support economic development [13], these enterprises have a crucial task of maintaining the quantity of commodity circulation. In recent years, delivering goods at the port of Vietnam has been exhibiting a higher trend with respect to economic development, even in the future, with a prediction of Danang port in Vietnam by the decomposition method based on long-term change in the time series data to give the status of the port operation in Danang port presenting an increased trend [14]. Besides, an assessment of the dry port in the Vinhphuc province of Vietnam by the multi-criterial decision-making analysis method [15] and an analysis of the Vietnamese port system [16] have also been conducted. Hence, there are many methods, such as the penal fixed affect model, stochastic frontier model [13], multi-criterial decision-making analysis method [15], and so on, which can be used for evaluating the performance and forecasting the status of port logistics, but this study applies the additive seasonal model in Tableau for predicting the future development of ports logistics in Vietnam and the super-SBM model for formulating and ranking port logistics companies.

Tableau is useful statistics analysis software for linear and branching time point-based temporal logics [17] in various application domains such as economics, science, and so on. For example, Tableau Workbench, with the function of “cut and paste”, gives various hooks for implementing blocking techniques using histories and variables, as well as hooks for defining optimization techniques [18]. Additionally, the temporalized belief logic provides the proposed labelled tableau calculus for the analysis, design, and verification of agent-based systems operating in dynamic environments [19], in addition to utilizing exponential smoothing to forecast the future when it is based on historical time series [20] and prediction data for the testing of quality metrics and smoothing coefficients. Conversely, additive trend methods use general exponential smoothing and the winters method for prediction [21]. The additive trend method in Tableau is an accurate prediction tool that measures full parameters, performance [20], and a large amount of data [22]. It comprises the additive trend and seasonality level, such as none, additive, and multiplicative, to quantify cumulative renormalization correction factors. The Holt-Winters method mentions double exponential smoothing, where the extension of exponential smoothing sets up trend and seasonal time series, and the forecasting business data obtains seasonality, changing trends and seasonal correlation [23]. As it has a high accuracy and is an inexpensive technique, exponential smoothing is an excellent forecast tool in a wide variety applications [24]. With regards to these characteristics, this study will use the additive trend method in Tableau to forecast the future values.

After obtaining all data for the past, current, and future scenarios, the super-SBM model is an analysis tool with a super-efficiency measure in DEA that can solve directly with slacks in inputs/outputs and compare values with the super-efficiency measures using the radial expansion or reduction of input/output directly. The rationality for the measure reduces the sort of weighted ${\iota }_1$ istance from an efficient DMU to production possibility [25]. The slack-based model denotes that the scalar measure deals directly with the input excesses and output shortfalls of the decision-making unit. In the traditional model, Charnes-Cooper-Rhodes (CCR) and Banker-Charnes-Cooper (BCC) also directly solve the input excesses and output shortfalls, but they do not have a scalar measure and do not take account of the existence of slacks. In addition, the score of an inefficiency unit is smaller than 1 [26]. With these characteristics, the super-SBM is applied in various researches. Estimating the super efficiency by the weights and the desirability of inputs and outputs determines the rank of each DMU [27]. Li demanded an improved super-SBM model for solving under a weak disposability assumption of undesirable outputs to conduct an energy efficiency analysis of Chinese industrial sectors [28]. Zhang and Zeng proposed the super-SBM model with undesirable outputs to measure the LCEE and dynamic low-carbon economy efficiency (ELCEE) of 30 provinces in mainland China from 2005 to 2012 [29]. Zhou and Zhu also used the super-SBM model with undesirable outputs for determining the efficiency of Chinese commercial banks [30]. Tessa and Liem defined the efficiency of the Indonesian manufacturing industry during the period of 2010–2014 when utilizing the none-parametric oriented super-SBM model [31]. These empirical analysis results suggest that the super-SBM model is the best measuring model for a comparison of the efficiency and ranking of each DMU because the DEA model can conduct the efficiency comparison. For most DEA models, the highest score is 1. But, too many DMUs will have a score of 1. For the same score, DEA models can distinguish which one is better, but the distinguish rate is not good. However, Super SBM can overcome this issue without a limitation for the highest score. So, the research can really distinguish the performances. No DMU will have the same score and the study can really distinguish the ranks.

Based on the theory of additive seasonal models and the super-SBM model, the study integrates two models to predict and then count the efficiency of port logistics in Vietnam. The rank of each port during the period of 2011–2022 is determined by the performance results of the rationality of inputs/outputs after analysis is completed by the super-SBM model.

3. Methodology

3.1. Proposal Research Framework

Figure 2 shows the four basic steps in forecasting and estimating the efficiency of airport and seaport logistics companies in Vietnam:

• Stage 1: Determine the theme and collect data on the input and output variables. The input and output factors must be reselected in another theme when they are unsuitable. The data of port logistics companies in Vietnam are posted on Vietstock [32]; the researcher chose two airport and six seaport logistics companies. Next, introduce the status of transportation in Vietnam and provide an overview of the additive trend methods and super-SBM model.
• Stage 2: When obtaining historical data, the additive trend method in Tableau is employed to analyze and compute the forecasting values. The additive trend method distinguishes three methods, i.e., Holt’s linear method, the additive Holt–Winters method, and the multiplicative Holt–Winters method, which are selected to predict future times for airport and seaport logistics companies in Vietnam. Their mean absolute percentage error (MAPE) indicators measure the accuracy level of the estimated data and propound the best result. The appreciate values are used for the next step in measuring efficiency. If no method is suitable, the input and output must be reelected.
• Stage 3: DEA is a type of statistics analysis is always “isotonic,” so the Pearson correlation must be tested before utilizing any model to formulate the performance. The Pearson correlation is suitable between −1 and +1, and the factors must be re-selected to exclude values from −1 to +1. The pertinent data are applied to calculating the efficiency of two airport and six seaport logistics companies in Vietnam by the super-SBM model in DEA. The performance index proposes the ranking of port logistics companies over each term.
• Stage 4: Comment on the empirical data, analyze the data via selecting the best estimated method, and present the performance and ranking of the airport and seaport logistics companies in Vietnam at the previous, current, and future time points.

3.2. Data Collection

The term “logistics” indicates the general transportation process, including all aspects of products, machines, and people, that the research will demand to transfer the goods at the ports in Vietnam. The study collects the input and output data of two airports and six seaports logistics companies in Vietnam from 2011 to 2017 that are listed on Vietstock [32]; the names of two airport and six seaport logistics companies are given in

Table 2. Names of airport and seaport logistics companies in Vietnam.

No	Code	Name	Type of Port
1	CDN	Danang Port Joint Stock Company	air
2	CLL	Cat Lai Port Joint Stock Company	sea
3	CMP	Chanmay Port Joint Stock Company	sea
4	DNL	Dang Nang Port Logistics JSC	sea
5	NCT	Noi Bai Cargo Terminal Service Joint Stock Company	air
6	PDN	Dongnai Port Joint Stock Company	sea
7	PHP	Port of Hai Phong Joint Stock Company	sea
8	QNN	Quangninh Port Joint Stock Company	sea

Source: Viet.stock [32].

.

Input and output variables describe the detail of circumstance in any sector; the investment sources include human resources, raw materials, information, technologies, and so on, and are identified as the inputs. After the performing process, investors will obtain their products under the classification “output”. Forecasting the future of enterprises and then evaluating a common efficiency based on their financial index is posted on Vietstock [32]. Thus, the research also chooses appreciative factors in economics to predict and define the ability operation of port logistics companies in Vietnam as follows:

(a)

Total assets (input): Totalizing the tangible and intangible assets of an enterprise.

(b)

Owner’s equity (input): Totalizing the tangible and intangible assets minus liabilities.

(c)

Net revenue (output): Income of an enterprise when they perform their business.

(d)

Gross profit (output): Profit valuation appraises a company’s efficiency.

These factors are key in finance to help illustrate a business; their values are used to help expose the efficient economics in previous time periods and also to predict future situations.

3.3. Additive Trend Method

Exponential smoothing is a forecasting future value tool which is based on the regular time series. Tableau is an analysist software that applies exponential smoothing to prediction values by selecting good optimal smoothing parameters when it gives an aggregative prediction by calculating from a closed form equation. Simple exponential smoothing measures forecast values from the weighted average of the last actual value and the last level. Besides, the visualization provides components such as trend and seasonality to compute an effective prediction values.

Setting up DMU₀ like the units of port logistics companies in Vietnam is conducted by using the primal time series (P_t, P_t+1, ..., P_t+n “t = 0, 1, 2, …”) and then estimating the forecasting values (F_t, F_t+1, F_t+2, …, F_t+n “t = 0, 1, 2, ...”). The sequence of observation for both primal time series and prediction values at the first period, t, also starts at a time point equaling 0, and the original mathematical procedure of exponential smoothing is formulated by the specific formula as follows:

$$\begin{array}{c}{F}_0=P_0\\ F_t=\alpha \times P_t+\left(1-\alpha \right)\times F_{t-1}\\ 0\le \alpha \le 1\end{array}$$

(1)

Holt (1957) [33] established standard exponential smoothing methods. From these methods, this study selects some formulae to apply to inferring the future of port logistics companies in Vietnam through three cases. The additive trend is used for all three instances and is combined with the seasonality; alternatively, no seasonality, additive seasonality, and multiplicative seasonality are applied. Single exponential smoothing is a simple model that is utilized to forecast a short time range in the future without a trend. Thus, Holt (1957) extended single exponential smoothing with a trend to predict the data of time series.

3.3.1. Holt’s Linear Method

(A, N) has one level and one trend, so Holt’s linear method is given as below:

$$\begin{array}{c}{F}_t=\alpha P_t+\left(1-\alpha \right)\left(F_t+A_{t-1}\right)\\ A_t=\beta \left(F_t-F_{t-1}\right)+\left(1-\beta \right)A_{t-1}\\ \widehat{P_t}\left(n\right)=F_t+n{A}_t\end{array}$$

(2)

The parameter β changes slowly in each term.

Holt-Winters was proposed by combining the work of Holt (1957) [33] and Winters (1960) [34] to catch up with seasonality. The Holt-Winters seasonality method not only captures the forecast equation, but also three smoothing equations such as the level, trend, and seasonal component, with parameters α, β, and γ. Two variations are displayed with the variations in the nature of the seasonal component, the seasonal variations in the additive method are constant through the series, and the seasonal component appears in all terms in the scale of the observed series. Additionally, the subtracting the seasonal component adjusts the series in the level equation. In contrast, in the multiplicative method, the seasonal variations are changed proportional to the level of the series, and the relative terms and the series in the seasonal component are adjusted by distinguishing them by the seasonal component. As a result, the seasonal component in the additive method is approximately zero and the seasonal component in the multiplicative method is up to approximately n.

3.3.2. Additive Holt-Winters Method

Overviewing the forecasting of the time series is denoted as follows:

$$\begin{array}{c}{F}_t=\alpha (P_t-I_{t-q})+\left(1-\alpha \right)\left(F_{t-1}+A_{t-1}\right)\\ A_t=\beta \left(F_t-F_{t-1}\right)+\left(1-\beta \right)A_{t-1}\\ I_t=\gamma \left(P_t-F_{t-1}-A_{t-1}\right)+\left(1-\gamma \right)I_{t-1}\end{array}$$

(3)

The seasonal component is given by:

$$I_t=\delta \left(P_t-F_t\right)+\left(1-\delta \right)I_{t-q}$$

(4)

The smoothing equation for the level of the component is expressed as:

$$\begin{array}{c}{I}_t=\delta \left(1-\alpha \right)\left(P_t-F_t-A_{t-1}\right)+\left(1-\delta \right)I_{t-q}\\ \widehat{P_t}\left(n\right)=F_t+n{A}_t+I_{t-q+n}\end{array}$$

(5)

3.3.3. Multiplicative Holt-Winters Method

The multiplicative Holt-Winters method is calculated as below:

$$\begin{array}{c}{F}_t=\alpha \left(\frac{P_t}{I_{t-q}}\right)+\left(1-\alpha \right)\left(F_{t-1}+A_{t-1}\right)\\ A_t=\beta \left(F_t-F_{t-1}\right)+\left(1-\beta \right)A_{t-1}\\ I_t=\gamma \left(\frac{P_t}{F_{t-1}+A_{t-1}}\right)+\left(1-\gamma \right)I_{t-q}\\ \widehat{P_t}\left(n\right)=F_t+n{A}_t+I_{t-q+n}\end{array}$$

(6)

Table 3. Notation for additive trend method.

Signal	Remark
α	Smoothing coefficients for the level of series $\left(0\le \alpha \le 1\right)$
β	Smoothing coefficients for discount factors $\left(0\le \beta \le 1\right)$
δ	Smoothing parameter for seasonal indication $\left(0\le \delta \le 1\right)$
$\gamma$	Smoothing coefficients for the trend $\left(0\le \gamma \le 1\right)$
Pt	The consequence of actual value in the historical period time t
Ft	The consequence of computing the prediction value at the time t
At	Smoothed additive trend at the end of period t
It	Smoothed seasonal index at the end of period t
n	Number of periods in the prediction lead time
q	Number of periods in the seasonal cycle
t	The length of time
$\widehat{P_t}$	Forecast value with n period from the original time t

expresses all notations for the additive trend method which are used in Section 3.3.

Forecasting values are calculated by the additive trend and three seasonal values in the exponential smoothing, and they must be tested accurately by the MAPE indicator, which is escalated as below:

$$\mathrm{MAPE}=\frac{100}{n}{\displaystyle \sum }_{t=1}^n\left|\frac{P_t-F_t}{P_t}\right|$$

(7)

Measuring MAPE conduces the exact qualification of forecasting values [35,36]. The interpretation of MAPE results shows the accuracy of the forecast: when MAPE is smaller than 10%, the prediction value is excellent; 10% to 20% indicates good forecasting data; the prediction value is reasonable when it ranges from 20% to 50%; and more than 50% is an unacceptable prediction [37,38] and the research must retest with another model.

3.4. Super SBM Model

Super-SBM expresses the principles of super efficiency and non-radial measurement which Tone [25] wrote after collecting and analyzing information of previous researchers including technical efficiency [39], relative efficiency [10], the non-parametric linear programming method [40,41], dealing multiple inputs to produce multiple outputs [42], the non-radial model [43], and so on. The Super-SBM model deals n DMUs with the input and output, setting input (A = a_hk) and output (B = b_hk). A and B must be positive and R⁺, hence the production possibility is denoted as follows:

$$P=\left(A,B\right)$$

(8)

Subject to

$$a\ge A\lambda , b\le B\lambda , \lambda \ge 0$$

Here, $\lambda$ is a non-negative vector in R⁺.

$$\begin{array}{c}{a}_0=A\lambda +s^{-};\\ b_0=B\lambda -s^{+}\\ \left\{\lambda ,s^{-},s^{+}\ge 0\right\}\end{array}$$

(9)

The vectors $s^{+}$ and $s^{-}$ belong to $R^{+}$ in order to define input excess and output shortfall with the condition $A\ge 0, \lambda \ge 0$, which satisfies $a_0\ge s^{-}$.

Following $s^{+}$ and $s^{-}$, $\rho$ is formulated as below:

$$\begin{array}{c}\rho =\frac{1-\frac{1}{m}{{\displaystyle \sum }}_{h=1}^m{s}_h^{-}/a_{h0}}{1-\frac{1}{s}{{\displaystyle \sum }}_{h=1}^s{s}_h^{+}/b_{h0}}\\ \left(0<\rho \le 1\right)\end{array}$$

(10)

The efficiency of (a₀, b₀) is calculated following:

$$Min \rho =\frac{1-\frac{1}{m}{{\displaystyle \sum }}_{h=1}^m{s}_h^{-}/a_{h0}}{1-\frac{1}{s}{{\displaystyle \sum }}_{h=1}^s{s}_h^{+}/b_{h0}}$$

(11)

Subject to

$$\begin{gathered} a_0=A\lambda +s^{-};b_0=B\lambda +s^{+} \\ \left\{\lambda ,s^{-},s^{+}\ge 0\right\} \end{gathered}$$

Setting up an optimal solution for the SBM model is ${\rho }^{*},{\lambda }^{*}, s^{-*}, s^{+*}$. X DMU is defined as the SBM model efficiency when it is based on the optimal solution under the condition ${\rho }^{*}=1,s^{-*}=0, s^{+*}=0$ and no input excess, and there is no output shortfall in any optimal solution.

$$\min \delta =\frac{\frac{1}{m}{{\displaystyle \sum }}_{h=1}^m\overline{a_h}/a_{h0}}{\frac{1}{s}{{\displaystyle \sum }}_{h=1}^s\overline{b_h}/b_{h0}}$$

(12)

Subject to

$$\begin{gathered} \overline{a}\ge {\displaystyle \sum }_{k=1,\ne 0}^n{\lambda }_k{a}_k, \overline{b}\le {\displaystyle \sum }_{k=1,\ne 0}^n{\lambda }_k{b}_k \\ \overline{a}\ge a_0, \overline{b}\le b_0, \overline{b}\ge 0, \lambda \ge 0 \end{gathered}$$

When the output r has no position, it is denoted as $\overline{b_r^{+}}=b_r^{+}=1$. Tone (2002) described the super-SBM model as follows:

$$\min \delta =\frac{1}{\frac{1}{s}{{\displaystyle \sum }}_{r=1}^s\overline{b_r/b_{r0}}}$$

(13)

Whereas

$$\begin{gathered} \overline{a}\ge {\displaystyle \sum }_{k=1,\ne 0}^n{\lambda }_k{a}_k, \overline{b}\ge {\displaystyle \sum }_{k=1,\ne 0}^n{\lambda }_k{b}_k \\ \left\{\overline{a}=a_0;0\le \overline{b}\le b_0; \lambda \ge 0\right\} \end{gathered}$$

(14)

4. Results

4.1. Estimated Valuation

A forecasting process in preceding and preparing must test the feasibility of original actual data that has time-series and trends. Each method is applied to reveal predictions under controlling parameter space and the measurement of performance within the case of time-series [44,45,46]; these parameters will be formulated to define the accuracy level of forecasting values. The additive trend method in Tableau displayed a clarification of parameter classification when the historical time-series data were used for estimating the future of two airport and six seaport logistics companies in Vietnam, as shown in Section 3.2.

4.1.1. Smoothing Coefficients

Based on the space condition, the alpha, beta, and gamma parameters are 0 to 1; the parameters of three models in exponential smoothing are utilized to formulate the future operation of port logistics companies.

Table A1. Forecasting parameters of port logistics companies in Vietnam by Season of none over the period of 2018–2022.

Code	TAS			OEY			NRE			GRP
	α	β	γ	α	β	γ	α	β	γ	α	β	γ
QNN	0.5	0	0	0.343	0	0	0.5	0	0	0.116	0	0
PHP	0.455	0	0	0.5	0	0	0.134	0.5	0	0.297	0	0
PDN	0.5	0.037	0	0.5	0.084	0	0.5	0.064	0	0.5	0.089	0
NCT	0.298	0.104	0	0.489	0.009	0	0.5	0.023	0	0.144	0.336	0
DNL	0.5	0	0	0.5	0.015	0	0.497	0	0	0.5	0	0
CMP	0.431	0	0	0.5	0	0	0.5	0	0	0.5	0	0
CLL	0	0.044	0	0.5	0	0	0.5	0	0	0.5	0.002	0
CDN	0.5	0.076	0	0.5	0.014	0	0.1	0.427	0	0.106	0	0

,

Table A2. Forecasting parameters of port logistics companies in Vietnam by season of additive over the period of 2018–2022.

Code	TAS			OEY			NRE			GRP
	α	β	γ	α	β	γ	α	β	γ	α	β	γ
QNN	0	0.045	0	0.072	0.467	0	0	0.045	0	0.5	0.064	0
PHP	0.163	0.5	0	0.175	0.5	0	0.215	0.5	0	0.243	0.5	0
PDN	0.5	0	0.5	0.5	0	0.252	0.5	0	0.5	0.5	0	0.5
NCT	0.128	0.5	0	0.148	0.5	0	0.197	0.5	0	0.5	0.167	0
DNL	0	0.044	0	0.5	0	0.5	0.234	0.5	0	0.183	0.5	0
CMP	0.5	0.017	0	0.5	0.006	0	0	0.046	0	0.5	0	0.5
CLL	0.211	0.5	0	0.5	0.106	0.023	0.248	0.5	0	0.203	0.5	0
CDN	0.106	0.5	0	0.218	0.5	0	0.135	0.5	0	0.5	0	0

and

Table A3. Forecasting parameters of port logistics companies in Vietnam by season of multiplicative over the period of 2018–2022.

Code	TAS			OEY			NRE			GRP
	α	β	γ	α	β	γ	α	β	γ	α	β	γ
QNN	0	0.045	0	0.08	0.5	0	0.444	0.5	0.5	0.5	0.174	0.044
PHP	0.214	0.5	0	0.292	0.5	0.181	0.227	0.5	0	0.345	0.5	0.017
PDN	0.5	0	0.458	0.5	0	0.148	0.5	0.5	0.5	0.5	0.5	0.5
NCT	0.152	0.5	0	0.179	0.5	0	0.5	0.283	0	0.5	0.365	0
DNL	0	0.044	0	0.5	0	0.5	0.225	0.5	0	0.178	0.5	0
CMP	0.445	0.107	0	0.5	0.032	0.12	0	0.046	0	0.5	0.5	0.5
CLL	0.224	0.5	0	0.355	0.195	0.248	0.248	0.5	0.174	0.217	0.5	0
CDN	0.197	0.5	0	0.233	0.499	0.5	0.136	0.5	0.098	0.049	0.5	0.499

indicate that all the parameters are appreciated, particularly with their empirical scopes of 0 to 0.5.

4.1.2. Accuracy Indication

The results will be retested by smoothing constants as a MAPE index to seek out the best estimated results.

Table 4. MAPE calculation results of Holt’s linear method.

Code	TAS	OEY	NRE	GRP
CDN	23.00%	39.20%	20.80%	40.60%
CLL	8.70%	13.40%	13.20%	3.90%
CMP	13.70%	12.80%	24.50%	30.10%
DNL	16.40%	10.70%	15.50%	19.40%
NCT	20.10%	18.90%	20.70%	21.90%
PDN	22.40%	9.10%	32.50%	18.40%
PHP	28.70%	47.70%	14.20%	37.70%
QNN	44.40%	12.00%	80.70%	44.60%
Average	24.37%

Note: TAS: Total assets; OEY: Owner’s equity; NRE: Net revenue; GRP: Gross profit.

,

Table 5. MAPE calculation results of the additive Holt-Winter method.

Code	TAS	OEY	NRE	GRP
CDN	11.00%	22.90%	22.10%	36.90%
CLL	12.10%	11.60%	10.70%	3.10%
CMP	12.70%	11.90%	13.40%	20.40%
DNL	12.40%	5.90%	12.40%	13.30%
NCT	12.90%	12.90%	14.40%	15.70%
PDN	11.60%	4.00%	13.80%	7.60%
PHP	20.10%	34.70%	12.80%	28.80%
QNN	16.70%	10.10%	29.60%	40.40%
Average	16.22%

and

Table 6. MAPE calculation results of the multiplicative Holt-Winter method.

Code	TAS	OEY	NRE	GRP
CDN	12.60%	35.90%	25.20%	54.00%
CLL	12.80%	13.90%	11.30%	3.20%
CMP	14.50%	13.20%	13.30%	21.50%
DNL	12.60%	5.90%	12.60%	13.40%
NCT	13.50%	13.50%	13.90%	15.50%
PDN	12.90%	4.30%	13.90%	8.00%
PHP	21.60%	48.20%	13.50%	31.00%
QNN	17.20%	10.30%	29.50%	46.90%
Average	18.43%

indicate the classification of three methods in the additive trend method; most of them obtained a standard qualification under 50% and the average percentages of Holt’s linear method, the additive Holt–Winter method, and the multiplicative Holt–Winter method are 24.37%, 16.22%, and 18.43%, respectively.

From Equation (7) and the principle of MAPE [37,38], the net revenue of QNN in Holt’s linear method is 80.70%, so the forecasted value proposition is absolutely inaccurate. Therefore, it affects a final test of Holt’s linear method directly; it does not get put through its paces. In the multiplicative Holt–Winter method, the gross profit of CND is higher than the benchmark at 54.00%; consequently, it excludes criteria and cannot move to the next step. All MAPE of ports in the additive Holt–Winter method obtained quality under 50%, as their percentages are 3.10% to 40.40%. For the reason that the additive Holt–Winter method is an exact forecasting tool of future Vietnam ports, the predicted values are authentic and utilized to monitor the efficiency in the period of 2018–2022 in the next stage. The best accurate forecasting data by the additive Holt–Winter method are shown in

Table A4. Estimated values of port logistics companies over the period 2018–2022 (VND in Millions).

Name of Ports	Year	(I) Total Assets	(I) Owner’s Equity	(O) Net Revenue	(O) Gross Profit
CDN	2018	504,669	196,323	1,304,010	1,024,266
CLL		312,502	117,620	650,418	628,270
CMP		99,134	65,839	475,675	357,562
DNL		35,902	13,118	48,392	49,104
NCT		827,101	437,209	677,610	579,552
PDN		606,204	177,454	929,363	439,431
PHP		2,771,517	998,564	7,316,593	4,973,681
QNN		980,608	147,488	808,823	682,506
CDN	2019	720,145	276,448	1,566,220	1,143,554
CLL		327,468	122,802	768,568	735,696
CMP		91,300	65,355	594,325	423,029
DNL		31,899	12,683	49,633	56,485
NCT		900,475	496,545	626,312	542,816
PDN		685,394	190,603	1,044,150	469,048
PHP		2,586,004	1,045,432	6,943,971	5,615,173
QNN		2,260,845	155,620	821,121	625,130
CDN	2020	554,062	233,754	1,521,173	1,222,758
CLL		348,509	122,442	690,509	726,776
CMP		104,408	85,842	542,282	412,394
DNL		37,261	13,860	50,487	54,645
NCT		931,716	476,841	768,371	659,034
PDN		772,962	216,502	1,125,091	497,863
PHP		3,015,200	1,154,983	8,425,751	5,858,369
QNN		1,379,383	181,118	879,931	749,442
CDN	2021	787,338	324,569	1,807,001	1,345,587
CLL		363,143	127,735	814,525	842,660
CMP		96,031	82,593	672,101	483,281
DNL		33,084	13,381	51,737	62,519
NCT		1,007,596	539,604	704,936	612,483
PDN		851,139	228,388	1,243,103	527,530
PHP		2,803,800	1,197,299	7,922,473	6,532,391
QNN		3,024,890	187,473	890,271	683,573
CDN	2022	603,454	271,185	1,738,336	1,421,251
CLL		384,515	127,264	730,600	825,282
CMP		109,681	105,846	608,888	467,227
DNL		38,620	14,601	52,582	60,186
NCT		1,036,330	516,473	859,131	738,516
PDN		939,720	255,551	1,320,819	556,295
PHP		3,258,882	1,311,403	9,534,908	6,743,056
QNN		1,778,157	214,749	951,040	816,378

.

4.2. Performance Index and Ranking

In data envelopment analysis, the relationship between input variables and output variables must be isotonic so the input quantity rises; the output quantity could not be deducted under the same condition. The correlation coefficient is from −1 to +1. The Pearson correlation has a perfect linear relationship when it is closer to $\pm 1$. The empirical result of the research, as shown in

Table A5. Pearson’s correlation.

Factors	TAS	OEY	NRE	GRP	TAS	OEY	NRE	GRP
Year	2011				2012
TAS	1	0.9846	0.9606	0.6245	1	0.9903	0.9814	0.8591
OEY	0.9846	1	0.9381	0.6211	0.9903	1	0.9663	0.8646
NRE	0.9606	0.9381	1	0.7621	0.9814	0.9663	1	0.9187
GRP	0.6245	0.6211	0.7621	1	0.8591	0.8646	0.9187	1
	2013				2014
TAS	1	0.9941	0.9684	0.7008	1	0.9984	0.96	0.8225
OEY	0.9941	1	0.9631	0.7123	0.9984	1	0.9653	0.8303
NRE	0.9684	0.9631	1	0.8436	0.96	0.9653	1	0.9443
GRP	0.7008	0.7123	0.8436	1	0.8225	0.8303	0.9443	1
	2015				2016
TAS	1	0.9987	0.9581	0.887	1	0.9979	0.9754	0.926
OEY	0.9987	1	0.9629	0.8938	0.9979	1	0.9763	0.9319
NRE	0.9581	0.9629	1	0.9766	0.9754	0.9763	1	0.9837
GRP	0.887	0.8938	0.9766	1	0.926	0.9319	0.9837	1
Year	2017				2018
TAS	1	0.9828	0.9204	0.8503	1	0.9973	0.9484	0.9349
OEY	0.9828	1	0.8564	0.8859	0.9973	1	0.9487	0.9364
NRE	0.9204	0.8564	1	0.8272	0.9484	0.9487	1	0.9547
GRP	0.8503	0.8859	0.8272	1	0.9349	0.9364	0.9547	1
	2019				2020
TAS	1	0.9967	0.7171	0.9142	1	0.9964	0.9128	0.9446
OEY	0.9967	1	0.7146	0.9173	0.9964	1	0.9106	0.9438
NRE	0.7171	0.7146	1	0.7172	0.9128	0.9106	1	0.9285
GRP	0.9142	0.9173	0.7172	1	0.9446	0.9438	0.9285	1
	2021				2022
TAS	1	0.9957	0.6122	0.9249	1	0.9957	0.8744	0.9512
OEY	0.9957	1	0.6074	0.9255	0.9957	1	0.8695	0.9486
NRE	0.6122	0.6074	1	0.6234	0.8744	0.8695	1	0.8986
GRP	0.9249	0.9255	0.6234	1	0.9512	0.9486	0.8986	1

, demonstrates that it displays a strong positive correlation when these correlation values are between 0.6074 and +1, with the result that the input factors and output factors are absolutely qualified.

Although many DEA models are used for calculating the performance, the ranking of some cases over each year cannot be distinguished. This research defines the efficiency of each port logistics company and their clear distinction ranking; thus, a super-SBM model is utilized to compute the performance. The rank of each DMU is determined by the weights and the desirability of inputs and outputs.

Figure 3 and

Table 7. Score of port logistics companies over the historical term.

DMU	2011	2012	2013	2014	2015	2016
CDN	1.10308	1.06952	0.42256	0.2269	0.38878	0.40679
CLL	0.32825	0.33977	0.27022	0.39477	0.28778	0.33058
CMP	0.24352	0.24457	0.21705	0.29977	0.16503	0.24013
DNL	6.89607	7.36205	7.9072	6.90754	9.12671	8.92694
NCT	6.16017	3.78382	5.95239	5.6909	5.23455	4.05713
PDN	0.36727	0.41517	0.37382	0.52197	0.46475	0.58014
PHP	1	1	1	1	1	1
QNN	0.39691	0.42146	0.28561	0.42124	0.45036	0.46161

and

Table 8. Score of port logistics companies over the future term.

DMU	2017	2018	2019	2020	2021	2022
CDN	0.38048	0.33888	0.29794	0.30289	0.28764	0.29065
CLL	0.30926	0.39296	0.26503	0.36733	0.25538	0.35123
CMP	0.27401	0.29396	0.2239	0.32964	0.24192	0.35998
DNL	7.05042	8.55567	9.73181	9.1439	10.3604	9.67142
NCT	4.91851	3.79334	4.64783	3.55591	4.40863	3.36177
PDN	0.61006	0.76097	0.50165	0.72984	0.50524	0.71933
PHP	1	1	1	1	1	1
QNN	2.41737	1.42161	7.19477	2.55652	9.2276	3.65386

denote the efficiency change of port logistics companies over the time period of 2011–2022. Most of the port logistics companies exhibit fluctuating values, with stable scores as one number in whole terms, excluding PHP, which received a stable efficiency. CLL and PDN have a particular efficiency change, i.e., one-year increases and one-year decreases smoothly with previous time and future time, respectively. CMP indicates value change as CLL and PDN during the time period of 2011–2016 and 2018–2022, and CMP rises softly from 2016 to 2018. DNL and QNN also present a dramatic efficiency rise and then drop slightly according to each year during the time period 2011–2022. DNL has an up-efficiency within two consecutive time periods from 2011–2013 and is down to two continual time periods from 2015–2017. CDN and NCT exhibit the action of deduction and accretion of performance during the time period of 2011–2022, respectively. Notably, the empirical experienced result shows that DNL always mantains the highest performance over the time period of 2011–2022, and its smallest value is 6.89607, with its largest value at 10.36043. Although CLL, CMP, and PDN express the “soft fluctuation” trend, they still have a low efficiency under 1.

The ranking of airport and seaport logistics companies is shown in Figure 4. Based on the performance indication, DNL always maintains a dominant position. NCT ranks in second position according to alternative years 2011–2018 and 2020; it is in third position for the years 2019, 2021, and 2022. PHP reaches the third classification from 2013 to 2016 and fourth position according to the years 2011, 2012, and 2017–2022. CLL obtains a sixth ranking in 2014, 2018, and 2020, respectively, and seventh ranking in other terms. CMP seems to be the worst port, as it is usually at the lowest point during the time periods of 2011–2013, 2015–2019, and 2021; it only went up one level in 2014 and 2020. However, the forecasting data indicates that CMP can reach sixth position in 2022. PDN will rank as the fifth class in the future time terms of 2017–2022 and go up from sixth to fourth position during the periods of 2011–2012, 2013, and 2014–2016, respectively. Besides, CDN and QNN are the two port logistics companies that have a sharp change consecutively; CDN remains at the third ranking in 2011–2012 and then it falls to the bottom position in the years 2014, 2020, and 2022. The actual values and prediction values show that CDN remains at the bottom; QNN remains in a high position when it obtains a high forecasting efficiency.

The empirical results of previous and future time periods in port logistics companies denote the actual efficiency and estimated performance by using the super-SBM for figuring out their values and the follow-up final mark indicates their ranking. By way of consequence, CDN always gets the highest efficiency with the first rank in all terms. NCT has a large performance ratio and stays in second position, but its ratio can be reduced and directly affects its ranking. PHP in the middle term 2013–2016 upgrades the point and rises one position, maintaining the classification within these four years. As a consequence, CDN, NCT, and PHP are the best port logistics companies, with a high efficiency above 1. On the other hand, CMP and CLL are ineffective ports, with a low performance of under 1. Per the analysed results, the number of efficient and inefficient port logistics companies in each term is shown in

Table 9. The efficient and inefficient index of port logistics companies.

Indicators	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021	2022
Efficient	4	4	3	3	3	3	4	4	4	4	4	4
Inefficient	4	4	5	5	5	5	4	4	4	4	4	4

. The number of efficient companies is four, and number of inefficient ones is four in 2011–2012 and 2017–2022. The number of companies becoming efficient is three, and five companies are inefficient over the period of 2012–2016. For the improvement of inefficient companies, they must increase their output variables such as revenue and gross profit. This denotes that they exist in an inefficient operating process.

5. Conclusions

In short, this valuable study presents an overview of port logistics companies in Vietnam from the past to the future, while combining the additive trend method and the super-SBM model. The application of the additive trend method in Tableau is used to predict the future, and the super-SBM is employed for calculating the efficiency. In general, most port logistics in Vietnam are experiencing a robust growth rate when based on real and forecast performance indicators. Both airport logistics companies and seaport logistics companies exhibit a development trend. Hence, these values express that the trade of Vietnam is experiencing a large demand to expand the products exchanged with foreign markets. The empirical results are analysed by integrating the additive trend method and super-SBM model.

The accuracy forecasting data in the period of 2018–2022 is employed by the additive Holt-Winters method when formulating results based on the historical data during the term of 2011–2017. Four variables, i.e., total assets, owner’s equity, net revenue, and gross profit, are key financial indicators that determine an enterprise’s operating status. The prediction results exhibit the future operation status of port logistics companies.

Furthermore, with the best function of the super-SBM model in measuring comparisons of efficiency and ranking of each port logistics company, the empirical analysis result computes the performance of port logistics companies in Vietnam through the super-SBM model. Further, their efficiency scores also define the ranking and capable operation of each port logistics company for every year. Consequently, port logistics companies can know about their position and their operation.

This research discusses the effectiveness of port logistics companies, but it still has limitations. First, indicators such as containers and labor forces of ports logistics companies are non-listed; thus, it is difficult to attain depth and specification overviews via port logistics companies. Therefore, more input and output factors are necessary in order to analyze the efficiency of port logistics companies in Vietnam. Second, information on many port logistics companies is not posted, which creates a lack of comparison; thus, future research should aim to reveal more relative inputs and outputs of other logistics companies.