Porcelain Supply Chain Coordination Considering the Preferences of Consumers against the Background of E-Commerce

: In e-commerce transactions, the packaging level of porcelain, to a certain extent, determines the loss rate of goods in the transportation process. Therefore, encouraging decisionmakers to improve the packaging level is key to coordinating the supply chain of porcelain. Considering consumers’ preferences for packaging level, this paper constructs three kinds of porcelain supply chain decision-making models, including the impact of the packaging level on porcelain transport losses and after-sales problems caused by transport losses. Using Stackelberg game knowledge, the equilibrium decision and supply chain proﬁt under three decision models are compared and analyzed. The main ﬁndings are as follows: the decision and proﬁt are better in the centralized decision-making mode. In the decentralized decision-making model, the proﬁt of the leader is higher than that of the follower. Consumers’ preferences for porcelain packaging and the value coefﬁcient of packaging protection have a positive effect on the improvement of supply chain proﬁts and the level of porcelain packaging. In addition, in view of the decentralized decision-making model led by suppliers, this paper introduces a joint contract to encourage the members of the supply chain to improve the packaging level of porcelain and achieve the perfect coordination of the supply chain.


Introduction
With the rise of the e-commerce industry, the diversified development of e-commerce commodities has become a trend and the online trading of fragile products such as porcelain is facing new opportunities and challenges. Porcelain is characteristically fragile and easily damaged during transportation; therefore, a higher level of logistics packaging cannot only reduce the loss rate of porcelain during transportation but also provide consumers with a better purchasing experience. However, due to the interest game between the enterprises in the supply chain, the logistics of the packaging of porcelain is often not up to the ideal level, which can bring certain threats to the transportation safety of porcelain and lead to an imbalance in the supply chain. Therefore, improving the cooperation between supply chain members and enhancing the level of porcelain packaging has become an important step in the coordination of the porcelain supply chain.
The transportation loss of goods is an unavoidable problem. Many scholars have carried out research on the safety function of commodities packaging during transportation. Wu and Gao [1] pointed out that fragile products such as porcelain have poor anti-collision ability and are easily damaged during transportation; therefore, it is necessary to improve the packaging level to reduce the occurrence of transportation damage. Zhou et al. [2] introduced the main problems faced in the packaging of fragile products, such as insufficient packaging and the easy damage of packaging. Their study also pointed out that inadequate packaging will easily cause damage to the goods during transportation. Hodge et al. [3] pointed out that 70% of container cargo losses could be avoided by improving commodity packaging. Zeng et al. [4], Sun et al. [5] and Wang et al. [6] also emphasized the necessity of transportation packaging design and discussed how to ensure the transportation safety of fragile products and agricultural products through packaging design. Zheng et al. [7], Alzubi et al. [8] and Guo et al. [9] proposed specific plans to improve the packaging in order to protect fruits and vegetables from mechanical damage during transportation. Chang et al. [10] designed an intelligent tape to monitor the safety of fragile goods during transportation and reduce the transportation losses of fragile goods in view of the vulnerable characteristics of fragile goods during transportation. In addition, Al-Dairi et al. [11], Zhang et al. [12] and Liao et al. [13] also put forward the view that improving the packaging of goods can reduce the loss rate of goods during transportation from the perspective of the packaging of e-commerce goods. Sun and Liu [14] and Ma et al. [15] considered the transportation loss of perishable products in the study of supply chain optimization without considering the packaging of products. Li et al. [16] and Qiu et al. [17] put forward ways to reduce the transportation damage of perishable goods from other perspectives. In addition, Zhang et al. [18]. considered the after-sales problems of products caused by transportation losses in the study of supply chain coordination.
Consumer preference is an important factor in supply chain decision making, and it is not rare to consider consumer preference in supply chain optimization. Han et al. [19] designed a supply chain optimization model for high-quality products and analyzed the influence of consumers with different product quality preferences on supply chain decision making. Cheng et al. [20] studied the supply chain decision-making problem for enterprises with high carbon emissions and enterprises with low carbon emissions. Li et al. [21] established a closed-loop model of sales channels for different types of remanufactured products and discussed the influence of consumers' dual preferences on the decision making of single-channel and dual-channel supply chains. Ke et al. [22] constructed a supply chain model composed of suppliers and manufacturers to study the optimization of a new energy supply chain based on consumers' preferences for smart technologies. Considering consumers' green preferences, Liu et al. [23] established a Stackelberg game model to study the decision-making problem of product pricing and greenness in a two-level supply chain. Both Zhang et al. [24] and Das et al. [25] considered consumers' preferences for environmental protection when studying supply chain coordination. The above literature considers the influence of consumer preference on supply chain decision making from various angles but does not consider the consumer's preference for commodity packaging.
When scholars have discussed supply chain coordination, they have constructed decentralized decision-making models dominated by different roles in different situations. Among them, many studies considered the manufacturer as the dominant player. Wang et al. [26] studied a manufacturer-led green supply chain model, whereas Yang et al. [27] discussed a manufacturer-led supply chain coordination in the context of constantly updating demand information. Feng et al. [28] studied the pricing and coordination of governmentled and manufacturer-led remanufacturing supply chains. However, few studies consider other roles as supply chain decision makers. Chen et al. [29] focused on pricing and service issues in a dual-channel supply chain dominated by publishers. Li et al. [30] focused on the option pricing and coordination mechanism in a supplier-dominated festival food supply chain. In the study by Ma et al. [31], the coordination model of a green supply chain led by retailers is considered. The above studies involve a decentralized decision-making model dominated by different roles, such as manufacturers, publishers, suppliers, etc.; however, there are few studies that consider multiple decisions as having the dominant role in supply chain decisions.
An important way to realize supply chain coordination is to establish a suitable contract mechanism, and the types of contracts are varied. To realize supply chain coordination by designing different types of contracts has become a hot research perspective in supply chain optimization. Ni et al. [32] transferred some suppliers' social responsibility costs to downstream enterprises through wholesale price contracts, improving the profits of upstream and downstream enterprises and the whole supply chain. Dong et al. [33] designed a fresh-keeping cost sharing contract for the supply chain of agricultural products. The contract improved the profits of both the suppliers and retailers and realized the perfect coordination of the supply chain. Liang et al. [34] realized dual-channel supply chain coordination between social responsibility and government subsidies for the use of combination contracts for e-commerce commodities. Wang et al. [35] designed a revenue-sharing contract for the coal power supply chain and verified that, under certain implementation conditions, the contract improved the profits of coal power enterprises. Chandra et al. [36] proved that the wholesale price contract had no coordinating effect on the vaccine supply chain and proposed a subsidy contract to coordinate the supply chain. Cai et al. [37] used a cost-sharing contract to solve the problem that both the suppliers and retailers were unwilling to make promotional efforts in a certain wholesale price range. Liu Shan et al. [38] designed a price contract to coordinate the dual-channel closed-loop supply chain, realizing the overall coordination of the supply chain system. In addition, Piao et al. [39], Yu et al. [40] and Cao et al. [41] all realized supply chain coordination through combination contracts.
To sum up, many scholars have carried out research on the transport loss of perishable products, the protective role of packaging, supply chain coordination, etc.; however, there are few studies on the supply chain of porcelain. Table 1 is a summary of previous studies.

References
Research Perspective Deficiency [1,2] The damage risk of fragile goods such as porcelain during transportation is put forward and the importance of packaging design for the safety of fragile goods is emphasized.
The coordination of the porcelain supply chain is not studied. [7,8] Researched how to reduce the transportation loss of perishable products through packaging design.
Supply chain coordination for perishable goods is not mentioned. [14,15] Considered transportation losses in supply chain optimization.
The impact of packaging on the loss of goods in transportation as well as the after-sales problems caused by the loss were not studied. [18] Studied the fresh-goods supply chain; after-sale refunds for fresh goods are considered.
The impact of logistics packaging on goods damage is not considered. [19] In the supply chain research, consumers have multiple consumption preferences, such as price, product greenness, product quality and so on.
Consumer preferences for packaging were not considered in the study. [26,27] Constructed a manufacturer-led decentralized decision model to study supply chain coordination.
Decision models led by other supply chain members are not considered. [35] Use contracts to coordinate supply chains. Contracts do not make supply chains perfectly coordinated.
In this paper, three supply chain decision-making models are proposed to solve the supply chain coordination problem of porcelain online trading. The main innovation of the model is to study the impact of logistics packaging on the supply chain decision-making of porcelain from two dimensions (consumer preference and packaging protection). The model also includes the after-sales problems when customers receive damaged porcelain. By analyzing and comparing the differences in the decision results and profits of the supply chain under different decision models, a theoretical basis for the coordination of the porcelain supply chain is sought. The following research is divided into five parts: the first part is the model construction and parameter setting, the second part is the model solution and comparison, the third part introduces the joint contract to coordinate the supply chain, the fourth part is the numerical example, the fifth part is the conclusion. The research mainly answers the following questions: (1) The influence of different supply chain decision models on supply chain decision results and supply chain profits; (2) How consumers' preferences for packaging affects supply chain decision results and supply chain profits; (3) How porcelain packaging affects supply chain decision results and supply chain profits; (4) How to realize the reasonable distribution of the benefits of the supply chain members and promote the perfect coordination of the supply chain.
Poor porcelain packaging will lead to a higher porcelain transport loss rate and reduced market demand, which is one of the main manifestations of the porcelain supply chain imbalance. When studying the coordination of the porcelain supply chain, the packaging level is introduced as the main consideration as it is of great significance in the improvement of the transportation safety of porcelain and can help to realize the sustainable development of the porcelain supply chain.

Description and Assumptions
This paper studies the coordination of a supply chain system that consists of a supplier, an online retailer and consumer markets around porcelain. The supply chain model structure is shown in Figure 1. The supplier determines the wholesale price of the goods and the retailer determines the market price and packaging level of the goods. In the model construction, the impact of porcelain packaging on the supply chain is mainly reflected in two aspects: the positive impact of packaging level on market demand and the negative impact on the transport loss rate of porcelain.
results and supply chain profits; (2) How consumers' preferences for packaging affects supply chain decision results an supply chain profits; (3) How porcelain packaging affects supply chain decision results and supply chai profits; (4) How to realize the reasonable distribution of the benefits of the supply chain mem bers and promote the perfect coordination of the supply chain.
Poor porcelain packaging will lead to a higher porcelain transport loss rate and re duced market demand, which is one of the main manifestations of the porcelain suppl chain imbalance. When studying the coordination of the porcelain supply chain, the pack aging level is introduced as the main consideration as it is of great significance in the im provement of the transportation safety of porcelain and can help to realize the sustainabl development of the porcelain supply chain.

Description and Assumptions
This paper studies the coordination of a supply chain system that consists of a sup plier, an online retailer and consumer markets around porcelain. The supply chain mode structure is shown in Figure 1. The supplier determines the wholesale price of the good and the retailer determines the market price and packaging level of the goods. In th model construction, the impact of porcelain packaging on the supply chain is mainly re flected in two aspects: the positive impact of packaging level on market demand and th negative impact on the transport loss rate of porcelain.  According to the decision order of supply chain members, the supply chain decision model is divided into three types: a centralized decision model (supply chain members make decisions together), a supplier-led decentralized decision-making model (supplier priority in decision-making) and a decentralized decision model dominated by the retailer (retailer priority in decision). Descriptions of the parameters of the supply chain model are shown in Table 2.
In addition, this study needs to make the following assumptions: Assumption 1. After receiving the damaged porcelain, consumers will contact the retailer to reissue it. The reissue rate of porcelain is affected by its packaging level. With reference to Zhang et al. [18], it is expressed as n = m − θe, where θ is the protection value coefficient of commodity packaging (the larger θ, the better the protection of commodity packaging in logistics transportation), the initial transport damage rate of the commodity is m and the initial packaging level is 0. Since the amount of retroshipment is small, the transportation loss rate during retroshipment is ignored.

Assumption 2.
In reference to [23,39], consumers have a certain perception of the packaging level of goods and market demand is affected by both the market price and the packaging level, that is: where a is the potential market size of the fragile product, b is the price sensitivity coefficient, r reflects the consumer's preference for packaging level and a, b and r are constant and greater than 0.
Assumption 3. The improvement of the commodity packaging level requires costs. Referring to Ha et al. [42], when the packaging level is e, the required cost c(e) is 1 2 ue 2 , where u reflects the relationship between the packaging level and the input cost of packaging and u > 0. Assumption 4. This paper does not consider the selling cost of goods, which does not affect the research conclusion.
Assumption 5. All members of the supply chain are rational decision makers and will not make extreme decisions.

Centralized Decision-Making Model
In the centralized decision-making model, the supplier and retailer can be regarded as a whole. At this time, the profit function of the supply chain is: Calculate the first order partial derivative of Π c1 with respect to p 1 and e 1 , respectively, then we have: and Thus, the second-order Hessian matrix of Π c1 is: Since the first-order principal sub formula of M 1 is −2b, which is smaller than 0, then the sufficient condition for M 1 to Π c1 can be a negative definite matrix with a second-order principal sub formula 2bu − 2θbcr − r 2 − θ 2 b 2 c 2 > 0 that is recorded as condition (C1). At this point, there is a joint concave function about p 1 and e 1 . Solve the equations ∂Π c1 ∂p 1 = 0 and ∂Π c1 ∂e 1 = 0 and we can obtain the solutions about p 1 and e 1 as follows: where N 1 = θacr + θ 2 abc 2 + θbc 2 mr + cmr 2 . Then, when the sales price is p * 1 and the packaging level is e * 1 , the supply chain profit reaches the maximum and the total profit of the supply chain is:

Decentralized Decision-Making Model Dominated by the Supplier
In the decentralized decision-making model dominated by supplier, as two independent individuals, the supplier and the retailer tend to make decisions to maximize their own interests without considering the interests of the whole supply chain. First, the dominant supplier has the priority to set the wholesale price of the goods. If the retailer can accept the wholesale price given by the supplier, the retailer will determine the retail price and packaging level of the goods according to the wholesale price. The profit function of supplier and retailer are: Now we use the reverse induction solution method to solve this model. First, the first-order partial derivative functions of the retailer profit function Π r2 with respect to p 2 and e 2 are, respectively: It is easy to prove that the sufficient condition for Π r2 is a negative definite matrix for the second-order Hessian matrix of p 2 and e 2 that is also condition (C1).
At this point, Π r2 is a joint concave function about p 2 and e 2 and there is a unique optimal solution for Π r2 . By the simultaneous equations ∂Π r2 ∂p 2 = 0 and ∂Π r2 ∂e 2 = 0, the optimal solution can be obtained as follows: Substitute Equations (11) and (12) into the supplier's profit function Π s2 and find out the first and second derivatives of Π s2 with respect to w 1 . It is easy to prove that, under the assumption of (C1), Π s2 can satisfy ∂ 2 Π s2 ∂w 2 1 < 0, that is, Π s2 has a maximum value with respect to w 1 . Let ∂Π s2 ∂w 1 = 0, the wholesale price that satisfies the supplier's profit maximization can be obtained as follows: Substitute w * 1 into Equations (11) and (12) and we can obtain the optimal sales price p * 2 and packaging level e * 2 under the decentralized decision-making model dominated by the supplier, and they have the following forms: where In this decision-making model, when the sales price is p * 2 and the packaging level is e * 2 , the supply chain profit reaches the maximum and we have: The retailer's maximum profit is: The total profit of the supply chain is:

Decentralized Decision-Making Model Dominated by the Retailer
When the retailer is the leader and the supplier is the follower, the retailer will have the priority to determine the retail price p 3 and packaging level e 3 of the goods for greater benefits and the supplier will then determine the wholesale price w 2 . Let p 3 = w 2 + x and x represent the premium of the wholesale price, that is, the retailer's unit profit on the commodity. In this model, the profit functions of the supplier and retailer are: Because the second derivative ∂ 2 Π r3 ∂w 2 2 = −2b < 0, Π s3 has an optimal solution. Let ∂Π s3 ∂w 2 = 0 to obtain the optimal solution of the supplier (i.e., the optimal wholesale price): Substitute w * 2 into the retailer profit function Π s3 , then we can get the first partial derivatives of Π s3 with respect to x and e 3 as follows: Thus, the second-order Hessian matrix of Π c1 with respect to x and e 3 is: It is easy to prove that under the assumption of (C1), Π s2 is a negative definite matrix. Let ∂Π r3 ∂x = 0 and ∂Π r3 ∂e 3 = 0. Now, we can solve the solutions about x and e 3 as follows: Because p 3 = w 2 + x, then: When the retailer's optimal retail price is p * 3 , the optimal packaging level is e * 3 and the supplier's optimal wholesale price is w * 2 . Therefore, the supplier's profit, the retailer's profit and the total profit of the supply chain reach the maximum.
The supplier's profit is: The retailer's profit is: The total profit of the supply chain is:

Comparison and Analysis of the Decision Models
Proof of Proposition 1. It is easy to obtain Remark 1. Proposition 1 shows that when the supplier is the leader of the supply chain decision, the supplier's profit is higher than the retailer. When the retailer is dominant, the retailer's profit is higher than that of the supplier. In other words, under the decentralized decision-making model dominated by two different dominant players, the interests of the dominant player are always higher than those of the follower. In addition, the total profit of the supply chain under the two decentralized decision-making models is smaller than that under the centralized decision-making model.
Proof of Proposition 2. It is easy to obtain Remark 2. Proposition 2 shows that under different dominant models, retailers make different decisions about the packaging level of goods. The packaging level of goods in the centralized decision-making mode is the highest, whereas the packaging level of goods in the retailer-dominated decentralized decision-making model is the lowest.
Proof of Proposition 3. Because e * 2 > 0, then, combined with (C1) we can deduce bc + bcm − a < 0. When −θ 3 b 3 c 3 + θ 2 b 2 c 2 r + 4θb 2 cu + 3θbcr 2 − 8bur + r 3 < 0, we obtain: Remark 3. Proposition 3 shows that under the three decision models, the packaging level of porcelain, the total profit of the supply chain and the profit of each member of the supply chain are all proportional to the consumer's packaging level preference.
Proof of Proposition 4. When θ 3 b 3 c 3 + 3θ 2 b 2 c 2 r − 8θb 2 cu + θbcr 2 + 4bur − r 3 < 0, we have: Remark 4. Proposition 4 shows that, under the three decision models, the packaging level of porcelain, the total profit of the supply chain and the profit of each member of the supply chain gradually increase as the coefficient of the protection value of the commodity packaging increases.

"Cost Sharing + Revenue Sharing + Wholesale Price Discount" Contract Model
Taking the decentralized decision-making model dominated by the supplier as an example, this paper introduces the combination contract of "cost sharing + revenue sharing + wholesale price discount" to enhance the cooperation among members of the supply chain to achieve the coordination of the supply chain. In the contract introduced in this paper, the supplier will not only give the retailer a discount on the wholesale price but will also help the retailer to share part of the input cost of improving the commodity packaging level; the sharing ratio is 1 − ρ (0 < ρ < 1). In return, the retailer shares part of the revenue with the supplier; the sharing ratio is 1 − λ(0 < λ < 1).
Under this combined contract, the profit functions of the supplier and retailer are: The inverse induction method will be used to continue the following discussion. First, the first partial derivative of Π r4 with respect to p 4 and e 4 is as follows: Thus, the second-order Hessian matrix of Π r4 with respect to p 4 and e 4 is: The sufficient condition to satisfy the negative definite of the second-order Hessian matrix is its second-order principal sub formula 2λρbu − 2λθbcr − λ 2 r 2 − θ 2 b 2 c 2 > 0, which is recorded as condition (C2).
At this point, Π r4 is a joint concave function about p 4 and e 4 . By solving equations ∂Π r4 ∂p 4 and ∂Π r4 ∂e 4 = 0, the optimal solutions about p 4 and e 4 can be obtained as follows: When the supplier first determines the wholesale price w 3 , the profit of each member of the supply chain reaches its maximum if the retailer decides the sales price and packaging level of the goods are p * 4 and e * 4 , respectively.

Coordination and Pareto Improvement of the Supply Chain Contract Model
In the joint contract, to make the supply chain achieve coordination, p * 4 = p * 1 and e * 4 = e * 1 should be satisfied, that is, the sales price and packaging level after the contract coordination are equal to the sales price and packaging level under the centralized decisionmaking model. At this time, the total profit of the supply chain is also equal to that under the centralized decision-making model. According to Equations (4), (5), (34) and (35), it can be obtained that if the joint contract parameter (w, λ, ρ) satisfies the following relationship: then the overall profit of the supply chain will be promoted to the level of the centralized decision-making model. The above conditions can ensure that the total profit of the supply chain is improved but cannot guarantee that the profit of the supplier and retailer is improved. To ensure that both the supplier and retailer accept the contract, according to the incentive compatibility principle, the contract parameters also need to meet: then we can obtain where Under the above conditions, the combination contract of "cost sharing + revenue sharing + wholesale price discount" can ensure that the profits of all members in the supply chain are improved and the total profit of the supply chain is optimal, which means that the contract can achieve Pareto improvement of the supply chain.

Numerical Example
A numerical example is used to verify and analyze the conclusions of this paper. The method for setting the model parameters in this article is adopted from reference [16]. In addition, the parameter setting should abide by the following principles: (1) The parameter setting should meet the assumptions and0of the model. (2) The values of each parameter should conform to the basic rules of the online sales market of porcelain. The parameter settings in this paper are shown in Table 3. According to the values of the above parameters, the optimal decisions of the supply chain under the centralized decision model can be obtained: p * and e * (p * ≈ 94, e * ≈ 1.5). In Figure 2, p and e are the independent variables and the total supply chain profit is the dependent variable. The figure shows that when p = p * and e = e * , the profit reaches the optimum. Therefore, Figure 2 can illustrate that there is a unique optimal solution for the function under the relevant conditional constraints.
According to the values of the above parameters, the optimal decisions of the supply chain under the centralized decision model can be obtained: * p and * e ( * p ≈ 94, * e ≈ 1.5). In Figure 2, p and e are the independent variables and the total supply chain profit is the dependent variable. The figure shows that when * p p = and * e e = , the profit reaches the optimum. Therefore, Figure 2 can illustrate that there is a unique optimal solution for the function under the relevant conditional constraints.

The Effect of Wholesale Price on the Benefit Distribution of Supply Chain Members in Coordinate Contract
The distribution of profits among members of the supply chain is affected by fluctuations in the wholesale prices. According to the parameter settings in this study, the fluctuation range of the wholesale price under the coordination of the contract is [6.0339,10.6893]. Within this range, the profits of both the supplier and the retailer are higher than their respective profits before the contract is coordinated.
It can be seen from Table 4 that under the coordination of the joint contract, when the wholesale price of goods increases, the level to which the supplier helps retailer to share the input costs of improving the commodity packaging level gradually decreases, and the proportion of profits shared by the retailer to the supplier also decreases. At the same time, with an increase in the wholesale price of goods, the profits of the supplier continue to decline, whereas the profits of the retailer continue to rise. A change in w within the effective range will not affect the coordination of the joint contract. The profits of both the supplier and retailer can be increased but the specific value of w is related to the improvement of the profits of both parties. Whether higher profits can be obtained or not depends on the negotiation ability of the supply chain members. For example, when the supplier has strong negotiation ability and the final wholesale price of goods approaches the minimum value, the supplier will obtain higher profits; when the negotiation ability of supplier is weak, they will get lower profits.

The Effect of Wholesale Price on the Benefit Distribution of Supply Chain Members in Coordinate Contract
The distribution of profits among members of the supply chain is affected by fluctuations in the wholesale prices. According to the parameter settings in this study, the fluctuation range of the wholesale price under the coordination of the contract is [6.0339, 10.6893]. Within this range, the profits of both the supplier and the retailer are higher than their respective profits before the contract is coordinated.
It can be seen from Table 4 that under the coordination of the joint contract, when the wholesale price of goods increases, the level to which the supplier helps retailer to share the input costs of improving the commodity packaging level gradually decreases, and the proportion of profits shared by the retailer to the supplier also decreases. At the same time, with an increase in the wholesale price of goods, the profits of the supplier continue to decline, whereas the profits of the retailer continue to rise. A change in w within the effective range will not affect the coordination of the joint contract. The profits of both the supplier and retailer can be increased but the specific value of w is related to the improvement of the profits of both parties. Whether higher profits can be obtained or not depends on the negotiation ability of the supply chain members. For example, when the supplier has strong negotiation ability and the final wholesale price of goods approaches the minimum value, the supplier will obtain higher profits; when the negotiation ability of supplier is weak, they will get lower profits. It can be seen from Figures 3 and 4 that: (1) the total profit of the supply chain under the centralized decision-making model is higher than that under the two decentralized decision-making models and (2) r and θ have a promoting effect on the improvement of the total profit of the supply chain, and the promoting effect is more significant in the centralized decision-making model.
In the centralized decision-making model, the supplier and retailer work closely to-gether to make decisions to maximize the overall profit. In contrast, in the decentralized decision-making model, the supplier and the retailer seek to maximize their own profits individually, ignoring the optimization of the overall profit of the supply chain. Therefore, the supply chain members making centralized decisions will make the total profit of the supply chain higher. In addition, the consumers' preferences for porcelain packaging level directly affects market demand; when consumers have a higher preference for a packaging level, the market demand for a specific packaging level will be higher and the total profit of the supply chain will be higher. Similarly, the higher the protective role of the packaging, the lower the transport loss rate of the commodity, which helps to reduce loss from the supply chain and improve the total profit of the supply chain. Supply chain decision-makers in the centralized decision model pay more attention to consumer preference and packaging level, so the total profit of the supply chain in the centralized decision model is more sensitive to changes in r and θ .   Description: "S-type" represents the decentralized decision-making led by supplier; "R-type" indicates the retailer-led decentralized decision-making.

The Effect of Changes in r and θ on the Profits of Supply Chain Members
It can be seen from Figures 5 and 6 that: (1) In the supplier-led supply chain decisionmaking model, the profit of the supplier is higher than that of the retailer. In the decision model dominated by retailer, the retailer's profit is higher than the supplier's profit. (2) In the two decentralized decision-making models, the profit of the supply chain members is positively correlated with r and θ , and the profit of the supply chain leader changes more obviously with r and θ . In the centralized decision-making model, the supplier and retailer work closely together to make decisions to maximize the overall profit. In contrast, in the decentralized decision-making model, the supplier and the retailer seek to maximize their own profits individually, ignoring the optimization of the overall profit of the supply chain. Therefore, the supply chain members making centralized decisions will make the total profit of the supply chain higher. In addition, the consumers' preferences for porcelain packaging level directly affects market demand; when consumers have a higher preference for a packaging level, the market demand for a specific packaging level will be higher and the total profit of the supply chain will be higher. Similarly, the higher the protective role of the packaging, the lower the transport loss rate of the commodity, which helps to reduce loss from the supply chain and improve the total profit of the supply chain. Supply chain decisionmakers in the centralized decision model pay more attention to consumer preference and packaging level, so the total profit of the supply chain in the centralized decision model is more sensitive to changes in r and θ.
Description: "S-type" represents the decentralized decision-making led by supplier; "R-type" indicates the retailer-led decentralized decision-making.

The Effect of Changes in r and θ on the Profits of Supply Chain Members
It can be seen from Figures 5 and 6 that: (1) In the supplier-led supply chain decisionmaking model, the profit of the supplier is higher than that of the retailer. In the decision model dominated by retailer, the retailer's profit is higher than the supplier's profit. (2) In the two decentralized decision-making models, the profit of the supply chain members is positively correlated with r and θ, and the profit of the supply chain leader changes more obviously with r and θ.    The leader of the supply chain decision making takes the initiative in decision making and has the advantage in the interest game, so the profit of the leader is often higher than that of the follower. In addition, with the increase in r and θ, the demand for porcelain increases, the transportation loss decreases and the overall profit of the supply chain shows an upward trend, which means that the members of the supply chain can obtain more profits. The supply chain leader gains more profit from the supply chain, and the profit is affected more by the supply chain decision. Therefore, changes in r and θ have a more significant impact on the supply chain leader. improves, the supply chain can obtain greater profits and retailers can also share more profits. Therefore, retailers tend to improve the packaging level of porcelain.  A comprehensive analysis of Figures 3-8 shows that R-type and S-type decentralized decision models have obvious differences in the total profit of supply chain, the packaging level and the profit of the supply chain members. The main reason for these differences is improves, the supply chain can obtain greater profits and retailers can also share more profits. Therefore, retailers tend to improve the packaging level of porcelain.  A comprehensive analysis of Figures 3-8 shows that R-type and S-type decentralized decision models have obvious differences in the total profit of supply chain, the packaging level and the profit of the supply chain members. The main reason for these differences is that the decision-making order of the supply chain members is different. For example, the Higher packaging levels can increase the market demand for porcelain and reduce the loss rate of porcelain, thereby improving the total profit of the supply chain. However, in a decentralized decision-making model, the retailer often controls packaging costs and does not package the goods well, which affects the profits throughout the supply chain. On the other hand, in the centralized decision-making model, the retailer gives priority to the optimization of the overall profit of the supply chain so that higher packaging levels can be achieved. In addition, when r and θ improve, the packaging level of porcelain improves, the supply chain can obtain greater profits and retailers can also share more profits. Therefore, retailers tend to improve the packaging level of porcelain.
A comprehensive analysis of Figures 3-8 shows that R-type and S-type decentralized decision models have obvious differences in the total profit of supply chain, the packaging level and the profit of the supply chain members. The main reason for these differences is that the decision-making order of the supply chain members is different. For example, the packaging level of porcelain in the R-type decentralized decision model is lower than that in the S-type decentralized decision mode because when the retailer is dominant, considering the input cost, the retailer will not raise the packaging level of porcelain to a higher level, whereas when the supplier is dominant, the retailer is a passive decision maker and the retailer's decision is based on the maximization of the supplier's profit. However, improvement of packaging level is beneficial to the profits of the supplier. Therefore, the packaging level of porcelain is higher when supplier is dominant.
Based on the above research conclusions, the following suggestions are put forward: in the process of supply chain decision making, each supply chain member should actively strive for a decision-making initiative to maximize their own interests. However, from the perspective of the overall coordination of the supply chain, all members should cooperate closely and make decisions together with the goal of the best interests of the whole supply chain. When considering the coordination of the porcelain supply chain, the supply chain decisionmakers should focus on the consumer's preference for porcelain packaging level; at the same time, they should also pay attention to the packaging measures needed for porcelain protection. When choosing packaging, we should pay greater attention to the protection value of packaging, try to avoid the excessive use of packaging and encourage the use of more environmentally friendly, recyclable green packaging in order to balance the needs of packaging protection and environmental protection.

Conclusions
In this paper, three kinds of supply chain decision models were constructed around the online trading of porcelain. Stackelberg knowledge was used to discuss the influence of porcelain packaging and supply chain member decision order on supply chain decisions and profits. The model comparison shows that: (1) Compared with decentralized decision making, centralized decision making for supply chain members makes the overall profit and packaging level of the supply chain optimal. The packaging level of the S-type decentralized decision-making model is higher than that of the R-type decentralized decision-making model. (2) In the two decentralized decision-making models, the profit of the supply chain leader is higher than that of its follower. (3) There is a significant positive relationship between consumer packaging level preference and the protection value coefficient of porcelain packaging and the total profit of the supply chain, as well as the level of porcelain packaging. Taking the decentralized decision-making model led by the supplier as an example, this paper introduces the joint contract of "cost-sharing + revenuesharing + wholesale price discount" to coordinate the cooperative relationship among the members of the supply chain to realize the reasonable distribution and overall optimization of the supply chain profit.
The coordination of the porcelain supply chain can begin with the improvement of transportation packaging, which can help reduce the loss rate of porcelain in the transportation process, reduce the waste of resources and have certain significance for environmental protection and the sustainable development of the porcelain industry. As consumers will generally have environmental preferences, we will further incorporate the protective role and environmental protection of porcelain packaging into the model and conduct research on the coordination of a porcelain multi-channel supply chain in future research.