Quality Effort Strategy of O2O Takeout Service Supply Chain under Three Operation Modes

This paper investigates channel selection and quality eﬀort in O2O takeout service supply chain consisting of a takeout platform, a catering business, and a distribution rider. By analyzing the three operation modes of platform distribution, business self-distribution, and business self-built platform +distribution, the proﬁt functions of O2O takeout service supply chain members are constructed, respectively. On the basis of game theory, the optimal quality eﬀort and proﬁts are obtained. Combined with numerical simulation, the eﬀects of revenue sharing rate and market size on the optimal quality eﬀort and proﬁts under diﬀerent scenarios are discussed. The results reveal that O2O takeout platform should cooperate with more catering businesses, and adopt appropriate strategies considering diﬀerent market sizes of catering businesses. Additionally, the catering business should properly consider the market size and adopt diﬀerent online and oﬄine prices. Meanwhile, the rider should choose a reasonable quality eﬀort according to the revenue sharing rate.


Introduction
O2O (online to offline) takeout service, as a new mode of catering industry in the era of "Internet +," has gradually become an efficient and convenient way to choose meals in China. Especially in the special period of COVID-19, young people are more likely to choose takeout to solve their dietary problems. Referring statistical report on the development of Internet in China issued by China Internet Information Center (CNNIC) in February 2021, as of December 2020, the number of online takeout users in China had reached 419 million, an increase of 21.03 million over March 2020. With the emergence of various PC and mobile platforms, online payment functions are becoming perfect.
ere are many modes of operation for takeout service industry.
Takeout business is considered to be an O2O business model applied to the catering industry [1]. With its convenient and fast characteristics, it has become the first choice for many people [2]. O2O takeout refers to the food that customers place orders through the online platform; then, the restaurant prepares and packages the food, and the deliverer (rider) delivers the food provided by the restaurant offline [3]. Online takeout platforms such as "Meituan" and "Ele.me" provide takeout ordering services for people in China. Meanwhile, with Alibaba's wholly owned acquisition company of "Ele.me," the competition of O2O takeout service industry is more and more vigorous [4]. Companies with greater market demand such as McDonald's and KFC can choose offline catering. Moreover, they can cooperate with online platforms such as "Meituan" for online sales or build their own platforms for online catering services [5]. erefore, choosing a reasonable operation mode to maximize revenue and increase market demand has become an important direction in the O2O takeout service supply chain [6]. e takeout industry brings convenience and choice to people's life, but it brings practical problems that cannot be ignored [7]. e online ordering platform "Ele.me" has been exposed to many unlicensed catering merchants using its online platform to sell catering, and some of its franchised restaurants have encountered serious food safety problems during the production process. O2O takeout service supply chain members need to be responsible for normal operation and choose reasonable service quality effort [8]. erefore, we should pay more attention to the efforts of O2O takeout supply chain members in terms of service quality. We designed the appropriate situation considering the above description. e objectives of this study inquire about the following questions: (i) Which is the optimal operation mode for O2O takeout supply chain members to choose? (ii) How will the prices of online and offline channels evolve in different operation modes? (iii) What is the impact of revenue sharing rate on optimal decision strategy and profits of O2O takeout service supply chain members?
In general, our research has three main contributions. Firstly, combined with the characteristics and actual operation of O2O takeout service supply chain, this paper further refines the online and offline channel, increases the number of supply chain members, and tentatively analyzes the operation strategy of O2O takeout service supply chain with three supply chain members (takeout platform, catering business, and riders). Secondly, this paper takes revenue sharing rate into consideration and attempts to build three special operation modes. Furthermore, the optimal quality effort strategy and optimal profit under different operation modes are optimized and compared. Research findings would help O2O takeout supply chain members to choose the appropriate operation mode and concentrate on increasing their quality effort and profits.
We explore channel selection and quality decision in O2O takeout service supply chain considering profit sharing. e remainder of the paper is organized as follows. Section 2 reviews relevant literature. Section 3 describes the problem and the benchmark model. Section 4 solves three different decision-making models and analyzes the impacts of profit sharing on quality effort and impact factor of utility. Section 5 provides numerical simulation to demonstrate some related issues. Section 6 illustrates managerial insights of the model. Finally, conclusions and suggestions of the research are provided in Section 7. All proofs in this paper are provided in the Appendix.

Service Supply Chain.
ere is a lot of research that has been done on service supply chain (SSC), and it has reaped excellent fruits. e rapid development of information technology has promoted the digital transformation of the service supply chain [9]. For the logistics service supply chain, Jia et al. [10] dealt with the multistage problem of pricing and time-to-market for multigeneration products sold through an online direct channel in a service supply chain with a manufacturer and a logistics service provider. Aiming at the carbon emission reduction service supply chain, He et al. [11] investigated a service supply chain consisting of a service provider who is in charge of carbon emission reduction and service, and a service integrator who is responsible for low-carbon advertising, considering corporate social responsibility. For platform supply chain, He et al. [12]considered an e-commerce platform service supply chain consisting of a manufacturer, an e-commerce platform, and a possible third-party logistics service company. ey explored the impacts of the manufacturer's channel encroachment and the e-commerce platform's logistics integration. Taking the hospitality and tourism industries as typical examples, He et al. [13] investigated three decision modes (i.e., decentralized, cost-sharing, and integrated) for the platform service supply chain. Results indicated that perceived service quality and brand image vary over time, and they gradually converge to a steady state. For the financial service supply chain, Chen et al. [14] derived the optimal ranking and production strategy with or without put options under service-level constraints. For service supply chains that focus on consumers, Ma and Hong [15] believed that retailers tend to provide presales services to attract more customers, and the services provided by retailers have a positive impact on manufacturers' sales. Meanwhile, Ma et al. [16] believed that the consumer's reference effect causes consumers to produce an "anchor mentality," which causes manufacturers and retailers to reduce quality levels. However, the existing research results are mainly explored from the perspectives of the logistics service supply chain, financial service supply chain, and so on, and there is a lack of specific research on takeout service supply chain, especially on the service quality effort of takeout service supply chain members.

Online to Offline.
In the era of digital economy, online to offline (O2O) has become a rapidly developing e-commerce model all over the world. Related issues have attracted extensive attention of scholars [17]. Taking the delivery service and the inconvenience of shopping in physical stores into account, consumers can choose online or offline channels to purchase products [18]. For O2O channel selection issues, Wang et al. [19] pointed out that when consumers choose channels, they should comprehensively consider online product price, perceived product quality, and business reputation, and balance perceived product quality, business reputation, and promotion intensity. Aiming at online channels, Forghani et al. [20] discussed the impact of digital marketing strategy on customers' purchase behavior in online shopping stores. He et al. [21] believed that the online presale of fresh agricultural products can reduce the circulation loss rate, while the traditional sales channels have a huge waste in circulation. Chen and Su [22] discussed the cooperation in the consignment supply chain with complementary products under O2O mode. On the coordination of dual-channel supply chain, Hosseini-Motlagh et al. [23] firstly researched reverse supply chain systems optimization and coordination with dual-channel and demand disruptions. And then, he discussed triparty reverse supply chain coordination with competitive product acquisition process [24]. Considering the low-carbon awareness of online shoppers, Wu et al. [25] proposed a demand function of online shopping supply chain based on O2O integration. In order to improve customer experience and service satisfaction of catering O2O, Shi, et al. [26] took "Meituan" takeout as an example, integrated big data analytics, and grounded theory to explore influencing factors of catering O2O customer experience. Meanwhile, for catering O2O, Xue et al. [3] introduced a two-stage model to optimize scheduling of riders for instant food deliveries. Considering deterioration property of products in dual-channel business models, He et al. [27] studied a single-retailer-single-vendor dual-channel supply chain model in which the vendor sells deteriorating products through its direct online channel and the indirect retail channel. Scholars have conducted extensive and in-depth research on some types of O2O supply chains and reached rich research conclusions. e previous literature mainly focused on the channel selection of O2O supply chain and partially analyzed two supply chain members (manufacturers and retailers).
ere are few studies on different operation modes and three members of O2O supply chain. Based on the realistic background, this paper proposes three different operation modes, increases the number of supply chain members, and analyzes the O2O takeout service supply chain problems of three supply chain members (takeout platform, catering business, and rider).

Service Quality Effort.
Service quality effort is the foundation and guarantee of sustainable development for SSC, and it determines the profit and performance of the whole SSC [28]. Gu et al. [29] considered a fresh product supply chain to research the optimal effort decision and pricing decision of quality effort and preservation. Yang et al. [30] considered the food supply chain and believed that the level of quality effort is very important for food safety and has positive externalities. For service quality efforts in the field of carbon emission reduction, Hosseini-Motlagh et al. [31] researched competitive channels coordination in a closed-loop supply chain based on energy-saving effort and cost-tariff contract. Hosseini-Motlagh et al. [32] indicated that coordinating the manufacturer's green quality and competing retailers' warranty periods increase the economic profitability of all supply chain members. Similarly, Sana [33] considered the income of sales projects, the cost of green quality, and the contribution of social responsibility activities, and its main goal is to find out the best price and green quality. Gupta et al. [34] studied the optimal pricing decisions and performance of multi-echelon supply chains under uncertainty by market power structure, advertising, and quality efforts. Likewise, Das Roy and Sana [35] investigated a multi-echelon green supply chain system and tried to reduce the expected integrated total cost by optimizing the investment. Moreover, Sana [36] investigated a production-inventory model and derived optimal buffer inventory to minimize the expected costs per unit item. It is assumed that the whole items are sold with free minimal repair warranty if any fault arises after sale. Ma et al. [37] investigated how quality efforts and patient concerns affect supply chain performance and the level of quality efforts of medical device manufacturers. erefore, the previous literature on quality efforts mainly focused on food quality, carbon emission reduction, medical treatment, and other fields. ere is a lack of research on the service quality efforts of O2O takeout service supply chain members, especially the specific research on the service quality efforts of rider and takeout platform.
In summary, firstly, the research content of the existing related literature mainly focuses on the logistics service supply chain, financial service supply chain, etc. ere is a lack of specific research on O2O takeout service supply chain, especially on the service quality effort of the members of the takeout service supply chain. Secondly, the previous literature mainly focused on the channel selection of O2O supply chain and partially analyzed two supply chain members (manufacturers and retailers).
ere are few studies on different operation modes and three members of O2O supply chain. erefore, based on the previous literature and combined with the characteristics of takeout service, this paper puts forward three different operation modes, increases the number of supply chain members, and analyzes the O2O takeout service supply chain problems of three supply chain members (takeout platform, catering business, and rider). is paper quantifies quality effort as a linear function related to market size and uses quantitative analysis methods to analyze the impact of quality effort on SSC.

Problem Description and Assumptions
(1) Our models consider a dual-channel takeout service supply chain for a single product. e catering business supplies the food to the consumer through a takeout platform online and sells the product directly offline. Consumers may choose the online channel or offline channel to obtain the food.
(2) e catering business has three models to choose, platform distribution model (PDM), business selfdistribution model (BSM), and business self-built platform + distribution model (SDM). In PDM, riders are hired by the platform. e platform extracts the catering business's revenue sharing rate and the rider's revenue sharing rate ( Figure 1). In BSM, the catering business distributes through its own capacity. e platform extracts the catering business's revenue sharing rate; the business pays the rider a fixed wage and extracts the rider's revenue sharing rate ( Figure 2). In SDM, the catering business establishes its own online platform and hires riders ( Figure 3).
(3) e platform determines the level of online service quality efforts, mainly involving matching algorithm, real-time accuracy of distribution information, improving the convenience of platform operation and user security, and other related services. e rider determines the delivery service quality effort level, including delivery efficiency, food integrity, and service attitude. e catering business decides on Complexity sales price and service quality level in dual channels, including shop cleanliness, service attitude, and dining environment. (4) Online demand is dependent on online price, o ine price, service quality e ort of the platform, and rider. O ine demand is dependent on o ine price, online price, and service quality e ort of the catering business. Supply chain contains a takeout platform, a catering business, and a distribution rider. ey have equal status, simultaneous action, and independent decision-making to maximize their own bene ts. (5) When the platform hires the rider, the platform does not pay xed wages. e rider can deliver takeout from multiple catering businesses, and the order volume is relatively large. e rider can get part of the distribution fee for each distribution. However, the catering business hires the rider to establish a long-term and stable cooperative relationship. ey are only responsible for the catering distribution of xed businesses. e order volume is relatively small, so they need to pay a stable wage M 1 . is is similar to the cost expression used by Liu, et al. [38]. (6) As is common in the literature, we further normalize the food cost of the catering business to zero [39,40]. ese assumptions aim to simplify the mathematical derivations of the models while preserving the fundamental qualitative results in the problem.

Notations and Benchmark Model.
Supply chain contains a takeout platform, a catering business, and a distribution rider. ey have equal status, simultaneous action, and independent decision making to maximize their own bene ts. We use the subscript p to represent the platform; use the subscript b to represent the business; and use the subscript r to represent the rider. e notations and corresponding de nitions involved in this research are shown in Table 1.
To obtain the demand functions of the online channel (D on ) and the o ine channel (D off ), this work extends the framework established by [41][42][43][44]. Accordingly, the demand function for online channel and o ine channel in this paper, respectively, can be expressed as follows: In (1) and (2), the demand function of each channel is reversely a ected by its own selling price and has a direct relationship with the other channel's price. e platform's service quality and the rider's service quality are the factors decided by the platform; the rider's service quality has a direct relationship with demand of online channel. O ine service quality has a direct in uence on demand of o ine channel. We can use function qe 2 /2 to describe the service quality e ort cost. Based on the assumed demand functions in (1) and (2), the problem will be modeled in three operation structures including PDM, BSM, and SDM.

PDM.
In PDM, riders are hired and managed by the platform. Consumers buy food through the platform at the price of p on and pay the distribution fee m for the rider. e platform charges the business a revenue sharing rate λ 1 and charges the rider a revenue sharing rate λ 2 . Furthermore, the platform decides the platform's service quality, and the  catering business decides on the food selling price in each channel and the quality of offline service. e rider decides on the quality of distribution service in the online channel.
Under the PDM, the profit functions of the platform, the catering business, and the rider in the dual-channel supply chain, respectively, can be formulated as follows: Equation (3) illustrates the profit of the platform in which the first part indicates marginal profit drawn from the catering business and the rider, and the second part denotes demand of online channel, and then, we subtract the cost of quality of service on the platform. In (4), the catering business's profits consist of online and offline parts. And the first part indicates profit that the catering business earns from online channel and the second part is the profit through offline channel. en, we subtract the cost of quality of offline service on the catering business (5). e first part represents the marginal profit of the rider, and the second part denotes demand of online channel, and then, we subtract the cost of service quality.

Proposition 1.
Under a Nash equilibrium, the optimal decisions are as follows: Average distribution cost for the rider b 1 Self-price elasticity coefficient b 2 Cross-price elasticity coefficient β Quality of service sensitivity parameter of the demand q p Cost factor for enhancing quality of online service for the platform q b Cost factor for enhancing quality of offline service for the catering business q r Cost factor for enhancing quality of distribution service for the distribution rider π Fixed wage for the distribution rider e proof process can be seen in Appendix B. We use nation A 1 , A 2 , A 3 , A 4 , A 5 , A 6 , A 7 to simply equilibrium solutions. Nations are presented in Appendix A.

Corollary 1.
Under the platform distribution mode, the optimal profits of O2O takeout platform, catering business, and distribution rider are π p * p , π p * b , and π p * r , respectively (see Table 2 for details).

BSM.
In BSM, the catering business distributes through their capacity. Customers buy food through the platform at the price of p on and pay the distribution fee m for the rider. e platform extracts the catering business's revenue sharing rate λ 1 and decides the quality of service on the platform. e catering business pays the rider fixed wages M 1 and extracts the rider's revenue sharing rate λ 2 .
e catering business makes decisions on the food selling price in each channel and the quality of offline service. e rider decides on the quality of distribution service in the online channel.
Under the BSM, the profit functions of the platform, the catering business, and the rider in the dual-channel supply chain, respectively, can be formulated as follows: Equation (11) illustrates the profit of the platform drawn from the catering business in the online channel. en, we subtract the cost of quality service on the platform. In (12), the first term denotes the profit earned by selling products through the online channel, and the second term indicates the earned profit from selling products via offline channel. Finally, we subtract the cost of service quality on the offline and fixed cost of the rider. Equation (13) represents the profit of the rider including the fixed wage and the cost of service quality effort.

Proposition 2.
Under a Nash equilibrium, the optimal decisions are as follows: We use nation B 1 , B 2 , B 3 , B 4 to simplify equilibrium solutions. Nations are presented in Appendix A.

Corollary 2.
Under the catering business distribution mode, the optimal profits of O2O takeout platform, catering business, and distribution rider are π b * p , π b * b , and π b * r , respectively (see Table 2 for details).

SDM.
In SDM, the catering business establishes its own platform and hires riders for distribution. Customers buy food through the platform at the price of p on and pay the distribution fee m for the rider. e business pays the rider fixed wages M 1 and charges the rider a revenue sharing rate λ 2 . e cost for the catering business to build its online platform is M 2 . e catering business makes decisions on the food selling price in each channel and the quality of online and offline service. e rider decides on the quality of distribution service in the online channel.
Under the SDM, the profit functions of the catering business and the rider in the dual-channel supply chain, respectively, can be formulated as follows: 6 Complexity In (19), the first term denotes the profit earned by selling products through the online channel, and the second term indicates the earned profit from selling products via offline channel. en, we subtract the cost of quality service on the platform. Finally, we subtract the cost of service quality on the offline and fixed cost of the rider. Equation (3) represents the profit of the rider including the fixed wage and the cost of service quality.

Proposition 3.
Under a Nash equilibrium, the optimal decisions are as follows: We use nation C 1 , C 2 , C 3 , C 4 , C 5 , C 6 , C 7 to simplify equilibrium solutions. Nations are presented in Appendix A.

Corollary 3.
Under the business self-built platform + distribution mode, the optimal profits of O2O takeout platform, catering business, and distribution rider are π s * p , π s * b , and π s * r , respectively (see Table 2 for details).

Comparison of Business Profits under ree Operation
Modes. According to Equations (27), (30), and (32), meanwhile, b , or vice versa; Obviously, if the fixed wage paid to riders is relatively large, the catering business should choose PDM mode; on the contrary, when the fixed wage is relatively small, the catering business can consider choosing BSM mode. Actually, the fixed wage of riders is a very important reference factor for catering businesses. Several large catering businesses, such as "Pizza hut" and "KFC," will choose to hire their own riders; on the contrary, generally small catering businesses prefer to cooperate with takeout platforms because of the high cost of hiring riders.
or vice versa; rough the above formula, it can be concluded that when the cost of built platform is relatively large, catering businesses should choose SDM mode; conversely, when the cost is in a relatively small range, BSM mode can be considered. e similarity of the two models is that both catering businesses employ the rider, and thus, catering businesses should pay more attention to the cost of building their own platform. If the catering business has strong strength, such as "McDonald's" and other chain enterprises, they can build their own platform to realize the sustainable growth of profits; if the catering business is a small enterprise, they try to cooperate with the takeout platform to obtain greater profits.

Comparison of Service Effort
Level. According to (6), (14), and (21), meanwhile, , further analysis shows that p , or vice versa; According to (7), (15), (22), meanwhile, , further analysis shows that , or vice versa; Noticeably, for takeout platforms and catering businesses, the extraction proportion has a great impact on them. O2O takeout platform should cooperate with more catering businesses and adopt different strategies considering different market sizes of catering businesses. On the one hand, it can improve the market share of the platform and urge the platform to ensure higher service quality. For catering businesses, they can adopt different online and offline price strategies to dynamically ensure dual-channel sales.

Numerical Analysis
Since there are many parameters in the model and the expressions are more complicated, in order to analyze the optimal strategy and optimal profit comparison under the three different operating modes more intuitively, numerical examples are used for analysis. In the numerical simulation studied, we consider α � 100; β � 1; θ � 0.5; b 1 � 0.8; b 2 � 0.2; m � 2; c � 2; λ 1 � 0.4; λ 2 � 0.2; q p � 20; q b � 20; and q r � 20.

Sensitivity Analysis on λ 1 and λ 2 .
To create more insights toward creating SSC, a set of sensitivity analyses on the extract proportion is λ 1 and λ 2 . In this regard, the impacts of change in the extract proportion λ 1 and λ 2 on decision variables and profit functions are investigated. Table 3 observes that in PDM and BSM, the platform's optimal service quality effort increases with the catering business's revenue sharing rate. However, in BSM the platform's optimal service quality effort decreases with the rider's revenue sharing rate. Moreover, in BSM, the catering business's service quality effort decreases with the revenue sharing rate. e platform can appropriately improve the revenue sharing rate to obtain higher service quality, gain a better reputation, and attract more catering businesses and consumers. Under the condition of maintaining service quality to satisfy consumers, the catering business should control costs for sustainable operation. In addition, if the catering business builds its own platform, it can keep its online and offline service quality similar. Furthermore, the rider prefers to cooperate with the catering business or platform with low revenue sharing rate. Table 4, in PDM and BSM, online price is positively correlated with λ 1 , while offline price is negatively correlated with λ 1 . In SDM, online and offline prices have nothing to do with λ 1 , while offline price is positively correlated with platform extracted proportion λ 2 . e platform should take a cautious attitude toward the increase of the revenue sharing rate, which may lead catering businesses to increase their online prices to maintain operations; obviously, if the catering business moderately increases the rider's revenue sharing rate, it can appropriately reduce online and offline prices to expand 8 Complexity market demand. Moreover, the online optimal price is less than the o ine optimal price. It can be concluded that the self-distribution catering business should formulate di erentiated online and o ine prices to achieve optimal pro t. Figure 4 illustrates that under the PDM and BSM, the optimal platform's pro t increases with λ 1 . Meanwhile, in PDM, the platform's optimal pro t increases with the λ 2 . By comparison, regardless of how the revenue sharing rate changes, the platform is more inclined to choose PDM mode to obtain higher pro ts. In reality, referring to the operation modes of "Ele.me" company and "Meituan" company, they are striving to build and improve their own takeout platforms to achieve sustainable pro t growth. Figure 5 demonstrates that the optimal pro ts of the catering business decrease with λ 1 . However, in PDM and BSM, the optimal pro t of the catering business increases with λ 2 . Consequently, when the catering business's revenue sharing rate is relatively small, catering businesses can choose PDM mode; on the contrary, when the revenue sharing rate exceeds a certain range, catering businesses should choose SDM mode to obtain higher pro ts. Obviously, for some large catering businesses, such as McDonald's and KFC, they can cooperate with takeout platforms and build their own platforms to expand multichannel sales; for small catering businesses, it is recommended to cooperate with the takeout platform to achieve a win-win situation. Figure 6, the rider's optimal pro ts increase with λ 1 . However, the rider's optimal pro t decreases with λ 2 . In BSM and SDM, the rider has a certain xed wage, and the decline is relatively slow.

e Rider's Optimal Pro t. As shown in
is symbolizes that the riders prefer the mode with xed wage, which is conducive to higher pro ts. erefore, the rider can choose BSM and SDM modes to obtain higher pro ts. Furthermore, with the change of revenue sharing rate, SDM mode is a better choice. In reality, the rider prefers to cooperate with a xed catering business. Referring to the employment model of "Burger King" company, we take the  Figure 4: Impact of change in λ 1 and λ 2 on the platform's optimal pro t.  xed wage as the basic income of riders and motivate riders by controlling the change of revenue sharing rate.

Sensitivity Analysis on Market Size α.
To create more insights on the investigated problem, Figures 7 and 8 illustrate the impact of market potential α for optimal online price and o ine price, respectively.

Price of Online and O ine.
As can be seen in Figures 7  and 8, in all modes, the optimal prices of both online and o ine are always positively correlated with α. When market size is the same, the online optimal price P p * on is always higher than P b * on and P s * on . However, the o ine optimal price P p * off and P b * off are always lower than P s * off . Meanwhile, the P * off of PDM and BSM is similar. In PDM mode, the platform charges a higher percentage of the catering business's revenue sharing rate; thus, the catering business will increase the online price to ensure pro ts, which makes the online price highest. Meanwhile, in SDM, the catering business needs to pay a xed wage to the rider and bears the cost of building the platform, which leads to the optimal o ine price greater than that in PDM and BSM mode. erefore, the catering business should set higher online prices and lower o ine prices to obtain optimal pro t. For consumers, SDM mode should be selected when ordering takeout online, PDM and BSM modes are better choices when choosing o ine restaurants.  Figure 9, it can be observed that under the given proportion, the optimal pro t of the platform increases with the market size under both modes. e optimal pro t of the platform under the PDM mode is larger than that under the BSM mode, which is π p * p > π b * p . is reveals that PDM mode is the best choice for takeout platform. In fact, with the increase of market size, companies such as "Meituan" are upgrading their takeout platforms to make greater pro ts. Figure 10 illustrates that the optimal pro t of the catering business increases with the market size under all modes. When the market size is small, the optimal pro t under PDM and BSM is larger than that under the SDM.

Optimal Pro t. From
When the market size a > a ″ , the optimal pro t of the catering business under the SDM exceeds that in the PDM and BSM. With the increase of market size, the pro t difference between SDM and PDM will be larger. is represents that PDM is the best choice for the catering business with small market size. For catering businesses with large market size, they can choose SDM mode, which is more bene cial to obtaining greater pro ts.
As observed in Figure 11, the optimal pro t of the rider increases with the market size under both modes. e optimal pro t under SDM is the largest. e bigger the market size is, the higher the pro t gap between the SDM and the BSM is. is reveals that the rider can get higher pro ts by choosing SDM and BSM mode. Meanwhile, with the increase of market size, SDM mode should be chosen. In addition, it represents that the rider prefers the mode with xed wage.

Managerial Insights
Due to the increasing demand of consumers for online ordering and o ine dining, managers are provided with the following suggestions to improve services and ultimately increase pro ts.
(a) e takeout platform should cooperate with more catering businesses and adopt di erent revenue sharing rates considering the catering businesses with di erent market sizes. (b) e takeout platform can optimize its service quality e ort by appropriately adjusting the revenue sharing rate. (c) e catering business should properly consider the market size and choose the corresponding operation mode to achieve sustainable pro t growth. Complexity offline prices, and obtain more profits by dynamically adjusting online and offline prices. (e) e rider who chooses to join the self-built platform mode can get more revenue.

Conclusions
is paper considers an O2O takeout service supply chain consisting of an O2O takeout platform, a catering business, and a rider. By establishing a mathematical model, this research analyzes and compares the optimal quality effort and the optimal profit under platform distribution, business self-distribution, and business self-built platform + distribution. e above results show that the optimal platform's service quality effort is positively correlated with revenue sharing rate; the optimal catering business's service quality effort is negatively correlated with revenue sharing rate. In addition, the online price is positively correlated with revenue sharing rate, while the offline price is negatively correlated with revenue sharing rate. Specifically, online and offline prices are different in the three operation modes, and the online price is slightly lower than the offline price. Obviously, the optimal profit of all supply chain members increases with the market size.
With the continuous improvement of economy, the takeout industry is developing rapidly. In the future development process, members of the takeout service supply chain should actively provide consumers with more highquality services. e takeout platform should improve consumer satisfaction by appropriately extracting the revenue sharing rate. e catering business should focus on formulating different online and offline prices to obtain more economic profits. e rider should cooperate with appropriate platforms or businesses to improve the service quality and win better customer experience.
In further research, the different sensitivities of consumers to the service quality of platforms, catering businesses, and riders can be explored. In addition, the model adopts the traditional linear demand function. However, there is a certain gap between this linear demand function and reality.