Coordination of Online Shop** Supply Chain Considering Fresh Product Preservation Efforts and Cargo Damage Costs

Abstract

To reduce the losses caused by insufficient preservation efforts during transportation, the preservation effort level has been the focus of research. In the fierce competition of online sales, it is particularly important to reduce the cost of damaged goods by improving the level of preservation efforts. Therefore, according to Stackelberg game theory, this article establishes five decision-making models and incorporates the damage rate and preservation effort level into the research. Finally, this article coordinates the online ship** supply chain (SC) through a joint contract. After comparing and analyzing the model results, research has found that: (1) in centralized model, the level of preservation effort reaches its optimal level and the system benefit is maximized; (2) under third-party logistics (TPL) leading decision-making, the different bearers of cargo damage costs will not affect the profits of both parties and the system; (3) among the four decentralized models, the level of preservation efforts and system profit are highest when the decision is led by online store and TPL bears the cost of damaged goods; and (4) under a given sharing ratio, when the logistics service quotation satisfies a certain range of condition, the online shop** SC can achieve Pareto improvement. This paper studies the differences and reasons for decision models in the supply and demand relationship between online stores and TPL, which provides fresh product e-commerce decision-makers with a theoretical basis.

1. Introduction

The e-commerce market has experienced rapid development during these years, and traditional industries have gradually opened up a new path of transformation. In e-commerce, the sales method of fresh food has ushered in new development opportunities, and consumers can purchase it on various online shop** malls and e-commerce platforms [1]. As purchasing methods become more convenient, the target audience for online fresh agricultural products is gradually becoming larger. According to relevant research, as of April 2022, the user base of fresh e-commerce had reached 70.214 million people [2]. However, considering the perishable nature of fresh produce and the uneven preservation technology within the industry, there are many problems with the preservation and decay of fresh agricultural products [3]. In the fierce e-commerce environment, it becomes particularly important to solve these problems as much as possible. Therefore, improving the preservation level of fresh products has certain value in reducing the loss of benefits for online stores and TPL, and it also offers a theoretical reference for managers of fresh food e-commerce.

The preservation treatment of fresh food is crucial for enhancing its integrity, and many scholars in the academic community have conducted different studies on how to elevate the preservation level of fresh food. Chen and Huang [4] introduced a “cost-sharing and subsidy” method to improve the freshness level of TPL (third-party logistics). Feng et al. [5] also utilized the same contract strategy to coordinate SC decisions. Li et al. [6] discussed optimal dynamic preservation from the perspective of blockchain and concluded that adopting blockchain technology can encourage suppliers to make freshness efforts. The study by Xu et al. [7] found that using fixed preservation efforts and variable preservation efforts models can elevate the profits of retailers and the preservation level. Guo and Zhong [8] introduced five government subsidy strategies and concluded that government subsidies for farmers alone can maximize SC profits and enhance product freshness. Tan et al. [9] incorporated product freshness and greenness into the research. Kamaruzaman and Omar [10] conducted research from a mathematical perspective, proposed an economic order quantity model by constructing differential equations, and then considered factors such as shelf life prices and inventory levels to elevate demand and profits while shortening the inventory time of perishable products. Yan et al. [11] designed a profit-sharing synergy between retailers and manufacturers under the Nash bargaining model to achieve optimal retail prices and preservation efforts. From the previous research, we can see that most scholars have focused on suppliers and retailers, while the focus of this article is on studying the decision models of online stores and TPL in the environment of online ship**, achieving the optimal preservation effort level by coordinating the decisions of both parties, which most studies have not considered.

This article studies an online shop** SC that considers the preservation effort level and cargo damage costs. According to Stackelberg game theory, centralized and decentralized models are established when online stores and TPL, respectively, bear the cost of damage. Then, the article studied the impact of different cost-bearers of goods damage on online shop** supply through comparison of model results and numerical simulation. Finally, a joint contract was designed to coordinate the issue of low preservation capacity in the online shop** SC. This article aims to address the following issues:

• What impact do different decision orders have on the benefits of stakeholders and system benefits?
• How do the different cost-bearers of agricultural product damage affect the decisions of stakeholders?
• What coordination method can be utilized to address the issue of low preservation levels in traditional models?

The main contributions of this article are divided into three points: Firstly, different from the perspective of previous suppliers and retailers, this article focuses on the online shop** SC between a single online store and TPL. Therefore, the innovative perspective of this article also contributes to the optimization of online shop** SC decision-making. Secondly, this article incorporates the influence of the level of preservation efforts of fresh products on the market and the cost of damaged goods into the model research, which is not covered by most studies. At the same time, it conducts comparative analyses of the different situations of the bearers of fresh food damage costs. Therefore, this article helps to study the influence of damage costs on online shop** SC. Finally, this article designs a joint contract to resolve the problem of the low freshness level of online shop** SC products, providing theoretical reference for decision-makers of e-commerce agricultural products.

The article structure is divided into the following seven sections: Section 2 elaborates on related literature, and the article describes the problems existing and defines parameter symbols and related assumptions in Section 3. In Section 4, the constructed equations are solved and analyzed. In Section 5, a cost–benefit sharing contract is established to resolve existing problems. The article conducts a numerical simulation to further illustrate the conclusions in Section 6. In Section 7, the article summarizes the conclusion obtained and briefly points out the existing shortcomings and future directions.

2. Literature Review

In numerous research on the fresh SC, many scholars have conducted research on consumer behavior [12], blockchain [13] and loops with value recovery [14]. Research in three directions is related to the theme of the research in this paper, that is, the improvement of preservation efforts, SC research with the participation of TPL, and the research status of the fresh SC.

2.1. Research on the Supply Chain Considering Preservation Efforts

Due to the perishability and fragility of fresh food, it is necessary to pay more attention to preservation during transportation and strive to sustain the integrity of products to meet the needs of customers. Some scholars reduced damage costs by quantifying the cycle of perishable products or adjusting pricing strategies. Herbon [15] explored the optimal pricing strategy of retailers by describing the quality consumption functions of different perishables. Wang et al. [16] explored a reasonable mechanism to increase retailers’ income by analyzing the consumption scenarios of perishable products with different freshness degrees. Cai et al. [17] believed that the loss of fresh food during transportation could be measured by quantity and quality. Wang and Shen [18] studied a dual-channel fresh SC, taking into account preservation efforts and corporate social responsibility. At present, some studies consider the quality loss of fresh food, which is influenced by the preservation technology and the preservation effort level. Wu et al. [19] explored the best decision-making by constructing product quantity and quality preservation functions that were, respectively affected by TPL service quality level and price. Wang et al. [20] also established a fresh product requirement function that is jointly influenced by freshness and price, and deeply studied the optimal preservation effort level of suppliers. There are also many scholars from the technical point of view who study preservation problems. Zhang et al. [21] discovered that the carbon dioxide refrigeration technology that can be applied to the storage of agricultural products can significantly improve the preservation level. Wu et al. [22] put forward suggestions on strengthening cold chain logistics technology by comparing the gap between domestic and foreign preservation technologies in cold chain logistics. In the direction of cold chain packaging, **. Li et al. [40] studied the free-rider problem of online retailers sharing benefits in online shop** and utilized cost-sharing methods to coordinate SC decisions. Zhang and Chen [41] built a three-level SC involving fresh suppliers, TPL, and fresh e-commerce and adopted cost-sharing ways to enhance the freshness preservation efforts of TPL. Ma et al. [42] studied the three-level cold chain system involving supplier, TPL, and retailer, taking into account factors such as carbon trading, freshness, and environmental preferences, and finally designed a contract incentive mechanism. According to the above research, we can see that most scholars coordinate traditional fresh SC from different perspectives. This article studies the online shop** SC from the perspectives of online stores and TPL, which has practical significance for guiding decision-making in fresh e-commerce.

3. Description and Assumptions

This article establishes an online shop** SC system built by a single online store and a single TPL. According to the theoretical knowledge of the Stackelberg game, the members participating in the game are divided into leader and follower, and the leader takes the lead in making decisions, while the followers make their own decisions according to the decision information of the former. In this system, consumers make purchases and place orders in online agricultural product stores. After receiving customer orders, the online store entrusts TPL to preserve the agricultural products and send them to consumers. As a leader, the TPL will take the lead in determining logistics service quotations and preservation efforts, and then the online store will determine online sales prices based on the decision-making information of the leader. This paper will consider the decision-making situations when online stores and TPL are decision-making leaders, respectively. The specific parameter definitions are presented in

Table 1. Parameter symbol definitions.

Symbol	Definitions
$R$	The abbreviation for fresh product online store
$L$	The abbreviation for TPL service provider
$p$	Unit sales price of fresh products
$p_L$	Unit logistics service quotation
$C_L$	Unit logistics service cost
$e_o$	The initial level of preservation efforts for fresh products
$e$	Effort level of fresh product preservation
$f$	Capacity coefficient of preservation cost for TPL
$n$	The damage rate of fresh food
$d$	The initial damage rate of fresh products
$\theta$	Preservation control effect
$b$	Sensitivity coefficient of fresh product sales prices
$w$	Unit loss cost of fresh products
$Q$	Potential market demand for fresh products
$\beta$	Sensitivity coefficient of preservation effort level
$D$	Market requirement for fresh products
$x$	The proportion of shared profits in online stores
$y$	The proportion of online stores bearing the cost of preservation
${\pi }_R$	Profit of online stores for fresh agricultural products
${\pi }_L$	Profit of TPL service providers
${\pi }_T$	Gross profit of the online shop** SC

.

The following assumptions are the basis for establishing the models in the article:

Assumption 1. 

The market requirement for fresh agricultural products is influenced by sales prices and the level of preservation efforts. This refers to the study by Feng et al. [43], denoted as $D=Q-bp+\beta e$, where $Q$ is the potential market requirement for fresh products, $b$ is the sensitivity coefficient of sales price, and $\beta$ is the sensitivity coefficient of preservation effort level.

Assumption 2. 

Referring to Ha et al. [44], when the preservation effort level is $e$ and the initial level of preservation effort is $e_o$, the preservation cost is $c_{(e)}$, $c_{(e)}=\frac{1}{2}f{(e-e_o)}^2$.

Assumption 3. 

The product damage rate is controlled by the preservation effort level, referring to Zhang and Ma [45,46], expressed as $n=d-\theta e$, where $n$ is the damage rate of fresh food, $d$ is the initial damage rate of fresh food, and $\theta$ is preservation control effect.

Assumption 4. 

Third-party logistics and online stores are both rational decision-makers who jointly possess information and will not make extreme decisions.

Assumption 5. 

Third-party logistics does not have inventory. After receiving orders from an online store, the agricultural products are freshened and distributed according to demand without incurring inventory costs.

This article constructs five decision-making models. In addition to the centralized model, the article also includes four decentralized models. There are four kinds of decentralized decisions; the first is expressed as “LR”, that is, the cost of damaged goods is borne by the online store. The second is that the TPL bears the cost of freight damage, which is expressed as “LL”. In the LR and LL decision-making models, the TPL is the dominant player, and the online store is the follower. The third kind of model is that the online store dominates the decision and the TPL bears the cost of damaged goods, which is expressed as “RL”. The fourth decision model is that the online store leads the decision and bears the cost of damaged goods, which is expressed as “RR”. In the RL and RR models, as a leader, the online store makes decisions first, while TPL serves as a follower. The models constructed in this paper are all based on Stackelberg’s game theory. The specific types of decentralized models are presented in

Table 2. Parameter values under different decision-making modes.

	TPL-First Decision (TPL-Led)	Online Store-First Decision (Online Store-Led)
The online store bears the cost of cargo damage	LR model	RR model
The TPL bears the cost of cargo damage	LL model	RL model

.

4. Analysis of the Model

Based on Stackelberg game theory, the model results in this paper are solved using the reverse induction method. All the calculation processes are realized by codes in Matlab software. The subscript of the centralized model is “3”. The decentralized decision subscript of the LR model is “1”. The decentralized decision subscript of the LL model is “2”. The decentralized decision subscript of the RL model is “4”. The decentralized decision subscript of the RR model is “5”. The equilibrium results of the five decision models are represented by the superscript “*”. All propositional proof processes in this article are presented in the Appendix A, Appendix B, Appendix C, Appendix D, Appendix E, Appendix F, Appendix G, Appendix H and Appendix I.

When the cost of agricultural product damage is borne by the online store, the revenue function of the online store and TPL is expressed as:

$${\pi }_{R1}=(p_1-p_{L1})(Q-b{p}_1+\beta e_1)-(d-\theta e_1)w(Q-b{p}_1+\beta e_1)$$

(1)

$${\pi }_{L1}=(p_{L1}-C_L)(Q-b{p}_1+\beta e_1)-\frac{1}{2}f{(e_1-e_o)}^2$$

(2)

When TPL bears the cost of cargo damage, the revenue function of the online store and TPL is expressed as:

$${\pi }_{R2}=(p_2-p_L{ }_2)(Q-b{p}_2+\beta e_2)$$

(3)

$${\pi }_L{ }_2=(p_L{ }_2-C_L)(Q-b{p}_2+\beta e_2)-\frac{1}{2}f{(e_2-e_o)}^2-(d-\theta e_2)w(Q-b{p}_2+\beta e_2)$$

(4)

4.1. Centralized Model

In this model, R and L are treated as a collective interest group to jointly bear the cost of preservation and damage to goods. So the overall revenue of the online shop** SC can be represented as:

$${\pi }_{T3}(p_3,e_3)=(p_3-C_L)(Q-b{p}_3+\beta e_3)-\frac{1}{2}f{(e_3-e_o)}^2-\left(d-\theta e_3\right)w(Q-b{p}_3+\beta e_3)$$

(5)

Proposition 1. 

To obtain the following optimal values, three points must be satisfied: $0<e_3{ }^{\ast }<1$, $Q-b{p}_3>0$ and ${\beta }^2+2\beta \theta bw+{\theta }^2{b}^2{w}^2-2fb<0$. The decisions of R and L are as follows:

The balanced result of the sales price is

$$p_3{ }^{\ast }=\left(\frac{\left({\beta }^2{C}_L-Qf-C_{L}bf-\beta f{e}_o+{\beta }^{2}dw-bdfw+{\theta }^{2}Qb{w}^2+\beta \theta Qw+\beta C_L\theta bw+\theta bf{e}_{o}w+\beta \theta bd{w}^2\right)}{{\beta }^2+2\beta \theta bw+{\theta }^2{b}^2{w}^2-2fb}\right).$$

The balanced result of the preservation effort level is

$$e_3{ }^{\ast }=\left(\frac{\beta C_{L}b-\beta Q-2bf{e}_o+C_L\theta b^{2}w+\theta b^{2}d{w}^2-\theta Qbw+\beta bdw}{{\beta }^2+2\beta \theta bw+{\theta }^2{b}^2{w}^2-2fb}\right).$$

The balanced result of market demand is

$$D^{\ast }=-\frac{bf\left(Q-C_{L}b+\beta e_o-bdw+\theta b{e}_{o}w\right)}{{\beta }^2+2\beta \theta bw+{\theta }^2{b}^2{w}^2-2fb}.$$

The balanced result of system profit is

$${\pi }_{T3}{ }^{\ast }=-\frac{f{\left(Q-C_{L}b+\beta e_o-bdw+\theta b{e}_{o}w\right)}^2}{2\left({\beta }^2+2\beta \theta bw+{\theta }^2{b}^2{w}^2-2fb\right)}.$$

Remark 1. 

In the centralized model, both parties determine their respective decision variables with the goal of maximizing overall benefits. However, this is an ideal situation and exactly the direction that decentralized models need to strive for.

4.2. Decentralized Model of LR

In this LR model, TPL dominates the SC decision-making, while the online store bears the cost of cargo damage. The decision-making sequence has been listed: first, TPL serves as a leader to set logistics service quotations and preservation effort levels to maximize its profit. Then, as followers, online stores set sales prices based on the decision information of TPL. The revenue function of the online store and TPL is shown in Equations (1) and (2).

Proposition 2. 

To calculate the optimal values, the point must be satisfied: ${\beta }^2+2\beta \theta bw+{\theta }^2{b}^2{w}^2-4fb<0$. The optimal values of both parties’ decisions can be presented as follows:

The balanced result of the sales price is

$$p_1{ }^{\ast }=\left(\frac{{\beta }^2{C}_L-3Qf-C_{L}bf-3\beta f{e}_o+{\beta }^{2}dw-bdfw+{\theta }^{2}Qb{w}^2+\beta \theta Qw+\beta C_L\theta bw+\theta bf{e}_{o}w+\beta \theta bd{w}^2}{{\beta }^2+2\beta \theta bw+{\theta }^2{b}^2{w}^2-4fb}\right).$$

The optimal third-party logistics service quotation is

$$p_{L1}{ }^{\ast }=\left(-\frac{-C_L{\beta }^2-2C{ }_L\beta \theta bw+2f{e}_o\beta -C{ }_L{\theta }^2{b}^2{w}^2+2f{e}_o\theta bw-2dfbw+2C{ }_{L}fb+2Qf}{{\beta }^2+2\beta \theta bw+{\theta }^2{b}^2{w}^2-4fb}\right).$$

The optimal preservation effort level is

$$e_1{ }^{\ast }=\left(\frac{\beta C_{L}b-\beta Q-4bf{e}_o+C_L\theta b^{2}w+\theta b^{2}d{w}^2-\theta Qbw+\beta bdw}{{\beta }^2+2\beta \theta bw+{\theta }^2{b}^2{w}^2-4fb}\right).$$

The optimal profit of the online store is

$${\pi }_R{{ }_1}^{\ast }=\frac{b{f}^2{\left(Q-C_{L}b+\beta e_o-bdw+\theta b{e}_{o}w\right)}^2}{{\left({\beta }^2+2\beta \theta bw+{\theta }^2{b}^2{w}^2-4fb\right)}^2}.$$

The optimal profit of the third-party logistics enterprise is

$${\pi }_L{{ }_1}^{\ast }=-\frac{f{\left(Q-C_{L}b+\beta e_o-bdw+\theta b{e}_{o}w\right)}^2}{2\left({\beta }^2+2\beta \theta bw+{\theta }^2{b}^2{w}^2-4fb\right)}.$$

The balanced result of system profit is

$${\pi }_T{{ }_1}^{\ast }=\left(-\frac{f\left({\beta }^2+2\beta \theta bw+{\theta }^2{b}^2{w}^2-6fb\right){\left(Q-C_{L}b+\beta e_o-bdw+\theta b{e}_{o}w\right)}^2}{2{\left({\beta }^2+2\beta \theta bw+{\theta }^2{b}^2{w}^2-4fb\right)}^2}\right).$$

Remark 2. 

In the LR model, the TPL takes the lead in deciding the quotation for logistics services and level of preservation efforts, so that the online store determines the sales price. However, the online store also bears the cost of damaged goods, which means that if the TPL does not keep the product fresh enough, the online store will pay for it. Therefore, this decision-making model may be unfavorable to the online store. This point will also be further elaborated in the numerical simulation.

4.3. Decentralized Model of LL

In this LL model, TPL dominates SC decision-making and bears the cost of cargo damage. The decision sequence of this model is consistent with the LR model. The profit function of the online store and TPL is shown in Equations (3) and (4).

Proposition 3. 

In the LL model, the optimal values of both parties’ decisions can be presented:

The balanced result of the sales price is

$$p_2{ }^{\ast }=\left(\frac{{\beta }^2{C}_L-3Qf-C_{L}bf-3\beta f{e}_o+{\beta }^{2}dw-bdfw+{\theta }^{2}Qb{w}^2+\beta \theta Qw+\beta C_L\theta bw+\theta bf{e}_{o}w+\beta \theta bd{w}^2}{{\beta }^2+2\beta \theta bw+{\theta }^2{b}^2{w}^2-4fb}\right).$$

The optimal third-party logistics service quotation is

$$p_{L2}{ }^{\ast }=\left(\frac{{\beta }^2{C}_L-2Qf-2C_{L}bf-2\beta f{e}_o+{\beta }^{2}dw-2bdfw+{\theta }^{2}Qb{w}^2+\beta \theta Qw+\beta C_L\theta bw+2\theta bf{e}_{o}w+\beta \theta bd{w}^2}{{\beta }^2+2\beta \theta bw+{\theta }^2{b}^2{w}^2-4fb}\right).$$

The optimal preservation effort level is

$$e_2{ }^{\ast }=\left(\frac{\beta C_{L}b-\beta Q-4bf{e}_o+C_L\theta b^{2}w+\theta b^{2}d{w}^2-\theta Qbw+\beta bdw}{{\beta }^2+2\beta \theta bw+{\theta }^2{b}^2{w}^2-4fb}\right).$$

The optimal profit of the online store is

$${\pi }_R{{ }_2}^{\ast }=\frac{b{f}^2{\left(Q-C_{L}b+\beta e_o-bdw+\theta b{e}_{o}w\right)}^2}{{\left({\beta }^2+2\beta \theta bw+{\theta }^2{b}^2{w}^2-4fb\right)}^2}.$$

The optimal profit of the third-party logistics enterprise is

$${\pi }_L{{ }_2}^{\ast }=-\frac{f{\left(Q-C_{L}b+\beta e_o-bdw+\theta b{e}_{o}w\right)}^2}{2\left({\beta }^2+2\beta \theta bw+{\theta }^2{b}^2{w}^2-4fb\right)}.$$

The balanced result of system profit is

$${\pi }_T{{ }_2}^{\ast }=-\frac{f\left({\beta }^2+2\beta \theta bw+{\theta }^2{b}^2{w}^2-6fb\right){\left(Q-C_{L}b+\beta e_o-bdw+\theta b{e}_{o}w\right)}^2}{2{\left({\beta }^2+2\beta \theta bw+{\theta }^2{b}^2{w}^2-4fb\right)}^2}.$$

Remark 3. 

In the LL model, the TPL determines the online ship** SC and bears the cost of damaged goods, which is similar to the actual situation, so the joint contract in the following paper is also designed on this basis.

4.4. Decentralized Model of RL

In this RL model, decision-making is led by the online store, and TPL bears the cost of damaged goods. The profit function of both parties is expressed as:

$${\pi }_{R4}=(p_4-p_L{ }_4)(Q-b{p}_4+\beta e_4)$$

(6)

$${\pi }_L{ }_4=(p_L{ }_4-C_L)(Q-b{p}_4+\beta e_4)-\frac{1}{2}f{(e_4-e_o)}^2-(d-\theta e_4)w(Q-b{p}_4+\beta e_4)$$

(7)

Proposition 4. 

In the RL model, the optimal values of both parties’ decisions can be presented:

The balanced result of the sales price is

$$p_4{ }^{\ast }=\left(\frac{\begin{array}{l}{e}_o{\beta }^3+2 e_o{\beta }^2 \theta b w+d {\beta }^2 b w+C_L{\beta }^2 b+Q {\beta }^2+e_o\beta {\theta }^2 b^2 w^2+d \beta \theta b^2 w^2+C_L\beta \theta b^2 w\\ +3 Q \beta \theta b w-3 f e_o\beta b+2 Q {\theta }^2 b^2 w^2+f e_o \theta b^2 w-d f b^2 w-C_{L}f b^2-3 Q f b\end{array}}{2 b \left({\beta }^2+2\beta \theta bw+{\theta }^2{b}^2{w}^2-2fb\right)}\right).$$

The optimal third-party logistics service quotation is

$$p_{L4}{ }^{\ast }=\left(\frac{\begin{array}{l}-e_o{\beta }^2 \theta w+2 d {\beta }^2 w+2 C_L{\beta }^2-2 e_o\beta {\theta }^2 b w^2+3 d \beta \theta b w^2+3 C_L \beta \theta b w+Q \beta \theta w-f e_o \beta \\ -e_o{\theta }^3 b^2 w^3+d {\theta }^2 b^2 w^3+C_L {\theta }^2 b^2 w^2+Q {\theta }^2 b w^2+3 f e_o\theta b w-3 d f b w-3 C_{L}f b-Q f\end{array}}{2 {\beta }^2+4 \beta \theta b w+2 {\theta }^2 b^2 w^2-4 f b}\right).$$

The optimal preservation effort level is

$$e_4{ }^{\ast }=\left(\frac{\begin{array}{l}{e}_o {\beta }^2+2 e_o\beta \theta b w+d\beta b w+C_L\beta b-Q \beta +e_o{\theta }^2 b^2 w^2\\ +d \theta b^2 w^2+C_L \theta b^2 w-Q \theta b w-4 f{e}_o b\end{array}}{2 {\beta }^2+4 \beta \theta b w+2 {\theta }^2 b^2 w^2-4 f b}\right).$$

The optimal profit of the online store is

$${\pi }_{R4}{ }^{\ast }=-\frac{f {\left(Q-C_{L}b+\beta e_o-b d w+\theta b e_o w\right)}^2}{4 \left({\beta }^2+2\beta \theta bw+{\theta }^2{b}^2{w}^2-2fb\right)}.$$

The optimal profit of the third-party logistics enterprise is

$${\pi }_{L4}{ }^{\ast }=-\frac{f {\left(Q-C_{L}b+\beta e_o-b d w+\theta b e_o w\right)}^2}{8 \left({\beta }^2+2\beta \theta bw+{\theta }^2{b}^2{w}^2-2fb\right)}.$$

The balanced result of system profit is

$${\pi }_{T4}{ }^{\ast }=-\frac{3 f {\left(Q-C_{L}b+\beta e_o-b d w+\theta b e_o w\right)}^2}{8 \left({\beta }^2+2\beta \theta bw+{\theta }^2{b}^2{w}^2-2fb\right)}.$$

Remark 4. 

In the RL model, due to the fact that the online store dominates the online ship** SC and the cost of cargo damage is borne by TPL, the advantage of the dominant player can bring more profits to the online store. The profit comparison between models will be presented in subsequent propositions.

4.5. Decentralized Model of RR

In this RR model, decision-making is led by the online store, which also bears the cost of damaged goods. The profit function of both parties is expressed as follows:

$${\pi }_{R5}=(p_5-p_{L5})(Q-b{p}_5+\beta e_5)-(d-\theta e_5)w(Q-b{p}_5+\beta e_5)$$

(8)

$${\pi }_{L5}=(p_{L5}-C_L)(Q-b{p}_5+\beta e_5)-\frac{1}{2}f{(e_5-e_o)}^2$$

(9)

Proposition 5. 

In the RR model, the optimal values of both parties’ decisions can be presented:

The balanced result of the sales price is

$$p_5{ }^{\ast }=\left(\frac{\begin{array}{l}{\beta }^2 Q+{\beta }^3{e}_o-3 Q b f+{\beta }^2 C_L b-C_L{b}^2 f+{\beta }^2 b d w\\ -b^2 d f w-3 \beta b f{e}_o+2 \beta \theta Q b w+{\beta }^2 \theta b e_{o}w+\theta b^2 f{e}_{o}w\end{array}}{2 b \left({\beta }^2+\theta b w \beta -2 b f\right)}\right).$$

The optimal third-party logistics service quotation is

$$p_{L5}{ }^{\ast }=\left(-\frac{Q f-2 {\beta }^2 C_L+3 C b f+\beta f{e}_o-b d f w-2 \beta C\theta b w+\theta b f{e}_{o}w}{2 {\beta }^2+2 \theta b w \beta -4 b f}\right).$$

The optimal preservation effort level is

$$\begin{array}{l} \\ e_5{ }^{\ast }=\frac{{\beta }^2 e_o-\beta Q+\beta C_{L}b-4 b f e_o+\beta b d w+\beta \theta b e_o w}{2 {\beta }^2+2 \theta b w \beta -4 b f}.\end{array}$$

The optimal profit of the online store is

$${\pi }_{R5}{ }^{\ast }=-\frac{f {\left(Q-C_{L}b+\beta e_o-b d w+\theta b e_o w\right)}^2}{4 \left({\beta }^2+\theta b w \beta -2 b f\right)}.$$

The optimal profit of the third-party logistics enterprise is

$${\pi }_{L5}{ }^{\ast }=\frac{f \left(2 b f-{\beta }^2\right) {\left(Q-C_{L}b+\beta e_o-b d w+\theta b e_o w\right)}^2}{8 {\left({\beta }^2+\theta b w \beta -2 b f\right)}^2}.$$

The balanced result of system profit is

$${\pi }_{T5}{ }^{\ast }=-\frac{f \left(3 {\beta }^2+2 \theta b w \beta -6 b f\right) {\left(Q-C_{L}b+\beta e_o-b d w+\theta b e_o w\right)}^2}{8 {\left({\beta }^2+\theta b w \beta -2 b f\right)}^2}.$$

Remark 5. 

In the RR model, while leading the online shop** SC, the online store is responsible for bearing the cost of damaged goods. When TPL does not make sufficient efforts to preserve the goods, online stores may increase product prices to compensate for the cost of damaged goods. Therefore, this model may not be beneficial for the overall revenue of the online shop** SC. The comparison of specific model results will be presented in the following propositions and numerical simulation.

Proposition 6. 

When $C_{L}b-Q+bdw<0$, the equilibrium results satisfy:$\frac{\partial {\pi }_{R2}{ }^{\ast }}{\partial \beta }>0$, $\frac{\partial {\pi }_{R1}{ }^{\ast }}{\partial \beta }>0$, $\frac{\partial {\pi }_{L2}{ }^{\ast }}{\partial \beta }>0$, $\frac{\partial {\pi }_{L1}{ }^{\ast }}{\partial \beta }>0$, $\frac{\partial {\pi }_{R4}{ }^{\ast }}{\partial \beta }>0$, $\frac{\partial {\pi }_{L4}{ }^{\ast }}{\partial \beta }>0$, $\frac{\partial {\pi }_{R5}{ }^{\ast }}{\partial \beta }>0$,$\frac{\partial {\pi }_{L5}{ }^{\ast }}{\partial \beta }>0$, $\frac{\partial e_5{ }^{\ast }}{\partial \beta }>0$,$\frac{\partial e_4{ }^{\ast }}{\partial \beta }>0$, $\frac{\partial e_3{ }^{\ast }}{\partial \beta }>0$, $\frac{\partial e_2{ }^{\ast }}{\partial \beta }>0$, $\frac{\partial e_1{ }^{\ast }}{\partial \beta }>0$.

Remark 6. 

The profit of online stores and TPL under different models is directly proportional to the sensitivity coefficient of the level of preservation efforts, indicating that improving the level of preservation efforts can increase the revenue of both decision-makers. This paper studies the decision-making models of online stores and TPL from the perspective of e-commerce, which is also the innovative perspective of this paper.

Proposition 7. 

When $C_{L}b-Q+bdw<0$, the equilibrium results satisfy: $\frac{\partial {\pi }_{R2}{ }^{\ast }}{\partial \theta }>0$, $\frac{\partial {\pi }_{R1}{ }^{\ast }}{\partial \theta }>0$, $\frac{\partial {\pi }_{L2}{ }^{\ast }}{\partial \theta }>0$, $\frac{\partial {\pi }_{L1}{ }^{\ast }}{\partial \theta }>0$, $\frac{\partial {\pi }_{R4}{ }^{\ast }}{\partial \theta }>0$, $\frac{\partial {\pi }_{L4}{ }^{\ast }}{\partial \theta }>0$, $\frac{\partial {\pi }_{R5}{ }^{\ast }}{\partial \theta }>0$, $\frac{\partial {\pi }_{L5}{ }^{\ast }}{\partial \theta }>0$, $\frac{\partial {\pi }_T{{ }_3}^{\ast }}{\partial \theta }>0$, $\frac{\partial e_5{ }^{\ast }}{\partial \theta }>0$, $\frac{\partial e_4{ }^{\ast }}{\partial \theta }>0$, $\frac{\partial e_3{ }^{\ast }}{\partial \theta }>0$, $\frac{\partial e_2{ }^{\ast }}{\partial \theta }>0$, $\frac{\partial e_1{ }^{\ast }}{\partial \theta }>0$.

Remark 7. 

We can see that the profit and level of preservation efforts of online stores and TPL under different decision-making models are directly proportional to the preservation effect, which proves that an increase in the preservation effect will have a beneficial effect on online ship** SC. The preservation effect is closely related to the cost of damaged goods, and the cost function of goods damage is rarely used in the research on online shop** SC, so the models in this paper are also a supplement to the previous research.

Proposition 8. 

When ${\beta }^2+\theta bw\beta -bf<0$, the equilibrium results satisfy: (1) $p_1{ }^{\ast }=p_2{ }^{\ast }>p_4{ }^{\ast }>p_3{ }^{\ast }$, $p_2{ }^{\ast }>p_4{ }^{\ast }$. (2) $e_3{ }^{\ast }>e_4{ }^{\ast }>e_1{ }^{\ast }=e_2{ }^{\ast }$, $e_4{ }^{\ast }>e_5{ }^{\ast }$. (3) ${\pi }_{L1}{ }^{\ast }>{\pi }_{R1}{ }^{\ast }$,${\pi }_{L2}{ }^{\ast }>{\pi }_{R2}{ }^{\ast }$, ${\pi }_{L1}{ }^{\ast }={\pi }_{L2}{ }^{\ast }$, ${\pi }_{R1}{ }^{\ast }={\pi }_{R2}{ }^{\ast }$, ${\pi }_{L4}{ }^{\ast }<{\pi }_{R4}{ }^{\ast }$, ${\pi }_{L5}{ }^{\ast }<{\pi }_{R5}{ }^{\ast }$. (4) ${\pi }_T{{ }_3}^{\ast }>{\pi }_{T4}{ }^{\ast }>{\pi }_{T1}{ }^{\ast }={\pi }_{T2}{ }^{\ast }$, ${\pi }_{T4}{ }^{\ast }>{\pi }_{T5}{ }^{\ast }$.

Remark 8. 

Under certain conditions, the sales prices under the LL and LR models are the same, and both are higher than those under the RL and centralized models. The sales price in the RL model is greater than the parameters in the RR model. The comparison of the level of preservation efforts also shows a corresponding situation, indicating that when TPL takes the lead in decision-making, the bearers of cargo damage costs will not affect the level of preservation and sales prices. According to Proposition 8, we can also find that the profit of the leader is always greater than that of the followers in the four types of decisions, which is also consistent with Stackelberg game theory.

According to the comparison of the final system profits, the system revenue in the centralized model is higher than that under other models. When TPL leads in decision-making, the different bearers of damage costs do not affect the overall system profit. From past research on the online shop** SC, few articles have studied the influence of different cargo damage cost-bearers on the SC, which is one of the innovations of the article. Due to the impact of dual marginal effects, it is crucial for decision-makers to utilize joint contracts to enhance the level of preservation capacity and reduce damage costs.

5. Coordination Mechanism

According to the analysis in the previous text, whether from the perspective of revenue or preservation service, the decentralized models still have many drawbacks. Therefore, if the online store and TPL jointly form a community of interests, it is more conducive to maximizing the system’s profit. This article will introduce a “cost–benefit sharing” contract to guide the decentralized model, ultimately improving the profitability of both parties and enhancing the freshness of fresh food.

Under this joint contract, the online store shares profits proportionally and helps TPL bear some of the preservation costs. As compensation for the online store, TPL will reduce the pricing of logistics services. The proportion coefficient of profit sharing is $x$ ($0<x<1$), and the online store retains $1-x$ of the sales profit. The coefficient for sharing preservation costs is $y$ ($0<y<1$), and TPL will retain $1-y$ of the preservation cost. The article uses the model of LL as an example to list the revenue functions of both. Under the conditions of a joint contract, the revenue functions of both parties can be presented as follows:

$${\pi }_R{ }_6=((1-x)p_6-p_L{ }_6)(Q-b{p}_6+\beta e_6)-\frac{1}{2}f{(e_6-e_o)}^{2}y$$

(10)

$${\pi }_L{ }_6=(p_L{ }_6-C_L+x{p}_6)(Q-b{p}_6+\beta e_6)-\frac{1}{2}f{(e_6-e_o)}^2(1-y)-(d-\theta e_6)(Q-b{p}_6+\beta e_6)w$$

(11)

Proposition 9. 

Under joint contract coordination, the balanced results and two proportional coefficients of the online shop** SC are expressed as:

The optimal sales price is $p_6{ }^{\ast }=\frac{-(p_{L6}b-(x-1\left)\right(Q+\beta e_6{ }^{\ast }\left)\right)}{(2b(x-1\left)\right)}$. The optimal preservation effort level is $e_6{ }^{\ast }=\left(-\frac{\begin{array}{l}(\beta C_{L}b-\beta p_L{ }_{6}b-\beta Qx-2bf{e}_o+\beta Q{x}^2+2bf{e}_{o}x+2bf{e}_{o}y+p_L{ }_6\theta b^{2}w\\ -\beta C_{L}bx+\beta p_L{ }_{6}bx-\theta Qbw+\beta bdw+\theta Qbwx-\beta bdwx-2bf{e}_{o}xy)\end{array}}{\left(x-1\right)\left(x{\beta }^2+2\theta bw\beta -2bf+2bfy\right)}\right).$

The proportional coefficient of revenue sharing of the joint contract is $x=\frac{Q+p_L{ }_{6}b-2p_3{ }^{\ast }b+\beta e_3{ }^{\ast }}{Q-2p_3{ }^{\ast }b+\beta e_3{ }^{\ast }}$. The cost-bearing ratio coefficient of the joint contract is

$$y=-\frac{\begin{array}{l}\beta Q^2+{\beta }^3{e}_3{{ }^{\ast }}^2+2{\beta }^2{e}_3{ }^{\ast }Q-2\beta e_3{{ }^{\ast }}^{2}bf+4p_3{ }^{\ast }{e}_3{ }^{\ast }{b}^{2}f+2\theta Q^{2}bw-4p_3{ }^{\ast }{b}^{2}f{e}_o+4p_3{{ }^{\ast }}^2\theta b^{3}w-\beta C_{L}Qb+2\beta p_L{ }_{6}Qb\\ -2\beta p_3{ }^{\ast }Qb-2e_3{ }^{\ast }Qbf+2Qbf{e}_o+2\beta C_L{p}_3{ }^{\ast }{b}^2-{\beta }^2{C}_L{e}_3{ }^{\ast }b-2\beta p_L{ }_6{p}_3{ }^{\ast }{b}^2+2{\beta }^2{p}_L{ }_6{e}_3{ }^{\ast }b-2{\beta }^2{p}_3{ }^{\ast }{e}_3{ }^{\ast }b+2\beta e_3{ }^{\ast }bf{e}_o\\ -\beta Qbdw-6p_3{ }^{\ast }\theta Q{b}^{2}w+2\beta p_3{ }^{\ast }{b}^{2}dw-{\beta }^2{e}_3{ }^{\ast }bdw+3{\beta }^2{e}_3{{ }^{\ast }}^2\theta bw+5\beta e_3{ }^{\ast }\theta Qbw-8\beta p_3{ }^{\ast }{e}_3{ }^{\ast }\theta b^{2}w\end{array}}{2bf\left(e_3{ }^{\ast }-e_o\right)\left(Q-2p_3{ }^{\ast }b+\beta e_3{ }^{\ast }\right)}$$

When the service quotation from TPL meets

$$\frac{2\left(X_1-X_2\right)\left(Q-2p_3{ }^{\ast }b+\beta e_3{ }^{\ast }\right)}{\left(Q-p_3{ }^{\ast }b+\beta e_3{ }^{\ast }\right)\left(2Q-2p_3{ }^{\ast }b+\beta e_o+\beta e_3{ }^{\ast }\right)}<p_L{ }_6<\left(\frac{2\left(X_3-\frac{f{\left(Q-C_{L}b+\beta e_o-bdw+\theta b{e}_{o}w\right)}^2}{2\left({\beta }^2+2\beta \theta bw+{\theta }^2{b}^2{w}^2-4fb\right)}\right)\left(Q-2p_3{ }^{\ast }b+\beta e_3{ }^{\ast }\right)}{\left(Q-p_3{ }^{\ast }b+\beta e_3{ }^{\ast }\right)\left(2Q-2p_3{ }^{\ast }b+\beta e_o+\beta e_3{ }^{\ast }\right)}\right),$$

the cost–benefit sharing contract can elevate the level of preservation efforts, profits for both parties, and system benefits in the online shop** SC, where

$$X_1=\frac{\left(e_3{ }^{\ast }-e_o\right)\left(\begin{array}{l}{\beta }^2{e}_3{ }^{\ast }+\beta Q-\beta C_{L}b-2e_3{ }^{\ast }bf+2bf{e}_o\\ -2p_3{ }^{\ast }\theta b^{2}w+2\theta Qbw-\beta bdw+3\beta e_3{ }^{\ast }\theta bw\end{array}\right)}{4b},$$

$$X_2=\frac{b{f}^2{\left(Q-C_{L}b+\beta e_o-bdw+\theta b{e}_{o}w\right)}^2}{{\left({\beta }^2+2\beta \theta bw+{\theta }^2{b}^2{w}^2-4fb\right)}^2},$$

$$X_3=\frac{\begin{array}{l}({\beta }^2{e}_3{{ }^{\ast }}^2+4p_3{ }^{\ast }{ }^2{b}^2+\beta e_3{ }^{\ast }Q+4C_{L}Qb-4p_3{ }^{\ast }Qb-\beta Q{e}_o-4C_L{p}_3{ }^{\ast }{b}^2-{\beta }^2{e}_3{ }^{\ast }{e}_o\\ -4p_3{ }^{\ast }{b}^{2}dw+3\beta C_L{e}_3{ }^{\ast }b-4\beta p_3{ }^{\ast }{e}_3{ }^{\ast }b+\beta C_{L}b{e}_o+4Qbdw-2e_3{ }^{\ast }\theta Qbw+3\beta e_3{ }^{\ast }bdw\\ -2\theta Qb{e}_{o}w+\beta bd{e}_{o}w-\beta e_3{{ }^{\ast }}^2\theta bw+2p_3{ }^{\ast }{e}_3{ }^{\ast }\theta b^{2}w+2p_3{ }^{\ast }\theta b^2{e}_{o}w-3\beta e_3{ }^{\ast }\theta b{e}_{o}w)\end{array}}{4b}.$$

Remark 9. 

We can see that when the logistics service quotation is within a specific range and profit sharing and preservation cost sharing are carried out at specific proportions, it is possible to achieve system profit and Pareto optimality. Under the coordination of this contract, the level of preservation efforts and market requirements have reached the optimal situation, and the increase in profits of both parties can enhance their enthusiasm for participating in coordination, ultimately achieving the optimal goal. The coordinated application of this cost–benefit sharing method in the online ship** SC also provides new insights for subsequent research.

6. Numerical Simulation

To prove the accuracy of the above propositions, this part analyzes the influence of different cost-bearers of goods damage on the online shop** SC and the effectiveness of coordination methods through numerical simulation. The article references the research of Zhang and Qin [45,46], setting $Q=100$, $b=2$, $\beta =0.8$, $d=0.1$, $\theta =0.1$, $C_L=10$, $w=20$, $e_o=0.2$, and $f=150$. By inputting parameters into symbolic operations, the scope of the logistics service quotation is $2.49<p_L<5.09$. The parameters set in the article satisfy the following conditions:

• The set parameters meet all the assumptions and conditions mentioned above.
• The parameter values set are consistent with the real-life situation of the agricultural e-commerce market.

The numerical simulation will compare the sales prices of fresh products, logistics service quotations, market demand, preservation efforts, decision-making parties, and system profits under different decision-making models. The specific results are presented in

Table 3. Parameter values under different modes.

Decision Types	$\mathit{p}$	${\mathit{p}}_{\mathit{L}}$	$\mathit{D}$	$\mathit{e}$	${\mathit{\pi }}_{\mathit{R}}$	${\mathit{\pi }}_{\mathit{L}}$	${\mathit{\pi }}_{\mathit{T}}$
Model of LR	40.397	29.617	19.617	0.514	192.406	377.424	569.830
Model of LL	40.397	30.589	19.617	0.514	192.406	377.424	569.830
Model of RL	40.203	20.964	20.008	0.521	384.960	192.480	577.440
Model of RR	40.418	19.682	19.364	0.251	372.562	187.280	559.843
Centralized model	30.328	—	40.017	0.840	—	—	769.920
Coordinated decision-making	30.328	2.5	40.017	0.840	192.725	577.195	769.920
	30.328	3	40.017	0.840	231.268	538.653	769.920
	30.328	3.5	40.017	0.840	269.810	500.110	769.920
	30.328	4	40.017	0.840	308.352	461.568	769.920
	30.328	4.5	40.017	0.840	346.895	423.025	769.920
	30.328	5	40.017	0.840	385.438	384.482	769.920

.

According to Table 3, the following four conclusions can be obtained:

(1)

The preservation effort level, the interests of both decision-making parties, and the system profit have all reached their optimal levels in the centralized model. For example, the preservation effort level and market demand in the centralized mode are the largest in the five models, at 0.840 and 40.017, respectively. At the same time, the system profit under the centralized model is also the largest, at 769.920. However, this differs from the actual situation, which also proves the necessity of a joint contract.

(2)

When TPL takes the lead in decision-making, it prioritizes its logistics service pricing and level of preservation efforts. In the LR and LL models, the logistics service quotation in the LL model is 30.589, while the logistics service quotation in the LR model is 29.617. The main reason for this difference is that TPL often tends to increase logistics service quotations to share costs rather than increase preservation efforts due to the need to bear damage costs. Therefore, in both the LR and LL models, the level of preservation efforts, both parties, and system profits are the same.

(3)

According to the simulation values, we can see that the sales price in the RR model is 40.418, slightly higher than the RL model, while the level of preservation effort is only 0.251, which is much lower than the RL model. This is because when the online store takes the lead in decision-making and bears the cost of damaged goods, they are more inclined to compensate for the loss of goods damage costs by increasing sales prices. In the RL model, TPL has to reduce the cargo damage costs by increasing the level of preservation efforts. Therefore, the level of preservation efforts and revenues of both parties in the RL model are higher than those in the RR model.

(4)

Under coordinated decision-making, we can also see that when the price of logistics services drops from 30 to the range of 2.5 to 5, the logistics service provider provides logistics services at a price lower than the logistics cost, but its profits actually increase. This indicates that the profit source of TPL has undergone a huge transformation from logistics service fees to profit sharing in the online store. This transformation also increases the cost of preservation, ultimately increasing the profits of both parties and achieving Pareto optimality.

6.1. Sensitivity Analysis

In Figure 1, Figure 2, Figure 3, Figure 4 and Figure 5, we can see the significant importance of the sensitivity coefficient of preservation control effect and preservation effort level in the online shop** SC. The higher the sensitivity coefficient of the preservation effort level, the more susceptible consumers are to the impact of preservation services on their consumption. So, in order to elevate the level of preservation efforts, we can obtain greater market demand for agricultural products. The high preservation control effect indicates that the return on freshness work will also be greater. So, the TPL also has greater motivation to elevate the level of preservation efforts. Overall, the improvement of these two parameters will bring more benefits to the online shop** SC, which also validates the conclusions of Propositions 6 and 7.

As Figure 6 showed, when the third-party logistics service quotation range is between 2.5 and 5, the system profit after implementing the joint contract is higher than the original situation, and the profits of both decision-making parties are higher than before. Meanwhile, after implementing contract coordination and the enhancement of logistics service quotations, the revenue of TPL continues to decrease while the profit of the online store continues to rise. This is because, within a reasonable range, the larger the logistics service quotation, the smaller the profit that the online store needs to share, and the smaller the logistics service quotation, the greater the proportion of profit sharing received by TPL. Therefore, the basis for sharing profits and preservation costs between the online store and TPL lies in the setting of TPL service quotations, and the specific value of logistics service quotations can only be determined after negotiation between the decision-making parties. Therefore, decision-makers with stronger bargaining power often gain greater benefits.

6.2. Discussion on the Results

This article mainly studies the impact of different bearers of agricultural product damage costs on online shop** SC decision-making and discusses the situations when online stores and TPL bear the cost of damaged goods, respectively. After solving the models and conducting numerical simulations on the results, the article can better discover the differences between the models. Firstly, when TPL takes the lead in decision-making, regardless of who bears the cost of damaged goods, the profits and preservation efforts of both parties remain unchanged. This is mainly because the cost of damaged goods will ultimately be reflected in the sales price and borne by consumers, which will be detrimental to the development of the online shop** SC. Secondly, in the LL model, TPLs that bear the cost of damaged goods are more inclined to increase logistics service quotations to compensate for this loss rather than improving the level of preservation efforts, which is also not conducive to the improvement of preservation efforts. Finally, when an online store takes the lead in decision-making and bears the cost of damaged goods, it will be more inclined to increase product prices to compensate for this loss. Therefore, RR’s sales price is the highest. If TPL bears the cost of damaged goods, they do not have the advantage of making decisions first. Therefore, they have to reduce the cost of damaged goods by improving the level of preservation efforts. This is why the preservation efforts under the RL model are the highest.

In response to the shortcomings of the above models, the article adopts a cost–benefit sharing contract to guide the existing models and verifies the effectiveness of the contract through numerical simulation. In previous research on the online shop** SC involving fresh products, there has been less discussion on the concept of cargo damage costs, especially the impact of different bearers of cargo damage costs on the SC. Therefore, the research in this article has certain value in reducing the revenue losses of both parties in the online shop** game and provides practical theoretical reference for decision-makers in the fresh e-commerce industry.

7. Conclusions

This article focuses on fresh food in the context of online shop**, considering the effect of preservation efforts on market demand and the cargo damage costs. By analyzing the different bearers of cargo damage costs, the article establishes five decision-making models and then uses the knowledge of the Stackelberg game to resolve the balanced results under different models. After comparing and analyzing the results, it is found that: (1) under the centralized model, the preservation effort level reaches its optimal level and the system benefits are maximized; (2) under TPL leading decision-making, the different bearers of cargo damage costs will not affect the revenues of both parties and the system; (3) among the four decentralized models, the level of preservation efforts and system revenues are highest when the decision is led by the online store and TPL bears the cost of damaged goods; (4) under a given sharing ratio, when the logistics service quotation satisfies a certain range of conditions, the online shop** SC can achieve Pareto optimum. Ultimately, the correctness of the conclusions is proven again by numerical simulation.

In response to the shortcomings in the traditional decision-making process, this article introduces a joint contract to coordinate the decentralized model. It is found that under the implementation of the joint contract, the online store and TPL will share profits and preservation costs proportionally and adjust logistics service quotations as profit transfers. When the logistics service quotation satisfies a certain reasonable range of conditions, the outcome of contract coordination can be achieved. Finally, this article verifies the effectiveness of contract coordination through numerical simulation, and the joint contract can achieve Pareto improvement for both decision-making parties and reduce the negative impact of double marginal effects.

This study offers a theoretical reference for the decision-making models of online stores and TPL in e-commerce. Among them, the implementation of joint contracts has practical significance in improving the preservation effort level of fresh food and the total profit of the system. However, this article still has certain limitations, such as the data in numerical simulations coming from existing literature. Future research can consider analyzing the actual data of enterprises to provide more realistic guidance for the online shop** SC. Meanwhile, how the bargaining power of both parties affects the specific pricing of logistics services has not been considered in the article. In future research, the bargaining models can be considered for further study.