The improved BP neural network supply chain performance evaluation model under the cross-border e-commerce marketing chain

Abstract

With the rapid development of Internet technology, foreign trade has been integrated with it, resulting in the rapid development of cross-border e-commerce, and for all kinds of enterprises to bring rich profits. However, in the fierce market competition, many enterprises ignore the importance of supply chain in the process of operation, which leads to the frequent bankruptcy of enterprises. To solve this problem, the research focuses on the supply chain performance evaluation of cross-border e-commerce enterprises, and proposes an improved error inverse propagation algorithm supply chain performance evaluation model. The results show that the model has improved the service capability of cross-border e-commerce, the performance of suppliers and the supply chain. The average relative error of the artificial neural network algorithm and the error reverse propagation algorithm is 3.26% and 10.23% respectively, while the average relative error of the expected output and actual output of the artificial neural network algorithm is 2.11%, and the average relative error of the expected output value and actual output of the error reverse propagation algorithm is 6.78%. It can be seen that the artificial neural network algorithm can effectively improve the performance level of the supply chain, and under this algorithm, the objectivity of the weights and the accuracy and efficiency of the prediction results are guaranteed. Therefore, this study has important scientific value and practical significance for understanding and improving the supply chain management of cross-border e-commerce enterprises.

Keywords

Cross-border e-commerce BP neural network supply chain performance LMBP algorithm supply chain management performance evaluation

1. Introduction

With the vigorous development of information technology, a new trade model of the Internet and cross-border e-commerce emerged [1]. Despite the challenges of the global epidemic and the international economy, China’s cross-border e-commerce industry has always maintained a healthy growth trend and played a vital role in the global trade supply chain [2]. China’s complete supply chain plays an important role in ensuring global supply. When the global economy enters the period of the normalization of the new coronavirus, China’s economy is also the first country in the global economy to recover [3]. Even in the face of the great changes in the Sino-US game and the international situation, and the international market is extremely unstable, China’s supply chain and industrial chain are still operating normally. It has become one of the most active and fastest growing national markets in the world, and its transaction scale has also ranked first in the world [4]. Cross-border e-commerce has the characteristics of short cycle, high communication efficiency, multi-frequency and data transparency, etc. Compared with traditional foreign trade, cross-border e-commerce has become the trend and direction of international trade development [5]. In view of the global competition of cross-border e-commerce enterprises and the diversification of customer demands, this paper proposes an improved BP neural network supply chain performance evaluation model under the cross-border e-commerce marketing chain, aiming to obtain the results of supply chain performance evaluation, and optimize and improve on this basis. The research content is divided into four parts. The first part is the introduction, which describes the Internet technology’s involvement in People’s Daily life under the background of the rapid development of science and technology. The second part is the literature review, the composition and realization of supply chain management and supply chain structure, and the research status of many scholars on this technology. In the first part of the third part, based on the selection and analysis of the supply chain performance evaluation index system, the evaluation index system conforming to the reality is constructed. The second section analyzes and improves the Back Propagation (BP) algorithm, and designs a cross-border e-commerce supply performance evaluation model based on artificial neural network (Levenberg Marquardt Back Propagation (LMB) algorithm. The fourth part is the performance test of the algorithm in the cross-border e-commerce supply chain performance evaluation model, and the application test of the cross-border e-commerce supply chain performance evaluation model.

2. Related works

The leading enterprises in modern SCs are mainly concentrated in developed countries, with multinational corporations leading the development direction of modern SCs. Many foreign scholars actively explore the essence of SC management and incorporate information technology into it, paying attention to its model construction and experimental analysis. Elia et al. investigated the driving factors of digital exports as a means for enterprises to leverage the opportunities brought by digital technology in B2C digital marketing activities. Using the dataset, it covers 102 Italian companies of different sizes active in three different industries. The research results indicate that companies that utilize digital technology are more likely to strengthen their digital exports, regardless of their size [6]. Zhou et al. conducted a systematic review of the supply chain management of cross-border e-commerce supported by blockchain through the data-driven analysis of literature metrology, and used VosViewer to visualize the collaboration relationship of the sampled literature and conduct a network co-word study. The research results show that blockchain technology has substantial applications in the field of cross-border e-commerce supply chain, in cross-border e-commerce platforms, supply chain operations, data governance and information management [7]. Steel has established a transnational relationship network to provide international products for online sales in Khartoum, expand the business scope, and sell their traditional perfume and cosmetics to the international public. The experiment shows that it has made innovative contributions to the development of information and communication technology, women’s entrepreneurship, and cross-border trade in the digital age [8]. Xu et al. [9] used the conbination of BP, particle swarm optimization and GA to explore the relationship between extraction requires and response values. The outcomes indicated that the model was more suitable for extraction and had better extraction indicator values, while the purified indicator values were the same. Zhang et al. put forward the concept of equilibrium state between elasticity and vulnerability of supply chain. In order to evaluate the equilibrium state of cross-border e-commerce supply chain, an evaluation model of the equilibrium state of cross-border e-commerce supply chain was constructed by combining fuzzy analytic hierarchy process (AHP) and fuzzy ideal solution similar preference ranking method. The results show the effectiveness of the model and keep elasticity and vulnerability in an appropriate state of balance, rather than pursuing high elasticity or low vulnerability without considering the others [10].

The SC revolved around the enterprise, from the processing of raw materials to the production, and from sales to purchasers. Mondal and Giri studied two return policies in the green e-commerce supply chain and constructed four decentralized models, designed a compensation-based profit-sharing contract to study channel coordination, analysis, and numerical studies for comparing and validating optimal decisions. The results show that replacement policies provide better results than refund policies, commissions are negatively correlated with manufacturer decisions and profits, and this study helps to identify the best return policies and improve channel performance through proper contract enforcement [11]. Negri et al. [12] developed a performance measurement system for major conflicts arising from a focus on efficiency and effectiveness. It evaluated the continuity and resilience performance of the SC, and clearly considered the time frame considered in these measurements. Zhang and Tian established a series of finite element models with different geometric features and hydrogen damage, and trained GA-BP neural networks for accurate and effective residual strength estimation considering hydrogen damage. The results indicate that hydrogen damage can alter the failure behavior of corroded pipelines and reduce their residual strength. The research results have certain reference value for further developing the integrity management of hydrogen transportation steel pipes [13]. Cavicchi and Vagnoni E used PMS to assess the contribution of CE partnerships to value chain sustainability, with case studies based on interviews with co-operative senior managers, supplemented by an analysis of external reports, relevant documents and direct observations. The study shows the role that PMS can play in tracking the contribution of eco-product partnerships to the sustainability of the wine value chain in value added [14]. Saha et al explore the impact of emerging technologies on supply chain performance in the context of the rise of the pharmaceutical industry, which was assessed through a survey of pharmaceutical companies in India. Manufacturing, distribution and consumption processes in the supply chain mediate the impact of emerging technologies on supply chain performance, and complex barriers weaken the mediating role. The results show that the interaction of emerging technologies in pharmaceutical supply chain performance has a positive effect [15].

To sum up, with the progress of The Times, the scope of supply chain performance evaluation of cross-border e-commerce is constantly expanding and enriching, and relevant applied studies are also increasingly mature, although most of these studies are still focused on the theoretical level. Therefore, for cross-border e-commerce, it is essential to effectively coordinate online and offline supply chain activities and realize the linkage between them. On this basis, the study will carry out in-depth exploration, and put forward the main idea of constructing a supply chain performance evaluation index system based on improved BP neural network, in order to simplify the complexity of supply chain management and enhance the survival and development ability of cross-border e-commerce.

3. Construction of a SCPE system under the CBEC marketing chain

In order to clearly define the cross-border e-commerce marketing chain and supply chain performance evaluation system, and build a set of practical evaluation standards [16]. At the same time, in order to better understand and use this evaluation system, in order to improve the competitiveness of cross-border e-commerce in the global market, improve its operation mode [17]. This chapter gives a detailed description of the core composition and operation process of the cross-border e-commerce marketing chain. Firstly, the definition and importance of cross-border e-commerce marketing chain are expounded. Secondly, the elements of cross-border e-commerce marketing chain are deeply studied. Based on empirical data and case analysis, the function and influence of each link are clarified, which lays a solid foundation for further analysis.

3.1 Construction of SC management and PMS

In the research field of cross-border e-commerce, economists continue to pay attention to a central question, whether the dominant force is the product itself or the market flow [18]. However, no matter which party is dominant, the importance of supply chain management is indisputable. Any company that wants to succeed in cross-border e-commerce must rely on an optimized supply chain management strategy and build its competitive advantage accordingly. Cross-border e-commerce supply chains include multiple links that meet customer needs, such as physical networks, inclusion carriers, entities, cycles, and systems. In order to achieve the maximum benefit of supply chain management, all the necessary elements such as inventory, logistics, customer relations, innovation and suppliers must be fully considered and integrated. The supply chain system of cross-border e-commerce can be broadly divided into three main parts: customer relationship management, integrated supply chain management and supplier relationship management. The system is shown in Fig. 1.

Figure 1.

Cross border e-commerce supply chain system.

Figure 1 shows the supply chain management system of cross-border e-commerce. Supply chain management covers a range of activities related to planning, organizing and monitoring supply chain efficiency. In the cross-border e-commerce environment, supply chain management puts more emphasis on process control, customer relationship management, and achieving win-win or multi-win profit indicators while pursuing interests. In addition, the management of inventory is gradually shifting to the detailed management of information. The evaluation of supply chain performance usually needs clear measurable indicators. Only in the evaluation process of these indicators can the output of supply chain performance be mastered more effectively. The supply chain performance evaluation process is shown in Fig. 2.

Figure 2.

Supply chain performance evaluation process.

Figure 2 displays a diagram of the SCPE process. Performance refers to an important tool in evaluating the completion of corporate goals and employee functions in an enterprise, which is a comprehensive indicator of performance and effectiveness. Under the guidance of evaluation objectives, it adjusts the evaluation model to achieve performance optimization. By calculating indicators, the coefficient of variation CV, also known as the standard deviation rate, can accurately measure the relative volatility of data. The expression for calculating the coefficient of variation is shown in Eq. (1).

$\displaystyle\textit{CV}=\frac{S}{V}$ (1)

In Eq. (1), $S$ means the standard error of the indicator value; $V$ denotes the average value of the indicator value, and CV ranges from 0 to 1. The SCPE is an important consideration for its effectiveness and implementation efficiency. The CBEC SC is a complex and challenging SC system, and building an objective and scientific CBEC SCPE system requires more scientific evaluation indicators. The performance EI system for CBEC SC determined in this study is shown in Fig. 3.

Figure 3.

A 6-level model for performance evaluation indicators of cross-border e-commerce supply chain.

The 6-level model of cross-border e-commerce supply chain performance evaluation index shown in Fig. 3 has become the core of this study due to its objectivity and scientificity. This index system is the result of simplifying and hierarchizing the complex system structure. The overall structure is analyzed by the principle of correlation matrix in order to understand complex systems. In this 6-level hierarchical structure, there are the following subdivisions: the initial layer is the overall performance of the supply chain, and the second layer corresponds to the core operational elements of the supply chain, such as order processing, inventory control and delivery performance. The third layer is the key capability indicator, which includes the flexibility, response speed and accuracy of the supply chain. The fourth layer shows the key operational processes in practice, such as logistics, information sharing and service. The next layer is strategic advantage metrics such as customer satisfaction, operational efficiency, and so on. Finally, the sixth layer shows the final performance outputs, such as cost, quality and speed of delivery. The subdivision system of the supply chain is the link through the whole system, which not only directly affects the supply chain performance, but also affects the whole system through the interaction between different levels. The final reachable matrix of the indicator is calculated from the adjacent order matrix, and the Boolean algebra calculation is performed on the matrix $\textit{AM}+I$ ( $I$ is the unit matrix). The final reachable matrix is shown in Eq. (2).

$\displaystyle\textit{RM}=(\textit{AM}+I)^{n}=(\textit{AM}+I)^{(n+1)}\neq(% \textit{AM}+I)$ (2)

In this way, a hierarchical structure diagram is constructed to depict the relationships between system elements. The structure of cross-border e-commerce supply chain performance indicators constructed in this study is a 6-level hierarchical structure, and the key indicators have a clear interaction relationship, and the size and direction of influence are also clearly displayed. For example, in this evaluation system, information sharing has a very large influence on the overall supply chain performance, and positively affects its performance. This provides a clearer reference for cross-border e-commerce enterprises when judging and optimizing supply chain performance. This layered and multi-angle evaluation helps all kinds of e-commerce enterprises better understand and improve their supply chain performance.

3.2 Optimization and improvement of BP algorithm

Neural network is a kind of model that imitates the characteristics of human biological neural network [19]. It simulates the working mode of human brain neurons by using artificial neurons to realize the simulation of information processing. The network is composed of multiple layers of neurons to complete a global task, which is not only adaptive, but also has strong fault tolerance. Based on this, BP neural network is a typical learning algorithm, which has the ability of self-learning. The weight is adjusted by gradient descending method, so as to reduce the total error of the network. However, there are some limitations when dealing with complex problems, especially in large-scale problems, you may fall into local optimal solutions, and the learning speed is slow. Therefore, it is combined with LM algorithm to improve the accuracy and efficiency of the algorithm by taking advantage of BP algorithm’s automatic learning and weight adjustment and LM algorithm’s high-speed learning and global search characteristics. Evaluate and optimize the supply chain performance of cross-border e-commerce, thereby reducing the total error of the network. The structure of the BP is expressed in Fig. 4.

Figure 4.

BP neural network structure.

In the forward propagation of the BP algorithm, a non zero initial weight value is set by inputting sample data to complete the initialization of the BP [20]. Then it calculates the net input and output in the hidden and output layer matrices in sequence, and finally calculates the output layer error based on this. It processes layer by layer to achieve the desired level of error. Under BP algorithm, $u_{i}^{k}$ means the input; $O_{t}^{k}$ denotes the target output vector; $N_{t}$ expresses the output layer unit output vector; $v_{jt}$ indicates the output layer connection weight; $r_{t}$ means the threshold; $w_{ij}$ expresses the weight correction; $\theta_{j}$ indicates the threshold correction. Sigmoid function is used to calculate the output $h_{j}$ , $\alpha$ and $\beta$ of the hidden layer as the learning rate. The response function of the BP network is shown in Eq. (3).

$\displaystyle f(x)=\frac{1}{1+e^{-x}}$ (3)

The error of the output layer is shown in Eq. (4).

$\displaystyle d_{t}^{k}=(O_{t}^{k}-N_{t})*N_{t}(1-N_{t})$ (4)

The errors of each unit in the middle layer are shown in Eq. (5).

$\displaystyle e_{j}^{k}=\left[{\sum_{t=1}^{q}{d_{t}*v_{jt}}}\right]*h_{j}(1-h_% {j})$ (5)

In addition, the weight $v_{jt}$ and threshold $r_{t}$ of the nodes connecting the hidden and output layers are shown in Eq. (6).

$\displaystyle\left\{{\begin{array}[]{l}v_{jt}(N+1)=v_{jt}(N)+\alpha*d_{t}^{k}*% h_{j}\\ r_{t}(N+1)=v_{jt}(N)+\alpha*d_{t}^{k}\\ \end{array}}\right.$ (6)

The weight correction quantity $w_{ij}$ and threshold correction quantity $\theta_{j}$ are shown in Eq. (7).

$\displaystyle\left\{{\begin{array}[]{l}w_{ij}(N+1)=w_{ij}(N)+\beta*e_{j}^{k}*u% _{i}^{k}\\ \theta_{j}(N+1)=\theta_{j}(N)+\beta*e_{j}^{k}\\ \end{array}}\right.$ (7)

When using gradient steepest descent method, the BP algorithm automatically converges when the mean squared error (MSE) of the selected input iteration meets the target accuracy when the learning speed is not large. Combining BP algorithm with LM algorithm, the LMBP algorithm can not only maintain the convergence characteristics, but also have the rate of convergence of Gauss Newton’s method. The LMBP algorithm structure is shown in Fig. 5.

Figure 5.

LMBP neural network structure.

The LMBP algorithm shown in Fig. 5 focuses on the weight update, which can effectively improve its rate of convergence while possessing the characteristics of gradient steepest descent method. The weight update expression under the Newton’s method is shown in Eq. (8).

$\displaystyle w_{k+1}=w_{k}-H_{k}^{-1}g_{k}$ (8)

In Eq. (8), $g$ means the gradient of the MSE function. Under the Gauss Newton’s method, the weight update expression is shown in Eq. (9).

$\displaystyle w_{k+1}=w_{k}-(J_{{}^{k}}^{T}J_{k})^{-1}J_{k}e_{k}$ (9)

In Eq. (9), $e_{k}$ denotes the error vector. The rate of convergence of this method is fast. In the LMBP algorithm, N and M mean the amount of input and output nodes, respectively; $j^{\text{th}}$ and represent the hidden and input layer units, respectively; $\textit{net}_{pj}$ and $x_{pi}$ refer to the input value of the hidden and input layers, respectively; $w_{ji}$ and $w_{jo}$ denote the weight and threshold, respectively; $g(\textit{net}_{pj})$ stands for the hidden layer’s excitation function; $W_{ko}$ expresses the $k$ layer’s threshold; y and $\hat{y}$ are the target and network outputs, respectively; $\hat{y}_{pk}$ means the $k^{th}$ ’s target output; $\eta$ means the learning rate. The sum of the MSE of the LMBP algorithm is shown in Eq. (10).

$\displaystyle E=\frac{1}{2}\sum_{p=1}^{N}\sum_{k=1}^{M}(y_{pk}-\hat{y}_{pk})$ (10)

In addition, the input value of the hidden layer is shown in Eq. (11).

$\displaystyle\textit{net}_{pj}=\sum_{j=0}^{N}{w_{jt}x_{pj}+w_{jo}}$ (11)

In Eq. (11), $w_{ji}$ represents the weight value, $x_{pi}$ is the value of the input layer unit, $w_{jo}$ is the threshold value.The excitation function of the hidden layer is shown in Eq. (12).

$\displaystyle g(\textit{net}_{pj})=1/(1+e^{-\textit{net}_{pj}})$ (12)

In Eq. (12), $\textit{net}_{pj}$ is the input value of the hidden layer, $\hat{y}_{pk}$ the expression of the target output is shown in Eq. (13).

$\displaystyle\left\{{\begin{array}[]{l}\textit{net}_{pk}=\sum\nolimits_{j=0}^{% M}{w_{kj}g(\textit{net}_{pj})+w_{ko}}\\ \hat{y}_{pk}=g(\textit{net}_{pk})\\ \end{array}}\right.$ (13)

In Eq. (13), $\textit{net}_{pj}$ is the input value of the hidden layer, $w_{kj}$ represents the weight update, $w_{ko}$ is the threshold value of layer $k$ , $g(\textit{net}_{pj})$ is the excitation function of the hidden layer, $\hat{y}_{pk}$ is the target output of $k^{th}$ , $g(\textit{net}_{pk})$ represents the excitation function of the output layer, the weight update formula is shown in Eq. (14).

$\displaystyle\Delta W_{kj}=-\left[{H+\mu I}\right]^{-1}J^{T}e$ (14)

In Eq. (14), $I$ is the identity matrix, $\mu$ is the identity, $J^{T}e$ matrix represents the second derivative, $H$ represents the second derivative. The updating of weights makes the learning of neural network more stable and fast, and it can also adapt to a large amount of computation. And in the process of modeling, the larger the amount of data, the more accurate the modeling. It is mainly divided into three parts: collecting and repairing data, using LMBP algorithm for data training and learning, and analyzing training results and optimizing performance plans. The performance evaluation model of the CBEC SC is shown in Fig. 6.

Figure 6.

A performance evaluation model for cross border e-commerce supply chain based on LMBP.

The three key stages of the cross-border e-commerce supply chain performance model are depicted in Fig. 6, which aims to provide a scientific and innovative evaluation method and become an important reference tool for studying cross-border e-commerce supply chain performance. First of all, in the collection and processing of data, including the collection of relevant business operation data, sorting out meaningful information, calculating all kinds of data needed for evaluation indicators, to ensure the accuracy and integrity of data. Secondly, the sorted data is used in depth, and the data is calculated based on the model. The performance indicators are quantitatively calculated through mathematical methods and models, and the feedback and adjustment of the training model are carried out according to the previous calculation results. Finally, the model is iterated by using the output of the model, analyzing and processing the results obtained in the early training. Record constantly updated weights, analyze the good and bad performance differences in evaluation indicators, and conduct in-depth analysis of performance gaps to optimize and improve supply chain performance. It can be seen that this model builds a comprehensive and hierarchical process, provides a set of scientific guidance for understanding and improving the performance of cross-border e-commerce supply chain, and brings powerful academic help for the study of this field, with a reference value that cannot be underestimated.

4. Validation and test of cross-border e-commerce supply chain performance evaluation model based on LMBP algorithm

In the current global business environment, an efficient supply chain performance evaluation model is crucial for cross-border e-commerce platforms. The actual effectiveness of LMBP-based cross-border e-commerce supply chain performance evaluation model was thoroughly verified and tested. To this end, a series of experiments are designed to thoroughly understand the applicability, advantages and disadvantages of this LMBP-based evaluation model in the real business environment. It aims to improve the predictive accuracy of the model to achieve supply chain optimization, so as to better meet the challenges of global cross-border e-commerce operations.

4.1 Algorithm performance test of cross-border e-commerce supply chain performance evaluation model

The research focuses on the performance difference between LMBP model and BP model. During the study, 30 groups of sample data were randomly selected, and the Relative Error (RE) between the expected output and the actual output of the model was calculated to conduct in-depth comparative analysis on the performance of the two models. The performance of the two algorithms is tested, and the comparison results are shown in Fig. 7.

Figure 7.

The relative error result between the expected output and the actual output of the model.

It can be seen from Fig. 7(a) that the expected and actual output RE of LMBP, among which the highest RE appeared in sample No. 5 with a value of 6.23%, the lowest RE appeared in sample No. 1 with a value of 1.78%, the difference between the upper and lower limits was 4.45%, and the average relative error was 3.26%. Figure 7(b) shows the RE results evaluated by BP. The highest RE appeared in sample No. 8, with a value of 16.11%; the lowest RE appeared in sample No. 26, with a value of 4.57%; the difference between the upper and lower limits was 11.54%; and the average relative error was 10.23%. On the whole, the average relative error between the expected output and actual output of LMBP is lower, and the difference between the upper and lower limits of the expected output of LMBP is lower. It is proved that LMBP has better control effect on desired output than BP, and has higher accuracy and stability. Under the optimal preset parameters, the comparison between LMBP and BP evaluation value and the real value is shown in Fig. 8.

Figure 8.

Comparison of the estimated values of different data sets with the true values under optimal preset parameters.

The 50 groups of data selected in Fig. 8 are the same as those in Fig. 8, and their true evaluation value is 66.89 points. Under the optimal preset parameters, the average evaluation score of the output of BP evaluation model is 69.99, and the average evaluation score of LMBP evaluation model is 67.06. In contrast, there was a 3.1% difference in the BP model and a 0.17% difference in the LMBP model. It is verified that the optimization of BP model by LM algorithm can significantly improve the accuracy of performance evaluation of cross-border e-commerce supply chain, and the difference is reduced by 89.99%. On the whole, under the optimal preset parameters, both BP and LMBP are closer to the true value, but compared with BP, LMBP is closer to the true value. In addition, FABP’s test results for each set of data are still more consistent. The accuracy and stability of LMBP were verified. In order to further investigate the optimal fitness value of LMBP model and BP model in the number of iterations, the results are shown in Fig. 9.

Figure 9.

Iterative optimal fitness value of BP algorithm and LMBP algorithm.

As can be seen from Fig. 9, the adaptation values of LMBP algorithm and BP algorithm gradually become stable with the increase of the number of iterations. When the LMBP algorithm is iterated to 559 times, the adaptation value gradually becomes stable. When BP algorithm is iterated to 751 times, the adaptation value gradually becomes stable. It can be seen that the optimization of BP model by LM algorithm has significantly increased the fitness of performance evaluation of cross-border e-commerce supply chain. Compared with BP algorithm, LMBP algorithm can iterate to the best value faster. In addition, during the testing process, the test results of LMBP algorithm tend to be stable earlier, which greatly saves time cost and verifies the accuracy and stability of LMBP.

4.2 Application test of cross-border e-commerce supply chain performance evaluation model

Under the test of the cross-border e-commerce supply chain performance evaluation model based on LMBP algorithm, the selection, processing and analysis of data are the verification of the scientificity and objectivity of the model. This study selected the data of a large cross-border e-commerce enterprise in 2022 for research. The data before and after processing under this model are displayed for comparative analysis. In order to verify the application effect of the model designed in this study in real life, as well as the accuracy and effectiveness of the model. Under this model, the results of data processing and analysis are shown in Table 1.

Table 1
Data processing and analysis of the company’s cross-border e-commerce supply chain in 2020

Month	Serviceability		Supplier		Supply chain
	Before treatment	After treatment	Before treatment	After treatment	Before treatment	After treatment
January	97%	98%	28.69%	27.69%	0.36%	0.47%
February	98%	98%	14.56%	16.89%	0.25%	0.75%
March	96%	97%	13.31%	12.77%	0.64%	0.51%
April	97%	99%	16.59%	18.99%	0.64%	0.83%
May	95%	96%	17.32%	16.61%	0.38%	0.67%
June	96%	98%	11.63%	16.03%	0.37%	0.42%
July	98%	97%	17.65%	17.79%	0.65%	0.84%
August	96%	98%	13.74%	18.39%	0.72%	0.64%
September	98%	99%	19.96%	19.57%	0.69%	0.64%
October	97%	99%	20.63%	21.93%	0.81%	0.67%
November	97%	98%	34.62%	33.11%	0.83%	0.89%
December	98%	97%	27.76%	28.25%	0.79%	0.89%

Table 1 shows the company’s cross-border e-commerce supply chain data in 2017, which consists of three data: supplier, cross-border e-commerce service capability and supply chain. Each set of data is compared before processing and after processing under this model. It can be seen from Table 1 that under the performance evaluation model of cross-border e-commerce supply chain based on LMBP algorithm. The company’s cross-border e-commerce service capability has increased by about 2% every month, the supplier data has increased by about 0.85% every month, and the supply chain data has increased by about 0.2% every month. It can be seen that this model can effectively improve the performance evaluation of supply chain. The determination of the number of hidden layers and the number of nodes requires comprehensive consideration of the number of nodes in the input layer and the output layer, and adjustment based on the actual situation, which is the focus of LMBP algorithm. The result of determining the maximum number of holiday points in the hidden layer is shown in Fig. 10.

Figure 10.

The relationship curve between the number of hidden layer and output layer nodes and mean square error.

Figure 10 shows the relationship curve between the number of hidden layers and the number of nodes and the mean square error. The number of nodes in the hidden layer is the number of neurons. While ensuring sufficient number, excessive number of nodes should also be avoided. Excessive number of nodes will cause excessive calculation and overfitting. In order to determine the optimal number of layers and nodes of the hidden layer, the mean square error of the training prediction results is referred to. The selected 12-month data is trained to continuously increase the number of layers and nodes of the hidden layer, and the data is repeatedly trained to obtain the best number of layers and nodes of the hidden layer. As can be seen from Fig. 10, in the data of this year, when the optimal number of hidden layers is 12, the mean square error value of the training prediction result is the smallest; when the most festival point value of the hidden layer is 16, the mean square error value of the training prediction result is the smallest. In order to reduce the impact of initial parameters on the model, the same population size and number of iterations were set in this experiment. After several iterations, the comparison between the evaluation value and the real value of BP model and LMBP model is shown in Fig. 11.

Figure 11.

The comparison between the assessed value and the real value of different data sets.

As can be seen from Fig. 11, the true value of 50 groups of supply chain performance evaluation indicators is 66.89 points. The average evaluation score of BP evaluation model output is 73.12 points; The average evaluation score of LMBP evaluation model output was 67.76. In contrast, there was a 6.23% difference in the BP model and a 0.87% difference in the LMBP model. It is verified that the optimization of BP model by LM algorithm significantly improves the accuracy of performance evaluation of cross-border e-commerce supply chain, and the difference is reduced by 81.03%. On the whole, compared with BP, LMBP is closer to the true value. In addition, the test results of LMBP for each group of data are more stable, and there are rarely large differences, which verifies the accuracy and stability of LMBP.

5. Conclusion

With the rapid development of information technology, cross-border e-commerce occupies the stage with its advantages in the foreign trade market and has made contributions to the development of international trade. In this paper, a supply chain evaluation model based on LMBP neural network is proposed based on the weight determination method of supply chain performance indicators and the automatic updating weight method of BP neural network algorithm. Under the best conditions, the number of hidden layers is 12, the number of nodes is 16, and the minimum mean square error value is obtained, which has the ability to optimize the performance of the supply chain. Compared with BP model, it shows better control effect and accuracy. For example, in the optimal preset parameters, the difference is only 0.17%, which is significantly better than 3.1% in BP model. At the same time, LMBP showed an average relative error of 2.11%, which was more stable and accurate than BP’s 6.78%. It can be seen that LMBP can effectively improve supply chain performance, and the objectivity of its weight and the accuracy of its prediction results have been verified by experiments, which has a significant impact on the evaluation method system of cross-border e-commerce supply chain. However, due to the limitation of the study sample, more practice verification is needed for full applicability.

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The improved BP neural network supply chain performance evaluation model under the cross-border e-commerce marketing chain

Abstract

Keywords

1. Introduction

2. Related works

3. Construction of a SCPE system under the CBEC marketing chain

3.1 Construction of SC management and PMS

4.1 Algorithm performance test of cross-border e-commerce supply chain performance evaluation model

Table 1 Data processing and analysis of the company’s cross-border e-commerce supply chain in 2020

References

Table 1
Data processing and analysis of the company’s cross-border e-commerce supply chain in 2020