Introduction

Ports play a crucial role in global trade, serving as vital gateways for the movement of goods and commodities1. Efficient operations and planning within ports are essential for ensuring smooth supply chains and economic growth. Accurately forecasting container throughput is a key aspect of port management, enabling port authorities and stakeholders to optimise resource allocation, plan infrastructure development, and enhance overall operational efficiency2.

Traditionally, container throughput forecasting has relied on statistical models based on historical data and expert knowledge3. However, these methods often struggle to capture the complex and dynamic nature of port operations, leading to limited accuracy in forecasting. Recognising the need for more robust and accurate forecasting, researchers have turned to advanced technologies such as deep learning4,5.

Deep learning, a subset of machine learning, has shown remarkable success in various domains, including computer vision6, natural language processing7, and time series analysis8. Its ability to automatically learn and extract intricate patterns from vast amounts of data makes it an ideal candidate for improving container throughput forecasting in ports.

In addition, one concept that has gained significant attention in recent years is the notion of a port’s bi-directional hinterland. The bi-directional hinterland refers to the area surrounding a port that serves as both a source and destination for cargo movements, including hinterland and foreland9. Hinterland refers to the geographical area connected with the port in some mode of transport, which generates a source of goods for the port or consumes goods imported from the port. Foreland refers to other countries or regions that are connected to the seaport by maritime vessels. Understanding the size and scope of a port’s bi-directional hinterland is crucial for accurately forecasting container throughput10.

The main motivation of this study is to release the potential and power of port’s bi-directional hinterland data in the forecasting of port throughput. The forecasting accuracy can be improved by introducing data related to port’s bi-directional hinterland. This research proposed a Grey-CNN model that combines Grey Correlation Analysis (GCA) and Convolutional Neural Networks (CNN). GCA is employed to solve the overfitting problem caused by too many input variables. CNN is used to mine non-linear features in data. This paper is the first time that the Grey-CNN model has been used in the field of port throughput forecasting.

The first step is to collect candidate factors that can influence port container throughput. When selecting these factors, two aspects, hinterland, and foreland, need to be considered. The second step is to filter the most relevant factors based on the output of GCA. The third step is to train the CNN model with selected factors. The combined use of GCA and CNN enables the model to not only select the most relevant variables from a variety of data and improve the interpretability of the model, but also capture the complex relationships and dependencies that may exist in the data, so as to achieve more accurate forecasting results. By leveraging historical data, hinterland and foreland information, this approach will enhance the accuracy of container throughput forecasting.

The implications of the study can be significant for port management and logistics planning. By better understanding and utilising the data related to a port’s bi-directional hinterland, port authorities can make informed decisions regarding infrastructure investments, resource allocation, and trade facilitation measures. Ultimately, accurate container throughput forecasting can contribute to reducing congestion, optimising operations, and fostering sustainable growth within ports.

The remainder of this manuscript is organised as follows. Literature review provided a literature review. The methodology and forecasting framework were introduced in Methodology. Empirical study presented and discussed the results of empirical study. Finally, Conclusion concluded this study with practical implications, limitations, and future research.

Literature review

Bi-directional hinterland

Port’s hinterland and foreland are interconnected concepts that define the relationship between a port and its surrounding areas, both on land and at sea. The hinterland refers to the inland regions connected to a particular port through various transportation corridors such as roads, railways, or waterways11. This expansive area extends beyond immediate proximity to the port into neighbouring territories. The hinterlands serve as an integral part of the logistics network supporting economic activities related to import/export operations facilitated by the port. They provide crucial links for transporting cargo between inland locations and the port facility itself.

On the other hand, the foreland serves as the ocean-ward mirror of the hinterland, encompassing ports and overseas markets linked by shipping services from a specific port12. It represents a maritime space where commercial relationships thrive, particularly with overseas customers13. Within this realm, ports play a vital role in facilitating trade activities by establishing connections through shipping services to reach international markets14. These connections extend beyond physical infrastructure to include destinations worldwide where goods are imported from or exported to via ships departing from or arriving at the port15.

The symbiotic relationship between hinterland and foreland is essential for fostering economic development and attracting investment in today’s global economy16. Ports rely on their hinterlands for access to domestic markets and sources of goods for exportation abroad while providing critical infrastructure like terminals, berths, and storage facilities necessary for efficient handling of goods within their forelands’ maritime spaces. The integration between these two entities enables ports not only to benefit from efficient cargo exchanges with overseas markets but also support the economic growth of industries in their hinterlands by improving accessibility to global trade networks. Developing robust transportation infrastructure and optimising logistical operations within the hinterlands can enhance overall supply chain efficiency, reducing time costs in logistics operations, minimising inventory holding requirements, resulting in significant cost savings, and facilitating just-intime delivery processes17.

Factors affecting container throughput

In view of the changing international situation, the development of the maritime industry will also be affected by it, how to establish a model for the forecast of port container throughput becomes a difficult problem. Moreover, forecasting port throughput is a complicated process, which is closely related to the geographical location, economic conditions, traffic, and natural conditions of the port hinterland. The research shows that the export trade volume of a country is the key macroeconomic variable affecting the container throughput18. This indicates that the port container throughput is affected by the market conditions of the export destination. Moreover, Li et al. pointed out that factors affecting port throughput can be roughly divided into three categories: economic factors, port factors, and other factors: (1) economic factors include world economic level, foreign trade and domestic trade; (2) the port itself factors include port location, port infrastructure construction and port supply and demand relations; (3) other factors include weather, government policy, and competition between ports19.

Some of these factors are uncertain and some will change with time, but all of them affect the establishment of the forecasting model, so that the change of port throughput has two linear and nonlinear situations. Li Y et al. also used univariate linear regression, multiple linear regression, and generalised learning system to forecast the container throughput of Lianyun Port and compared the experimental results of single variable and combined two economic factors. The results showed that the port throughput could be more effectively forecasted by adding two economic factors20. Dai employed GCA to analyse the relationship between Tangshan port logistics and regional economic development. The results showd that the tertiary industry and the fixed assets investment of the whole society are highly correlated with port logistics21.

Univariate container throughput forecasting

Container throughput forecasting is a popular research topic in the fields of forecasting and maritime research. In the past few decades, researchers proposed many innovative models to forecast the container throughput. From the perspective of data types used, these models can be divided into two categories. The first category is a forecasting model that only uses historical container throughput; the second category is a model that uses both historical container throughput and economic data of the port city.

For the first category, Niu et al. proposed a hybrid decomposition-ensemble model based on Variational Mode Decomposition (VMD) and Hybridising Grey Wolf Optimisation (HGWO). In their study, they collected monthly container throughput of the Port of Singapore (January 1995 - May 2016) and the Port of Shanghai (January 2001 to May 2016. Then the time series were decomposed into low and high frequency components by the VMD algorithm. Then the low frequency components were used to train ARIMA and high frequency components are used to train Support Vector Regression (SVR) using HGWO algorithm22. Mo et al. collected monthly container throughput of the Port of Xiamen and the Port of Shanghai (January 2001 - December 2015). Then the Seasonal Autoregressive Integrated Moving Average (SARIMA) was used to forecast the linear trend of the original time series. After that, the nonlinear residual series was analysed by the BP neural network, genetic programming and SVR, and the Group Method of Data Handling (GMDH) neural network was used to select the optimal complexity model. Then the results of linear and nonlinear parts are added together to get the final results23. Similarly, Xie et al. collected monthly container throughput of the Port of Singapore and the port of Log Angeles (January 1995 - January 2017). Then they employed the decomposition method to analyse the original time series. Data characteristic analysis was conducted to select the suitable model for the decomposed parts. Finally, the results of the models were aggregated to get the forecasting result24. Furthermore, Hassan et al. built a reinforcement learning framework to forecast freight demand using historical demand data. They first cluster historical demand time series into different groups according to their spatial-temporal characteristics. And then the committee of predictors of each cluster were constructed. Finally, the predictive component models were fed into reinforcement learning model to get the forecasting results. Their results showed that the proposed approach is able to generate accurate results25. Moreover, Yang and Chang proposed a mixed-precision model based on CNN and LSTM to forecast container throughput26. Xiao et al. employed attention mechanism to further improve the performance of VMD-CNN-LSTM model27.

It can be found from the above research cases that for the research with only historical container throughput data, the usual method is to use decomposition algorithm to decompose the original time series, then analyse and forecast the decomposed parts, and finally aggregate all the parts together to get the final result28,29,30. However, there is still something that can be improved in the above studies. That is, these studies are all based on the univariate forecasting model, while ignoring other factors around the research object which may have effect on it. Therefore, it is necessary to incorporate these kinds of data to build multivariate forecasting model. The next section is going to review previous studies that employed multivariate models to forecast target variable.

Multivariate container throughput

It is limited to forecast the future container throughput based only on the historical container throughput of the port. Historical container throughput can only provide partial information related to the target, but not all information related to container handling. Therefore, the introduction of more data related to container throughput has become an effective means to improve the forecasting accuracy, which is the second category of container throughput forecasting studies.

For instance, Geng et al. collected yearly port throughput data and corresponding socio-economic indicator data for the Port of Shanghai (1978–2013). Then the candidate input variables were analysed using Multivariable Adaptive Regression Splines (MARS) to determine the final input variables. When all input variables were determined, the authors used SVR with an optimisation algorithm to obtain the final forecasting model31. Intihar et al. employed dynamic factor analysis and Autoregressive Integrated Moving Average with Exogenous Variables (ARIMAX) to forecast the container throughput of the Port of Koper. The dynamic factor analysis method was used to analyse influential external macroeconomic indicators and ARIMAX was then used to forecast future container throughput32. Moreover, Rashed et al. proposed a combined approach to forecast container throughput demand. They first employed AutoregRessive Distributed Lag (ARDL) model to estimate the link between the economic the activity and container throughput. Then the future growth rates for exogenous variables were calculated using scenario analysis. The final step involved combining the outputs of the first two steps to forecast container throughput33. Additionally, Tang et al. selected an optimal model based on multiple factors for container throughput forecasting. They collected five external factors, including the total retail sales of consumer goods, the gross domestic product of the local city, import and export trade volume, total output value of the second industry and total fixed asset investment. These factors were then used to train several forecasting methods. They determined that the back-propagation neural network generated the best results for the Port of Shanghai and the Port of Lianyungang34.

It was noted that the usual process for container throughput forecasting involves selecting suitable variables from candidate economic data of the port city using analytic methods. Then, the forecasting model can be trained by the selected economic variables and historical container throughput. However, the existing studies only focus on the impact of economic development of the port hinterland on the container throughput, ignoring the impact of the port foreland. It is necessary to develop a method approach that considers the above two factors to forecast container throughput.

Methodology

Proposed Grey-CNN model

The proposed model is presented in Fig. 1. This section will provide a detailed explanation of each step.

Step 1. Collection of relevant data.

Port container throughput is affected by the development of hinterland and foreland, so data related to these two aspects should be collected.

For hinterland, this study collects influencing factors related to port construction and economic development. However, different cities may not provide exactly the same data. If this is the case, similar data of the same type can be selected as input.

For foreland, this study collects port throughput and Gross Domestic Product (GDP) data for several countries with which the study subjects have the closest trade relations. These two kinds of data can be regarded as a synthesis of other information, which can represent the changes of the entire foreland market5. Furthermore, for different types of ports, such as production-export ports (e.g., Shanghai Port, Ningbo Port), transshipment ports (e.g., Port of Singapore), when selecting foreland data, the selection of countries will not be affected by the different port types. Because we chose the countries with which they trade most closely.

In addition, the historical container throughput of the port is also used as input data to train the forecasting model.

Step 2. Grey correlation analysis.

When there are many candidate influencing factors, it is more beneficial to extract the factors that are strongly related to the port container throughput to avoid overfitting problems. Grey correlation analysis is employed to screen the influencing factors.

Step 3. Model training.

In this study, CNN is used as the basis for the forecasting model because it was found in previous studies to be more effective for mining multi-dimensional time series. Due to the limited amount of data used in this study, the cross-validation method cannot be used, so this study adopts the early stop strategy to solve the overfitting problem. To verify the performance of proposed Grey-CNN model, nine models are selected as the benchmark models, which are:

  • Naïve method: The naive method in time series forecasting assumes that the future value will be the same as the most recent observed value, making it a simple but limited approach that ignores patterns or trends in the data.

  • ARIMA: Autoregressive Integrated Moving Average (ARIMA) is a common time series analysis method, widely used for data with obvious trends and seasonality, and widely used in economics, finance, meteorology, and other fields.

  • ARIMAX: AutoRegressive Integrated Moving Average with Exogenous Variables (ARIMAX) is a forecasting model that combines the ARIMA model with additional exogenous variables. It incorporates the autoregressive and moving average components to capture the time series’ internal dynamics, while also considering the impact of external factors. By including exogenous variables, ARIMAX can provide more accurate and robust forecasting by accounting for factors beyond the time series itself, such as economic indicators or weather data.

  • u-LSTM: Univariate LSTM is a type of recurrent neural network (RNN) used for time series forecasting with a single variable. It can capture temporal dependencies and patterns in the data by utilising memory cells and gates. It is trained on historical data and can generate forecasting results for future time steps based solely on the input variable’s past values.

  • m-LSTM: Multi-variate LSTM is for time series forecasting with multiple input variables. It can capture complex relationships and dependencies between multiple variables, enabling more accurate forecasts by incorporating information from multiple sources in the input data.

  • u-GRU: Univariate GRU is another variant of recurrent neural networks (RNN) used for time series forecasting with a single variable. It employs gated mechanisms to capture long-term dependencies and patterns in the data, making it effective for modelling and forecasting sequential data with a single input variable.

  • m-GRU: Multi-variate GRU is similar to m-LSTM. It utilises gated mechanisms to capture dependencies and patterns between multiple variables, improving the accuracy of forecasts in multi-dimensional data.

  • u-CNN: Uni-variate CNN is a type of neural network commonly used for time series forecasting with a single input variable. It applies convolutional filters to capture local patterns and learns hierarchical representations, enabling effective feature extraction and forecasting in uni-dimensional data.

  • u-Transformer: Uni-variate Transformer is a variant of the Transformer model designed for time series forecasting with a single input variable. It utilises self-attention mechanisms to capture global dependencies and learns contextual representations, enabling accurate forecasts and handling long-range dependencies in uni-dimensional data.

Step 4. Comparison and analysis.

This step is to compare the assessment criteria of each model and validate the performance of the proposed Grey-CNN model for container throughput forecasting.

Fig. 1
figure 1

A flowchart of the proposed approach.

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Grey correlation analysis

Grey correlation analysis, also known as Grey System Theory, is a statistical technique that measures the relationship between variables when data is limited or incomplete. It was developed as an extension of classical correlation analysis. Grey correlation analysis is particularly useful in situations where historical data or complete information is not available, making it applicable in various fields such as engineering, economics, and social sciences.

At the core of grey correlation analysis is the concept of grey numbers, which represent incomplete or uncertain information. Grey numbers consist of a definite value, an indeterminate value, and a grey relational coefficient. The grey relational coefficient quantifies the relationship between variables, indicating the degree of correlation between them.

The following steps present the main process of Grey Correlation Analysis.

Step 1

Suppose there is the reference sequence, in this study, is the time series of container throughput, and n is the number of observations. Then the candidate influence factors can be represented as is the number of candidate factors. The sequences of can be expressed as a matrix.

$$\:\left({\varvec{X}}_{1},\:{\varvec{X}}_{2},\:\dots\:,\:{\varvec{X}}_{\varvec{m}}\right)=\left[\begin{array}{ccc}{x}_{11}&\:{x}_{12}&\:\begin{array}{cc}\dots\:&\:{x}_{1 m}\end{array}\\\:{x}_{21}&\:{x}_{22}&\:\begin{array}{cc}\dots\:&\:{x}_{2 m}\end{array}\\\:\begin{array}{c}\dots\:\\\:{x}_{n1}\end{array}&\:\begin{array}{c}\dots\:\\\:{x}_{n2}\end{array}&\:\begin{array}{cc}\begin{array}{c}\dots\:\\\:\dots\:\end{array}&\:\begin{array}{c}\dots\:\\\:{x}_{nm}\end{array}\end{array}\end{array}\right]$$

Step 2: The reference sequence \(\:\varvec{Y}\) and the sequences of the candidate factors \(\:\left({\varvec{X}}_{1},\:{\varvec{X}}_{2},\:\dots\:,\:{\varvec{X}}_{\varvec{m}}\right)\) should be standardised using one of the following methods: (1) the initial value transform; (2) the average value transform; and (3) the polar difference transform. The transformed matrix would be:

$$\:{\varvec{Y}}^{\varvec{{\prime\:}}}=\left[\begin{array}{c}{y}_{1}^{{\prime\:}}\\\:{y}_{2}^{{\prime\:}}\\\:\begin{array}{c}\dots\:\\\:{y}_{n-1}^{{\prime\:}}\\\:{y}_{n}^{{\prime\:}}\end{array}\end{array}\right]$$
$$\:\left({\varvec{X}}_{1}^{\varvec{{\prime\:}}},\:{\varvec{X}}_{2}^{\varvec{{\prime\:}}},\:\dots\:,\:{\varvec{X}}_{\varvec{M}}^{\varvec{{\prime\:}}}\right)=\left[\begin{array}{ccc}{x}_{11}^{{\prime\:}}&\:{x}_{12}^{{\prime\:}}&\:\begin{array}{cc}\dots\:&\:{x}_{1 m}^{{\prime\:}}\end{array}\\\:{x}_{21}^{{\prime\:}}&\:{x}_{22}^{{\prime\:}}&\:\begin{array}{cc}\dots\:&\:{x}_{2 m}^{{\prime\:}}\end{array}\\\:\begin{array}{c}\dots\:\\\:{x}_{n1}^{{\prime\:}}\end{array}&\:\begin{array}{c}\dots\:\\\:{x}_{n2}^{{\prime\:}}\end{array}&\:\begin{array}{cc}\begin{array}{c}\dots\:\\\:\dots\:\end{array}&\:\begin{array}{c}\dots\:\\\:{x}_{nm}^{{\prime\:}}\end{array}\end{array}\end{array}\right]$$

Step 3

Compute the absolute difference value between reference sequence and the candidate factors.

$$\:{\varDelta\:}_{ti}=\left|{y}_{t}^{{\prime\:}}-{x}_{ti}^{{\prime\:}}\right|,\:t=\text{1,2},\dots\:,n,\:i=\text{1,2},\dots\:,m$$

Step 4

Calculate mm and MM.

$$\:mm={min}_{i}^{m}{min}_{t}^{n}{\varDelta\:}_{ti}$$
$$\:MM={max}_{i}^{m}{max}_{t}^{n}{\varDelta\:}_{ti}$$

Step 5

Calculate the relational coefficient matrix of the reference sequence and the candidate factors.

$$\:\left[\begin{array}{cccc}r({y}_{1}^{{\prime\:}},\:{x}_{11}^{{\prime\:}})&\:r({y}_{1}^{{\prime\:}},\:{x}_{12}^{{\prime\:}})&\:\dots&\:r({y}_{1}^{{\prime\:}},\:{x}_{1 m}^{{\prime\:}})\\\:r({y}_{2}^{{\prime\:}},\:{x}_{21}^{{\prime\:}})&\:r({y}_{2}^{{\prime\:}},\:{x}_{22}^{{\prime\:}})&\:\dots\:&\:r({y}_{2}^{{\prime\:}},\:{x}_{2 m}^{{\prime\:}})\\\:\dots\:&\:\dots\:&\:\dots\:&\:\dots\:\\\:r({y}_{n}^{{\prime\:}},\:{x}_{n1}^{{\prime\:}})&\:r({y}_{n}^{{\prime\:}},\:{x}_{n2}^{{\prime\:}})&\:\dots\:&\:r({y}_{n}^{{\prime\:}},\:{x}_{nm}^{{\prime\:}})\end{array}\right]$$

Where \(\:r\left({y}_{t}^{{\prime\:}},\:{x}_{ti}^{{\prime\:}}\right)=\frac{mm+\rho\:\times\:MM}{{\varDelta\:}_{ti}+\rho\:\times\:MM},\:t=\text{1, 2},\dots\:,n,\:i=\text{1, 2},\dots\:,m.\) For most cases, the value of \(\:\rho\:\) is 0.5.

Step 6

Calculate the grey relational degree.

$$\:r\left(Y,{X}_{i}\right)=\frac{1}{n}\sum_{t=1}^nr\left({y}_{t}^{{\prime\:}},\:{x}_{ti}^{{\prime\:}}\right),\:i=\text{1, 2},\dots\:,m$$

CNN

The CNN architecture comprises an input layer, convolution layer, pooling layer, fully connected layer, and output layer. In the input layer, the input data undergoes convolution using a convolution kernel to create the convolution layer. Subsequently, the pooling layer applies pooling methods like max pooling or average pooling to effectively reduce the size of the parameter matrix, thereby decreasing the number of parameters in the fully connected layer. This addition of the pooling layer not only accelerates computation but also helps prevent overfitting. Following the pooling process, the pooled data is forwarded to the fully connected layer, which can be considered as a conventional multi-layer perceptron. The input for the fully connected layer consists of features extracted from both the convolution layer and the pooling layer. The final output layer can utilise logistic regression, soft-max regression, or even support vector machine to generate the ultimate output. To enhance network accuracy, the network model employs the gradient descent method to minimise the loss function, enabling iterative adjustment of weight parameters across network layers during frequent training iterations.

The CNN was initially developed to address computer vision tasks, with the default input being an RGB image. This specific type of CNN is referred to as 3DCNN since the RGB image can be divided into three sub-images based on the RGB colours. However, when the input data consists of time series, the CNN is referred to as 1DCNN. Figure 2 illustrates the fundamental structure of a 1D-CNN.

Fig. 2
figure 2

Basic structure of CNN.

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Evaluation criteria

In order to compare the forecasting accuracy of different models, this study uses five evaluation criteria for comparison, and the smaller the value of these criteria, the higher the forecasting accuracy of the model. The five evaluation criteria are calculated as follows.

Mean absolute error (MAE):

$$\:MAE=\sqrt{\frac{1}{n}\sum_{i=1}^{n}\left|{A}_{i}-{F}_{i}\right|}$$
(5)

Root-mean-square error (RMSE):

$$\:RMSE=\sqrt{\frac{1}{n}\sum_{i=1}^{n}{({A}_{i}-{F}_{i})}^{2}}$$
(6)

Mean percentage error (MPE)

$$\:MPE=\frac{1}{n}\sum_{i=1}^{n}\frac{{A}_{i}-{F}_{i}}{{A}_{i}}$$
(7)

Mean absolute percentage error (MAPE)

$$\:MAPE=\frac{1}{n}\sum_{i=1}^{n}\left|\frac{{A}_{i}-{F}_{i}}{{A}_{i}}\right|$$
(8)

Symmetric mean absolute percentage error (SMAPE)

$$\:SMAPE=\frac{100}{n}\sum_{i=1}^{n}\frac{\left|{A}_{i}-{F}_{i}\right|}{(\left|{A}_{i}\right|+\left|{F}_{i}\right|)/2}$$
(9)

Where \(\:n\) is the number of observations, \(\:{A}_{i}\) is the actual value of the \(\:{i}_{th}\) observation, \(\:{F}_{i}\) is the forecast value of the \(\:{i}_{th}\) observation.

Empirical study

Data collection and pre-processing

In this study, Shanghai Port and Ningbo Port are taken as experimental objects. Because these two ports are the largest container ports in Asia, the forecasting of them has strong practical significance and research value.

Shanghai Port is in the middle of the coastline of mainland China and the estuary of the Yangtze River, connecting the north and south coasts of China and the world ocean before, and then traversing the Yangtze River basin, Jiang-Zhe-Wan River basin and Taihu Lake basin. Considering that the port container throughput will be affected by a variety of factors, this study collects two types of influencing factors, which are shown in Table 1. All the data are annual data from 2000 to 2021. Please refer to Appendix Table A1 and Table A2 for detailed data. According to the research, 80/20 is a common ratio of training and testing sets35. Therefore, the training set and the testing set contain 18 and 4 observations, respectively.

Ningbo port is a major container transportation hub in China. It boasts state-of-the-art facilities, efficient operations, and extensive connectivity, making it an ideal choice for global trade. With its strategic location, it offers seamless logistics solutions and plays a vital role in facilitating international container shipments. The influencing factors of Ningbo port are collected from 1990 to 2021. Please refer to Appendix Table A3 and Table A4 for detailed data. The name of the candidate variables are shown in Table 1. Therefore, the training set and the testing set contain 26 and 6 observations, respectively.

It can be seen that the number of data points used in this study is much smaller than that in other fields of research. But this does not affect the conclusion of this study and the forecasting power of the model. Although the deep learning model can better capture the patterns from of data when there is a large amount of data, as long as the model can converge, no matter the amount of data is large or small, it can form effective forecasting results.

Table 1 Candidate influencing factors.
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Results

According to the proposed model, the first step is to collect candidate influencing factors for Shanghai Port and Ningbo Port. This step has been done in Data collection and pre-processing. Then, this section will present the output of Grey Correlation Analysis and forecast result of the proposed model.

The grey correlation degree for each candidate factor is shown in Tables 2 and 3. It can be seen that all the degree are larger than 0.5. After comprehensive consideration of the calculation results, 0.77 is chosen as the cut-off point36. Therefore, for Shanghai Port, 7 factors of hinterland and 2 factors of foreland are selected to train the model. For Ningbo Port, 10 factors of hinterland and 4 factors of foreland are selected.

By comparing the factors that affect the container throughput of Shanghai Port and Ningbo Port, this study finds that the influence of foreland on Shanghai port mainly comes from the GDP factors of Japan and the United States, which indicates that the import and export of goods from Shanghai Port is closely related to the economic development of these two countries. The container throughput of Ningbo Port is mainly affected by hinterland, which shows that the containers of Ningbo Port are mainly export goods, while Shanghai Port is mainly responsible for imported goods.

Table 2 The grey relational degree ranking of each index of Shanghai Port.
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Table 3 The grey relational degree ranking of each index of Ningbo Port.
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After sifting out the main influencing factors from the candidate factors, these selected factors are used to train the models mentioned in Proposed Grey-CNN model. The forecasting results of Shanghai Port and Ningbo Port are shown in Tables 4 and 5.

Table 4 Forecasting result of each model of Shanghai Port.
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Table 5 Forecasting result of each model of Ningbo Port.
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Discussion

By analysing the results in Tables 4 and 5, there are several findings.

First, the most notable observation is that, in most cases, the multivariate model outperforms the univariate model, with the exception of the ARIMAX model for Shanghai Port. This observation suggests the powerful ability of multivariate models to effectively leverage the additional information provided by multiple variables and potential challenges faced by univariate models in capturing the complexity and interdependencies present in the datasets. This observation also supports the study’s hypothesis that using both hinterland and foreland data can improve the accuracy of forecast results.

Second, for the exception case, the forecast accuracy of ARIMAX model is not as good as that of ARIMA for Shanghai Port. The possible reason is that ARIMAX is a linear model, which can only excavate the linear relationship between input variables and the target. However, in this study, the container throughput at Shanghai Port is affected by a number of nonlinear factors, so ARIMAX is unable to produce a more accurate result.

Third, among all the multivariate models, the model proposed in this study has the best performance. In the context of multi-variate time series forecasting, Convolutional Neural Networks (CNNs) have several advantages over models like GRU and LSTM, which are recurrent neural networks: (1) CNNs can perform parallel computation, allowing them to process multiple time steps simultaneously, which improves training and inference efficiency. In contrast, RNN-based models typically process time steps sequentially; (2) CNNs excel at extracting features from local regions, which is beneficial for recognising local patterns in time series data. Through convolution and pooling operations, CNNs can effectively capture local structures in the data; (3) the parameter sharing mechanism in CNNs reduces the model’s parameter count, enhancing generalisation and reducing the risk of overfitting. This parameter sharing feature enables CNNs to better utilise the correlations between variables in multi-variate time series data; (4) compared to LSTM, GRU and other models, CNNs are less prone to gradient vanishing issues during training, making them better at capturing long-term dependencies; (5) for certain time series data, local patterns and translation invariance may be crucial features. CNNs may be more effective in handling these types of data as they are naturally adept at capturing such features. While CNNs offer advantages in certain aspects, the choice of model for time series data should be based on the specific characteristics and requirements of the problem. Sometimes, RNN-based models like LSTM and GRU may be more suitable for capturing long-term dependencies in time series data. Therefore, researchers should carefully consider the strengths and weaknesses of different models based on the specific context and data characteristics when selecting the most appropriate model for accurate forecasting in multi-variate time series tasks. But in this study, the observations of time series were limited. LSTM and GRU were therefore unable to capture long-term dependencies, so CNN performed better than them.

Forth, comparing the performance of simpler models like Naive method with more complex models like LSTM, CNN, and Transformer, it is evident that increased model complexity does not always guarantee better forecasting accuracy. The proposed Grey-CNN model, despite being more complex than some models, outperforms others in terms of forecast accuracy. This highlights the importance of not just model sophistication but also the relevance of the architecture to the specific forecasting task at hand.

Fifth, while complex models like LSTM, GRU, and Transformer may offer high accuracy in forecasting, they often come at the cost of interpretability. On the other hand, simpler models like Naive forecasting or ARIMA are easier to interpret but may lack the forecasting power of more complex models. Balancing between model interpretability and forecasting performance is crucial, especially in scenarios where stakeholders require transparency in the decision-making process.

Sixth, the two ports selected in this study are both production-export ports. In addition, there are some important ports that serve other functions, such as the Port of Singapore. Therefore, when collecting the data, it is necessary to choose according to the types of different ports.

Managerial implications

Tables 4 and 5 illustrated that the proposed method can generate more accurate forecasting results than the other. It also showed that container throughput, as a key indicator in the shipping industry, has a close connection with economic growth. When the economy is growing, there is an increased demand for goods and services. Manufacturers produce more products, and consumers have higher purchasing power. This leads to a greater volume of goods being transported by containers. However, during economic recessions, demand for goods declines, and so does container shipping. For instance, during the 2008–2009 global financial crisis, many countries experienced a significant drop-in economic activity. This led to a decrease in consumer spending and a slowdown in industrial production. As a result, container throughput plummeted as there was less trade and fewer goods being shipped.

For the Shipping Market, a container throughput forecasting model has several managerial implications. Firstly, it helps with planning and resource allocation. Shipping companies can use it to determine the appropriate number of vessels for different routes, and port authorities can invest in infrastructure based on predicted demand. Logistics providers can also manage warehouse space and transportation fleets more effectively. Secondly, it aids in pricing and revenue management. Shipping lines and freight forwarders can set competitive prices by understanding market trends. They can identify peak and off-peak periods to adjust rates and attract business. Additionally, it enables risk management by allowing managers to anticipate disruptions and develop hedging strategies.

For economic growth, the forecasting model is also crucial for economic growth. For policymakers, it helps in formulating trade and transportation policies. They can identify areas for infrastructure investment to support the flow of goods and promote regional development. For investors, it provides a basis for making informed decisions about investing in the shipping industry and related sectors. A positive forecast can attract investment and encourage long-term planning, contributing to overall economic prosperity. In summary, the model is valuable for both the shipping market and economic growth.

Conclusion

The analysis of forecasting models for Shanghai and Ningbo Ports reveals the superiority of multivariate models in capturing complex interdependencies, with exceptions like the ARIMAX model’s limitations in handling nonlinear relationships. The Grey-CNN model’s success highlights CNN advantages in multi-variate time series forecasting. Despite model complexity, the Grey-CNN outperforms simpler and more complex models, emphasising the importance of model relevance to the forecasting task. The trade-off between interpretability and accuracy underscores the need for a balanced approach in model selection, ensuring transparency in decision-making processes for stakeholders.

Furthermore, this study highlights the importance of considering a port’s two-way hinterland concept and utilising deep learning techniques to enhance container throughput forecasting accuracy. The findings contribute to the advancement of port management practices and provide valuable insights for stakeholders involved in maritime logistics and trade.

Insufficient data is the main limitation of this study. In future studies, we will collect data over a longer period of time and input variables of more dimensions to further improve the accuracy of the forecasting model. In the following research, our team will focus on proposing more innovative forecasting models that are more suitable for this research field.

The implications of this research are significant for port authorities, logistics companies, and policymakers. Accurate container throughput forecasting enables better resource planning, improved efficiency, and enhanced decision-making in the maritime industry. Furthermore, a deeper understanding of a port’s two-way hinterland can facilitate the development of targeted strategies to promote economic growth and regional integration.

Data Availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.