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Optimization algorithm and simulation of supply chain coordination based on crossborder Ecommerce network platform
EURASIP Journal on Wireless Communications and Networking volumeÂ 2021, ArticleÂ number:Â 23 (2021)
Abstract
With the rapid development of crossborder ecommerce, the improvement of consumer satisfaction has become the focus of crossborder ecommerce platform optimization. Relying on advanced algorithm technology, it can realize the accurate and efficient matching between massive information and users, which is conducive to improving the user experience. Based on the consideration of consumer satisfaction, this paper constructs a dual channel supply chain composed of crossborder suppliers, crossborder ecommerce enterprises, retailers and consumers and studies the revenue and cost sharing contract of the supply chain under the conditions of centralized decision and decentralized decision. The research shows that crossborder ecommerce enterprises can choose to form revenue and expenditure sharing contracts through online and offline channels, optimize decentralized decisionmaking, and achieve winâ€“win cooperation among supply chain entities.
1 Introduction
With the support of national policies and the promotion of Internet technology, crossborder ecommerce industry has contributed an important force to China's economic growth. China's crossborder ecommerce enterprises are growing rapidly and the market scale is expanding continuously. In 2019, more than 6000 crossborder ecommerce enterprises have been added, with 300 million packages being sent to the world, and the total import and export volume of crossborder ecommerce has reached 186.21 billion yuan. Crossborder ecommerce has gradually become an important part of foreign trade. However, the development of crossborder ecommerce is still faced with the problems of slow logistics, high price and difficulty for users to directly contact products, which has affected consumer satisfaction. Therefore, we can improve consumer satisfaction, improve enterprise profits and achieve winâ€“win cooperation through online and offline channels.
From the perspective of crossborder ecommerce, in the context of the development of Internet technology and economic globalization, crossborder ecommerce has gradually penetrated into all aspects of social life. Under the background of big data, considering the personalized needs of customers, Li Jiahua studied the intelligent recommendation algorithm of crossborder ecommerce shopping guide platform through big data technology [1]. In order to solve the problem of privacy leakage in gene research, Wu Xiang et al. proposed a motif search algorithm, which can protect privacy and obtain highquality model results [2]. Liang Haibo et al. used the improved genetic algorithm to optimize the traditional controller and proved the superiority of the method by comparing the model of the traditional controller with the optimized controller [3]. Under the background of the development of artificial intelligence, Chen Zhijun and others know the driver's driving state through unsupervised road test [4]. Zheng Haifeng and others proposed a data relay scheme to improve the performance of wireless sensor networks [5]. Liu Dingrui et al. take overseas manufacturers and crossborder manufacturers as research objects and take the service level and product perceived value of offline and online channels as key indicators to analyze the optimal decisionmaking and profit change of each member of the dual channel supply chain [6]. Based on the establishment of trade gravity model, Zhao Y N analyzes the factors influencing the cooperation between other countries and China [7]. Wu Xiang et al. use natural language processing (NLP) technology and grey relational analysis (GRA) to improve the performance and resource utilization of applications [8]. Considering the competition and cooperation between upstream and downstream enterprises, Liu Zheng et al. studied how to use the responsibility sharing and resource sharing among enterprises to manage the carbon emission of supply chain [9]. Liang Haibo et al. applied artificial intelligence to oil drilling leakage cases and proposed an algorithm based on PSOSVR to dynamically evaluate the risk in the drilling process [10].
From the perspective of algorithm optimization, relying on cloud computing, big data, artificial intelligence and other advanced technologies, it can realize the accurate and efficient matching between massive information and crossborder ecommerce users, which is conducive to improving the user experience. According to the trajectory of human behavior, we can observe people's movement. In order to ensure public safety, Chen Zhijun and others proposed a method that can automatically identify the trajectory of pedestrian behavior to reduce the workload of monitoring work [11]. Based on association rules, Yang Hongyan et al. track the consumer satisfaction data of a province and analyze the change trend of consumer satisfaction and the factors that affect these changes [12]. Liu Zheng and others used the bus simulation data to design the bus pricing model to improve the company's profit and customer satisfaction [13]. Ma Fengcai et al. used the review information of Jingdong ecommerce platform, selected logistics speed, product packaging, service quality and product price as key indicators to study the overall situation of customer satisfaction with fresh products [14]. Xiong N et al. analyzed and summarized the networkbased GCC scheme by combing the background of green cloud computing [15]. SEO et al. conducted a questionnaire survey on consumers to study the influence of the image of imported products and wordofmouth on consumer satisfaction and purchase intention and evaluated the influence of familiarity on consumer satisfaction and purchase intention [16]. Based on the probability model, Zhang Mingyang et al. evaluated the human error in ship navigation and reduced the probability of risk occurrence [17]. Guo Wenzhong et al. have developed an algorithm that can schedule tasks in wireless sensor networks, and its effectiveness has been proved by simulation [18].
From the perspective of supply chain coordination, with the changes of consumers' requirements for product quality and time, how to design a scientific coordination mechanism for the supply chain is a problem that enterprises need to solve [19]. Taking the channel disputes caused by customers' delivery time requirements into account, Xu Fei et al. established an optimization model for the cooperation between manufacturers and retailers with different delivery dates and designed a scheme for online and offline channel optimization and coordination [20]. Shu et al. constructed a supply chain composed of manufacturers and online retailers and considered the logistics service and product price under the condition of whether they cooperated or not, and realized the supply chain coordination through contract [21]. Taking the twolevel supply chain composed of suppliers and retailers as the research object, Li Yanbing et al. analyzed the optimal decisionmaking under the conditions of centralized decisionmaking, decentralized decisionmaking and repurchase contract and conceived a coordination optimization method of repurchase contract considering cost profit rate [22]. Ma Xueli et al. constructed a threelevel supply chain composed of farmers, logistics suppliers and retailers. Taking agricultural products as the research object, they conceived coordination contracts to realize the income balance of supply chain members [23]. Liu Zheng et al. studied the optimization of supply chain through the comparison of optimal decisions and met the requirements of carbon emission and profit of enterprises [24]. Based on the uncertainty of retailers' demand and risk attitude, HĂŞriĹźGolpĂ®ra et al. designed a profitoriented contract and considered the coordination problem of power supply chain by using newsboy model [25].
After literature review on crossborder ecommerce, consumer satisfaction and supply chain coordination, we can see that crossborder ecommerce is closely related to consumer satisfaction, and consumer satisfaction is an important factor to evaluate crossborder ecommerce enterprises [26,27,28]. However, few literature can consider improving consumer satisfaction from the perspective of crossborder ecommerce supply chain coordination [29,30,31,32]. Through the coordination of online and offline channels of crossborder ecommerce enterprises, it not only brings better consumer experience, improves consumer satisfaction, but also improves the profits of the main body of the supply chain [33,34,35]. From the perspective of consumer satisfaction, this paper considers the coordination and optimization between online and offline channels in the supply chain of crossborder ecommerce enterprises [36,37,38,39].
The remainder of this paper is organized as follows: the hypothesis and basic decisionmaking model under the constraint of the carbon tax are introduced in Sect.Â 2 and Sect.Â 3. Experimental results are presented in Sect.Â 4 and Conclusions are drawn in the last section.
2 Related work
2.1 Model hypothesis
Taking the supply chain of crossborder ecommerce enterprises as the research object, this paper constructs a dual channel supply chain composed of crossborder suppliers, crossborder ecommerce enterprises, overseas retailers and overseas consumers, as shown in Fig.Â 1. Based on consumers' satisfaction with products, this paper analyzes and compares the optimal decisionmaking of supply chain in three situations: decentralized decisionmaking centralized decisionmaking and revenue and cost sharing contract, with online channel as the leading factor. This paper aims to study the following problems:

1.
The game models of centralized decisionmaking, decentralized decisionmaking and revenue and cost sharing contract are established, and the optimal decisionmaking under different modes is compared, and the optimal way is selected to coordinate the crossborder ecommerce supply chain [40,41,42].

2.
We should improve consumers' satisfaction with products, improve their online and offline consumption experience, establish brand image, improve product competitiveness and attract consumers to become loyal users of crossborder products [43,44,45,46].

3.
One of the purposes of supply chain coordination of crossborder ecommerce enterprises is to improve the overall profit of the supply chain. By comparing the profits of the supply chain system under different modes, the most suitable mode of supply chain optimization is selected [47,48,49,50].
2.2 Parameters description
In Table 1, we can see affected by the estimated utility of products, product price and logistics speed, it can be assumed that the consumer satisfaction function of online channels is \(S_{1} = \alpha \lambda  P1  \eta T\). When overseas consumers purchase products through offline channels, they can directly contact the products. At this time,\(\lambda = 1\), and not limited by the delivery time, but by the travel factors of consumers, resulting in travel and time costs, the consumer satisfaction function of offline channels is \(S_{2} = \alpha  P2  \beta\). If the consumer's offline product satisfaction is greater than the online product satisfaction, there is \(S_{1} < S_{2}\), consumers choose offline channel to purchase products. If the consumer's offline product satisfaction is less than the online product satisfaction, there is \(S_{1} > S_{2}\), consumers choose online channel to purchase products. \(\alpha_{1}\) is used to represent the estimated utility value (critical value) when the online channel customer satisfaction is zero, \(\alpha_{1} = \frac{P1 + \eta T}{\lambda }\), \(\alpha_{2}\) is the estimated utility value (critical value) when the offline channel consumer satisfaction is 0, \(\alpha_{2} = P2 + \beta\), and \(\alpha_{3}\) is the estimated utility value when the online and offline channel satisfaction is equal, \(\alpha_{3} = \frac{P2 + \beta  P1  \eta T}{{1  \lambda }}\). In order to ensure the existence of dual channels, we only consider the case of \(\alpha_{1} < \alpha_{2} < \alpha_{2}\), that is, when \(P2 > \frac{P1 + \eta T}{\lambda }  \beta\), because the estimated utility a of the consumer to the product obeys (0,1) uniform distribution, we can get that the demand of crossborder products of online and offline channels is \(Q_{1} = \int_{{\alpha_{1} }}^{{\alpha_{3} }} {1\text{d}x = } \frac{P2 + \beta  P1  \eta T}{{1  \lambda }}  \frac{P1 + \eta T}{\lambda }\), \(Q_{2} = \int_{{\alpha_{3} }}^{1} 1 \text{d}x = 1  \frac{P2 + \beta  P1  \eta T}{{1  \lambda }}\), respectively. In addition, it is assumed that the costs of customs duties and late penalties generated in the online circulation of crossborder products per unit are \(c_{1} = a + (t  T)b\). In the process of offline sales, the storage cost and staff service cost are \(c_{2} = \frac{{k\beta^{2} }}{2}\).
2.3 Basic operation mode of crossborder ecommerce dualchannel supply chain
2.3.1 Centralized decision mode
Under centralized decisionmaking, the online and offline channels of crossborder ecommerce cooperate. At this time, the profit function \(\pi_{sc}\) of the whole supply chain system can be obtained.
The firstorder and secondorder partial derivatives of online channel price \(P1\), offline channel price \(P2\) and planned arrival time \(T\) of crossborder ecommerce are obtained from Eq.Â (1): \(\frac{{\partial^{2} \pi_{sc} }}{{\partial P1^{2} }} = \frac{2}{\lambda (\lambda  1)}\), \(\frac{{\partial^{2} \pi_{sc} }}{{\partial P2^{2} }} = \frac{2}{\lambda  1}\), \(\frac{{\partial^{2} \pi_{sc} }}{{\partial T^{2} }} = \frac{2b\eta }{{\lambda (\lambda  1)}}\), \(\frac{{\partial^{2} \pi_{sc} }}{\partial P2\partial P1} = \frac{{\partial^{2} \pi_{sc} }}{\partial P1\partial P2} =  \frac{2}{\lambda  1}\), \(\frac{{\partial^{2} \pi_{sc} }}{\partial P2\partial T} = \frac{{\partial^{2} \pi_{sc} }}{\partial T\partial P2} =  \frac{b + \eta }{{\lambda  1}}\), \(\frac{{\partial^{2} \pi_{sc} }}{\partial T\partial P1} = \frac{{\partial^{2} \pi_{sc} }}{\partial P1\partial T} = \frac{b + \eta }{{\lambda (\lambda  1)}}\). Based on this, we can get that the profit of supply chain system is a strictly concave function about \(P1\), \(P2\) and \(T\). According to the order of the function \(H_{1} = \frac{2}{\lambda (\lambda  1)} < 0\), \(H_{2} = \frac{4}{\lambda (1  \lambda )} > 0\), \(H =  \frac{8b\eta }{{\lambda^{2} (\lambda  1)^{2} }} < 0\), Hess are negative qualitative, so there is a unique solution to the function. By solving the firstorder partial derivative equations of online channel price \(P1\), offline channel price \(P2\) and planned arrival time of crossborder ecommerce \(T\), we can get the following results:
2.3.2 Decentralized decision mode
Under decentralized decisionmaking, the online and offline channels of crossborder ecommerce pursue their own profit maximization. At this time, the profit functions \(\pi_{1}\) and \(\pi_{2}\) of online and offline channels can be obtained, respectively.
Lemma 1
Under decentralized decisionmaking, the online and offline product prices, demand, consumer satisfaction and total profit of crossborder ecommerce lines are, respectively, \(P1^{N}\), \(P2^{N}\), \(T^{N}\), \(S_{1}^{N}\), \(S_{2}^{N}\), \(\pi_{sc}^{N}\).
Prove
The online channel of crossborder ecommerce enterprises, as the leading party, first defines the price \(P1^{N}\) and the prescribed arrival time of products \(T^{N}\), and then uses the reverse induction method to obtain \(P2^{N} = \frac{{k\beta^{2}  2\beta + 2P1^{N}  2\lambda + 2w + 2T^{N} \eta + 2}}{4}\). By substituting the obtained function expression about \(P2^{N}\) into Eq.Â (9), we can get new functional expressions about \(P1^{N}\) and \(T^{N}\). We can get the first and second partial derivatives of the two variables in the formula to get the determinant of Hess matrix. Because of \(\frac{{\partial^{2} \pi_{1} }}{{\partial (P1^{N} )^{2} }} = \frac{2  \lambda }{{\lambda (\lambda  1)}} < 0\), the online price \(P1^{N}\) and the required arrival time of the product \(T^{N}\) have unique solutions. Through the calculation of simultaneous equations, we can get the online price \(P1^{N}\) and the product arrival time \(T^{N}\), and then get the offline channel price \(P2^{N}\), the online and offline channel consumer satisfaction \(S_{1}^{N}\) and \(S_{2}^{N}\), and the online and offline channel total profit \(\pi_{sc}^{N}\). The results were as follows:
Lemma 2
Under decentralized decisionmaking, the offline channel product price, the prescribed arrival time, the online and offline channel consumer satisfaction and the supply chain system profit of crossborder ecommerce enterprises are lower than the optimal value under centralized decisionmaking. When \(\lambda > \frac{2\eta }{{b + \eta }}\), the online channel product price of crossborder ecommerce enterprises is greater than that under centralized decisionmaking.
Prove
According to the hypothesis of the model and the symbol setting \(\beta > 1\) in the symbol description part, \(k\beta^{2} + 2\beta + 2w  2 = k\beta^{2} + 2w + 2(\beta  1) > 0\) can be obtained. Through calculation, we compare the online product price, offline product price, prescribed arrival time, online channel consumer satisfaction, offline channel consumer satisfaction and supply chain system profit under decentralized and centralized decisionmaking. The results were as follows:
From the proof of Lemma 2, it can be found that under decentralized decisionmaking, the offline channel product price, the prescribed arrival time, the online and offline channel consumer satisfaction and the supply chain system profit of crossborder ecommerce enterprises are lower than the optimal value under centralized decisionmaking. However, through Eq.Â (16), it can be found that only when \(b\lambda  2\eta + \lambda \eta > 0\), that is \(\lambda > \frac{2\eta }{{b + \eta }}\), the online product price under decentralized decision is higher than that under centralized decision. Under the decentralized decisionmaking, the product price rises, but the prescribed arrival time of the product is prolonged, the consumer's satisfaction with the product decreases, and the profit of the whole supply chain system also decreases. This is because there is competition between online and offline channels under decentralized decisionmaking. In order to ensure product quality, infrastructure purchase and product storage increase product cost and price. When the online and offline channels cooperate, the basic cost is reduced, the logistics speed is accelerated, and the consumers can receive the products in time with lower price, and the overall profit is improved.
Lemma 3
Under decentralized and centralized decisionmaking, consumer satisfaction is affected by both the consumer experience and the estimated utility of the product. Under centralized decisionmaking, with the increase of consumers' experience of using products, the satisfaction of online and offline channels increases. With the increase of estimated utility of products, the satisfaction of consumers in online and offline channels will not be affected; in decentralized decisionmaking, with the increase of consumers' experience of using products, the satisfaction of both online and offline channels will increase with the increase of the estimated utility of products, the consumer satisfaction of online channel first increases and then decreases, while that of offline channel decreases.
Prove
The firstorder partial derivatives of \(S1\) and \(S1^{N}\) with respect to the estimated utility of the product and the consumer's experience of the product are obtained, respectively, and \(\frac{\partial S1}{{\partial \alpha }} = \lambda > 0\),\(\frac{\partial S1}{{\partial \lambda }} = \frac{{4\alpha  2\beta  2w  k\beta^{2}  2}}{4} > 0\), \(\frac{{\partial S1^{N} }}{\partial \alpha } = \lambda > 0\), \(\frac{{\partial S1^{N} }}{\partial \lambda } = \frac{{4\alpha  2\beta + 4\lambda  2w  4\alpha \lambda  k\beta^{2} + \alpha \lambda^{2}  \lambda^{2}  2}}{{(\lambda  2)^{2} }}\) are obtained. Because we cannot distinguish the positive and negative of \(\frac{{\partial S1^{N} }}{\partial \lambda }\), we can get \(\frac{{\partial^{2} S1^{N} }}{{\partial \lambda^{2} }} = \frac{{2(k\beta^{2} + 2\beta + 2w  2)}}{{(\lambda  2)^{3} }} < 0\) by solving the second partial derivative. Therefore, affected by the estimated utility of products, the consumer satisfaction of online channels under centralized decisionmaking and decentralized decisionmaking is on the rise; affected by the use experience of consumers on products, the consumer satisfaction of online channels under centralized decisionmaking is increasing, while that of online channels under decentralized decisionmaking first rises and then decreases. We obtain the firstorder partial derivatives of \(S2\) and \(S2^{N}\) with respect to the estimated utility of the product and the consumer's experience of the product, respectively, and obtain \(\frac{\partial S2}{{\partial \alpha }} = \frac{{\partial S2^{N} }}{\partial \alpha } = 1\), \(\frac{\partial S2}{{\partial \lambda }} = 0\), \(\frac{{\partial S2^{N} }}{\partial \lambda } = \frac{{2  2\beta  2w  k\beta^{2} }}{{2(\lambda  2)^{2} }} < 0\). Therefore, affected by the estimated utility of products, the consumer satisfaction of online channels under centralized decisionmaking and decentralized decisionmaking shows an upward trend; the consumer satisfaction of online channels under centralized decisionmaking is not affected by consumers' use experience of products, and the consumer satisfaction of online channels under decentralized decisionmaking continues to decrease under the influence of consumers' use experience of products.
3 Methods
Relying on cloud computing, big data, artificial intelligence and other advanced technologies, it can realize the accurate and efficient matching between massive information and users, improve the service quality of crossborder ecommerce enterprises and improve the user experience. When the online and offline channels of crossborder ecommerce enterprises cooperate in the form of revenue and expense sharing contract, it is assumed that the online channel shares part of the cost for the offline channel, and the sharing proportion is \(\theta\). Meanwhile, the offline channel can share part of its revenue to the online channel, and the sharing proportion is \(z\). At this time, the profit functions of the online channel and the offline channel are obtained as follows:
Lemma 4
If the online and offline channels of crossborder ecommerce enterprises cooperate in the form of revenue and cost sharing contract, the decisionmaking combination of online and offline channels is \((P1^{Y} ,P2^{Y} ,T^{Y} )\), and the consumer satisfaction and profit of online and offline channels can be obtained as \(S1^{Y}\), \(S2^{Y}\), \(\pi_{1}^{Y}\), \(\pi_{2}^{Y}\).
Prove
When online channels and offline channels cooperate by contract, online and offline channels pursue their own profit maximization. The online channel of crossborder ecommerce determines the price of online products and the specified arrival time of products, and the offline channel determines the price of its offline products. The first and second partial derivatives of \(\pi_{1}^{Y}\) with respect to \(P1^{Y}\) and \(T^{Y}\) are obtained, and the first and second partial derivatives of \(\pi_{2}^{Y}\) with respect to \(P2^{Y}\) are obtained. We can get \(\frac{{\partial^{2} \pi_{1}^{Y} }}{{\partial (P1^{Y} )^{2} }} = \frac{2}{\lambda (\lambda  1)}\), \(\frac{{\partial^{2} \pi_{1}^{Y} }}{{\partial (T^{Y} )^{2} }} = 0\), \(\frac{{\partial^{2} \pi_{1}^{Y} }}{{\partial P_{1}^{Y} \partial T^{Y} }} = \frac{{\partial^{2} \pi_{1}^{Y} }}{{\partial T^{Y} \partial P_{1}^{Y} }} = \frac{\eta }{\lambda (\lambda  1)}\), \(\frac{{\partial^{2} \pi_{1}^{Y} }}{{\partial P_{1}^{Y} \partial P_{2}^{Y} }} = \frac{  (z + 1)}{{\lambda  1}}\), \(\frac{{\partial^{2} \pi_{1}^{Y} }}{{\partial T^{Y} \partial P_{2}^{Y} }} = \frac{  \eta z}{{\lambda  1}}\), \(\frac{{\partial^{2} \pi_{2}^{Y} }}{{\partial (P2^{Y} )^{2} }} = \frac{  2(z  1)}{{\lambda  1}}\), \(\frac{{\partial^{2} \pi_{2}^{Y} }}{{\partial P_{2}^{Y} \partial T^{Y} }} = \frac{\eta (z  1)}{{\lambda  1}}\), \(\frac{{\partial^{2} \pi_{2}^{Y} }}{{\partial P_{2}^{Y} \partial P_{1}^{Y} }} = \frac{z  1}{{\lambda  1}}\). Therefore, the Hess matrix of crossborder ecommerce dual channel profit function with respect to \(P1^{Y}\), \(T^{Y}\) and \(P2^{Y}\) is \(\left H \right = \left {\begin{array}{*{20}c} {\frac{2}{\lambda (\lambda  1)}} & {\frac{  (z + 1)}{{\lambda  1}}} & {\frac{\eta }{\lambda (\lambda  1)}} \\ {\frac{z  1}{{\lambda  1}}} & {\frac{  2(z  1)}{{\lambda  1}}} & {\frac{\eta (z  1)}{{\lambda  1}}} \\ {\frac{\eta }{\lambda (\lambda  1)}} & {\frac{  \eta z}{{\lambda  1}}} & 0 \\ \end{array} } \right\). According to the order principal subformula of the function \(H_{1} = \frac{2}{\lambda (\lambda  1)} < 0\), \(H_{2} = \frac{(1  z)(4  \lambda z  \lambda )}{{\lambda (1  \lambda )^{2} }} > 0\), \(H = \frac{\eta (z  1)(\lambda z + \lambda  4)}{{\lambda^{2} (\lambda  1)^{3} }} < 0\), it can be known that the Hessian matrix is negative definite, and the unique optimal solution of the function can be obtained by solving after judgment. By solving the firstorder partial derivative equations and taking the solution results into the response function of offline product price, the decision combination can be obtained as follows:
Lemma 5
After the cooperation in the form of revenue and cost sharing contract, when the contract cooperation satisfies \(z(1 + \frac{2w}{{k\beta^{2} }}) < \theta < \frac{\lambda (1  z)}{2} + z + \frac{\lambda (\beta + w  1)(1  z) + 2wz}{{k\beta^{2} }}\), there are \(P_{2}^{N} > P_{2}^{Y} > P_{2}\), \(T^{N} > T^{Y} > T\), \(\pi_{sc} > \pi_{sc}^{Y} > \pi_{sc}^{N}\), \(S_{1} > S_{1}^{Y} > S_{1}^{N}\), \(S_{2} > S_{2}^{Y} > S_{2}^{N}\).
Prove
When the contractual cooperation satisfies \(z(1 + \frac{2w}{{k\beta^{2} }}) < \theta < \frac{\lambda (1  z)}{2} + z + \frac{\lambda (\beta + w  1)(1  z) + 2wz}{{k\beta^{2} }}\) \(\left\{ \begin{gathered} k\theta \beta^{2}  2wz  kz\beta^{2} > 0 \hfill \\ \lambda (2  2\beta  2w  k\beta^{2} )(1  z) + 2(k\theta \beta^{2}  kz\beta^{2}  2wz) < 0 \hfill \\ \end{gathered} \right.\) can be obtained. And because of \(\begin{gathered} \lambda (2  2\beta  2w  k\beta^{2} )(1  z) + (k\theta \beta^{2}  kz\beta^{2}  2wz) = \lambda (2  2\beta  2w  k\beta^{2} )(1  z) \hfill \\ + 2(k\theta \beta^{2}  kz\beta^{2}  2wz)  (k\theta \beta^{2}  kz\beta^{2}  2wz) < 0 \hfill \\ \end{gathered}\), so \(P2  P2^{Y} = \frac{{\lambda (2  2\beta  2w  k\beta^{2} )(1  z) + (k\theta \beta^{2}  kz\beta^{2}  2wz)}}{4(\lambda  2)(z  1)} < 0\),\(P2^{Y}  P2^{N} = \frac{{k\theta \beta^{2}  kz\beta^{2}  2wz}}{2(\lambda  2)(1  z)} < 0\), \(P2^{Y}  P2^{N} = \frac{{k\theta \beta^{2}  kz\beta^{2}  2wz}}{2(\lambda  2)(1  z)} < 0\), \(P_{2}^{N} > P_{2}^{Y} > P_{2}\). At this time, by comparing the required arrival time of the product, it can be found that the product conforms to \(T^{Y}  T^{N} = \frac{{\lambda z(\lambda  1)[2\beta (z  1) + k\beta^{2} (\theta  1) + 2(1  w  z)]}}{{(\lambda  2)^{2} (z  1)(b  \eta )}} < 0\) and \(T  T^{Y} = \frac{\lambda (\lambda  1)}{{2(\lambda  2)^{2} (1  z)(b  \eta )}}[(2\beta + 2\lambda + 4w + 4z  2\lambda \beta  4z\beta  k\lambda \beta^{2} + 2k\beta^{2}  4)(1  z)  2kz\beta^{2} (1  \theta )  2z(\beta + 2w  \lambda w)] < 0\). According to the \(\pi_{1}^{Y}\) and \(\pi_{2}^{Y}\) obtained above, the system profit of the supply chain is compared, and \(\pi_{sc}^{Y} = \frac{{(2w + 2z + 2\beta + k\beta^{2}  2\beta z  k\theta \beta^{2}  2)}}{{4(\lambda  2)^{2} (z  1)^{2} }}[k\theta \beta^{2} + (2\beta + 2w + k\beta^{2}  2)(1  \lambda )(1  z)  kz\beta^{2}  2wz]\) is calculated. Comparing the profit of supply chain system under contract with that under centralized decision, we can get \(\pi_{sc}^{Y}  \pi_{sc}^{N} = \frac{{  (k\theta \beta^{2}  kz\beta^{2}  2wz)[\lambda (2  2\beta  2w  k\beta^{2} )(1  z) + (k\theta \beta^{2}  kz\beta^{2}  2wz)]}}{{4(\lambda  2)^{2} (z  1)^{2} }} > 0\) and \(\pi_{sc}  \pi_{sc}^{Y} = \frac{{[\lambda (2  2\beta  2w  k\beta^{2} )(1  z) + 2(k\theta \beta^{2}  kz\beta^{2}  2wz)]^{2} }}{{16(\lambda  2)^{2} (z  1)^{2} }} > 0\), so we can get \(\pi_{sc} > \pi_{sc}^{Y} > \pi_{sc}^{N}\). Comparing the changes of customer satisfaction, we can get that \(S_{1}^{Y}  S_{1}^{N} = \frac{{\lambda (k\theta \beta^{2}  kz\beta^{2}  2wz)}}{2(\lambda  2)(z  1)} > 0\), \(S_{2}^{Y}  S_{2}^{N} = \frac{{k\theta \beta^{2}  kz\beta^{2}  2wz}}{2(\lambda  2)(z  1)} > 0\). \(S_{1}  S_{1}^{Y} = \frac{{\lambda [\lambda (2  2\beta  2w  k\beta^{2} )(1  z) + 2(k\theta \beta^{2}  kz\beta^{2}  2wz)]}}{4(\lambda  2)(1  z)} > 0\), and \(S_{2}  S_{2}^{Y} = \frac{{\lambda (2  2\beta  2w  k\beta^{2} )(1  z) + 2(k\theta \beta^{2}  kz\beta^{2}  2wz)}}{4(\lambda  2)(1  z)} > 0\), so we can get \(S_{1} > S_{1}^{Y} > S_{1}^{N}\), \(S_{2} > S_{2}^{Y} > S_{2}^{N}\). This shows that the optimal decision of revenue sharing contract is between centralized decision and decentralized decision when the cost sharing ratio is in a certain range. Therefore, the decentralized decisionmaking can be optimized by adjusting the cost sharing ratio.
4 Results and discussion
In order to verify the rationality of the model and reveal the changes of crossborder ecommerce supply chain system profit and optimal decisionmaking under different modes, this section verifies the above conclusions. In the dual channel supply chain composed of crossborder suppliers, crossborder ecommerce enterprises and consumers, the parameter values are selected according to the parameter range in the above model, assuming that consumers' offline channel inconvenience cost \(\beta = 10\), consumers' sensitivity index to crossborder logistics speed \(\eta = 0.2\), wholesale price of products of crossborder suppliers \(w = 2\), tariff cost in the process of transportation \(a = 5\), and unit penalty for failing to arrive on schedule \(b = 3\), the cost coefficient of product storage service \(k = 0.3\), the actual arrival time of online channel products \(t = 6\), and the revenue ratio shared by offline channel to online channel \(z = 0.3\).
4.1 The impact of consumer experience \(\lambda\) on optimal decision and supply chain profit
According to the condition \(\lambda > \frac{2\eta }{{b + \eta }}\) in Lemma 2, the consumer's experience \(\lambda > 0.125\) is obtained, and according to the condition \(z(1 + \frac{2w}{{k\beta^{2} }}) < \theta < \frac{\lambda (1  z)}{2} + z + \frac{\lambda (\beta + w  1)(1  z) + 2wz}{{k\beta^{2} }}\) in lemma 5, \(\theta > 0.34\) is obtained. In order to study the impact of consumer experience on the optimal decisionmaking and system profit of crossborder ecommerce products, suppose \(\theta = 0.4\), the following table shows the changes of online channel product price, offline channel product price, product specified arrival time and supply chain system profit under decentralized decisionmaking, centralized decisionmaking and revenue and cost sharing contract when \(\lambda\) rises from 0.2 to 0.8. Table 2 shows the results of parameter changes under decentralized and centralized decision.
It can be seen from the above table with the increase of consumers' use experience of products, the online price of products under centralized decisionmaking presents an upward trend, while the specified arrival time of products presents a downward trend. However, since consumers can directly contact offline products, offline prices and system profits are not affected by consumers' use experience of products. Under decentralized decisionmaking, the online and offline prices of products increase with the increase of consumers' use experience of products, while the prescribed arrival time of products and the profit of supply chain system decrease with the increase of consumers' use experience of products. Under the revenue and cost sharing contract, the online price, offline price, prescribed arrival time and system profit of supply chain have similar trend with decentralized decision. This is because, whether in the decentralized decisionmaking mode or the contract mode, the higher the consumer's experience of using the product, the smaller the impact of consumer's contact with the product on the estimated value of the product, and the closer the evaluation value of the product to the fixed value, the more stable the consumer's demand will be. When crossborder ecommerce enterprises set the prices of online and offline channel products and the prescribed delivery time of products, they should provide different prices and product delivery time according to the consumers' experience of using the products. That is to say, when consumers have high acceptance of products, they can be equipped with higher online and offline prices and shorter product receiving time to attract consumers and gain profits. In order to observe the trend of decentralized decisionmaking and revenue and cost sharing contract mode more intuitively and clearly, and to select the more advantageous model among them, Figs.Â 2, 3, 4 and 5 are shown as follows.
It can be seen from Figs.Â 2, 3, 4 and 5 that with the increase of consumers' experience of using products, the rising trend of product prices in online and offline channels of crossborder ecommerce under contract mode is significantly lower than that of decentralized decisionmaking, while the downward trend of prescribed arrival time of products under contract mode is stronger than that of decentralized decisionmaking. Generally speaking, the model under contract mode has more advantages than the model under decentralized decisionmaking. Enterprises can obtain higher profits of supply chain system, and consumers can buy products with higher consumer experience with more affordable product price and faster expected arrival time. Crossborder ecommerce enterprises can choose to reoptimize decentralized decisionmaking by forming contracts through online and offline channels, so as to achieve effective coordination.
4.2 The influence of cost sharing ratio \(\theta\) on optimal decision
In the case of decentralized decisionmaking, centralized decisionmaking and revenue and expense sharing contract, if the cost sharing ratio between the two channels changes, then the optimal decisionmaking in the three situations will change, and the optimization mode of enterprise selection will also change accordingly. In order to make a more intuitive and simple comparison, suppose \(\alpha = 19\), \(\lambda = 0.5\), and get the offline channel product price, product specified arrival time, supply chain system profit, online channel consumer satisfaction and offline channel consumer satisfaction in three cases, as shown in Figs.Â 6, 7, 8, 9 and 10.
It can be seen from these five pictures that the price of offline products under the contract agreement decreases with the increase of cost sharing proportion, the specified arrival time of products and the satisfaction of online and offline consumers present an upward trend, while the profit of supply chain system increases first and then decreases with the increase of cost sharing proportion. This is because the offline channel as the leader, when the higher proportion of cost sharing, reduce the cost pressure of offline channel, the lower the product price of offline channel. With the increase of cost sharing ratio, crossborder ecommerce enterprises can provide better products for consumers, and consumer satisfaction of both channels will increase. At the same time, it is found that when the cost sharing ratio is in the range of \([0.34,0.643]\), the offline channel product price, the product specified arrival time, the online and offline channel consumer satisfaction and the supply chain system profit value are between decentralized decision and centralized decision. At this time, we can optimize the decisionmaking and improve customer satisfaction by adjusting the cost sharing ratio, and at the same time improve the profit of the supply chain. Therefore, the choice of revenue and cost sharing contract model can regulate the supply chain and achieve winâ€“win cooperation.
5 Conclusion
Based on the consideration of consumer satisfaction, this paper constructs a dual channel supply chain composed of crossborder suppliers, crossborder ecommerce enterprises and consumers and studies the decisionmaking optimization problems of the supply chain under the conditions of centralized decisionmaking, decentralized decisionmaking and revenue and cost sharing contract. The research shows that the profit of crossborder ecommerce supply chain system and the satisfaction of online and offline customers are low under decentralized decisionmaking, which cannot meet the profit demand of enterprises and satisfy consumers. The model under contract mode has more advantages than the model under decentralized decisionmaking. Enterprises can obtain higher profits of supply chain system, and consumers can buy products with higher consumer experience with more affordable product price and faster expected arrival time. Cooperation through revenue and cost sharing contract can play a very good regulatory role, which can improve consumer satisfaction and ensure the interests of the main supply chain, so as to achieve winâ€“win cooperation. In order to improve the satisfaction of consumers, this paper chooses the optimal supply chain coordination method for research and finally finds that the revenue cost sharing contract can be used to coordinate the supply chain, which is meaningful to promote the decisionmaking optimization of the supply chain and improve the satisfaction of consumers. However, the consumer demand in this paper is continuous and stable, and the research on the supply chain of crossborder ecommerce enterprises under demand interruption needs to be discussed in the future.
Availability of data and materials
Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.
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This work was supported by National Social Science Foundation of China [Grant Number: 18CGL015].
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DW designed research, performed research, analyzed data and wrote the paper. WL analyzed the data and was involved in writing the manuscript. Both authors read and approved the final manuscript.
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Wang, D., Li, W. Optimization algorithm and simulation of supply chain coordination based on crossborder Ecommerce network platform. J Wireless Com Network 2021, 23 (2021). https://doi.org/10.1186/s13638021019084
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DOI: https://doi.org/10.1186/s13638021019084
Keywords
 Cross border ecommerce
 Consumer satisfaction
 Stackelberg game
 Supply chain coordination