Supply Strategies and Business Model Options for Online Retailers of Agricultural Products

Abstract

Online retail of agricultural products is an emerging form of online shopping that has enormous value for researching sustainable agricultural product logistics and the sustainability of e-commerce. By reviewing these practices in China, this paper summarizes three models of online retail of agricultural products: community group buying, prepositioned warehousing, and a mixed model in which the former two are carried out simultaneously. This paper considers the uncertainty of demand and applies the newsboy model to obtain the expected profit function of the three models. The paper proves that the objective functions of the optimization models are all convex functions of the supply capacity. The optimal supply strategy and the expression for each business model are then derived. Next, the intervals for enterprises to choose the profit-optimal business model are given and visually demonstrated through graphs. These findings lead to managerial insights: in economically underdeveloped regions, it is appropriate for enterprises to conduct community group buying businesses; in economically developed regions, it is appropriate for enterprises to conduct prepositioned warehouse businesses; and in regions with average economic development, it is appropriate for enterprises to conduct both businesses. Finally, this paper verifies the optimal supply strategy for the online retail model for agricultural products through numerical experiments and sensitivity analyses for different cost parameters.

1. Introduction

The online purchase of agricultural products was a rapidly growing consumption pattern in China after the outbreak of COVID pandemic in 2020. The market size for fresh produce e-commerce in China will reach approximately 650 billion yuan in 2024; compared with a size of 29 billion yuan in 2014, the market size of fresh produce e-commerce in China will have grown 22 times in nine years.

The rise of e-commerce platforms has promoted the digital development of agriculture, with information technology gradually being applied in agricultural production, processing, logistics, and other links, improving efficiency. The online retail model for agricultural products can significantly shorten the circulation chain of agricultural products, effectively addressing farmers’ need to increase their income and consumers’ need for high-quality fresh agricultural products. Online retail enterprises for agricultural products deeply integrate scattered logistics resources, farmers, and consumers into the logistics network of agricultural products so that the urban and rural consumer markets are directly linked, which is highly important to the agricultural sector. Agricultural product e-commerce can expand sales channels through diverse sales models such as direct sales, group buying, and pre-sales, helping farmers flexibly adjust their sales strategies according to different seasons and market demands. Consumers can easily purchase fresh agricultural products through e-commerce platforms, enhancing their shopping experience.

Overall, the online retail of agricultural products plays an important role in optimizing and developing the agricultural product supply chain by enhancing market efficiency, broadening sales channels, improving product quality, increasing farmers’ income, and promoting the upgrading of the agricultural industry. With continuous technological advancements, the impact of e-commerce on the agricultural product supply chain will become even more profound in the future.

With the development of online social software and mobile payments, the online retailing of agricultural products has gradually become one of the more popular business models in China. In its splendor, online retailing of agricultural products has also produced a variety of different models according to different regions as well as different market demands.

The community group buying model centers on “pre-sale + self-pickup”, connecting consumers with platforms through community leaders, facilitating the centralized procurement and distribution of agricultural products, which effectively reduces logistics costs and improves fulfillment efficiency [1]. However, community group buying faces challenges such as a loose organization and management by group leaders and unstable supply chains, which directly impact consumer experience and satisfaction.

The prepositioned warehouse model establishes small storage units within urban areas, shortening transportation distances and enabling rapid delivery and instant service, making it particularly suitable for consumers who prioritize efficiency and high quality [2]. However, the profitability and sustainability of the prepositioned warehouse model are influenced by factors such as business model innovation and financing conditions [3].

The “community group buying + prepositioned warehouse” mixed model combines the advantages of both approaches, enhancing delivery efficiency and user experience through prepositioned warehouses while leveraging the low costs and high penetration of community group buying to achieve broader market coverage [4]. The complexity of the hybrid model also brings about higher operational and management challenges, particularly in terms of supply chain stability and logistics cost control.

Through reasonable supply strategies, enterprises can better understand and predict changes in consumer demand, allowing them to adjust the variety and quantity of products in a timely manner, thereby improving customer satisfaction. Before launching an online retail business for agricultural products, a company needs to establish an appropriate logistics network, estimate consumer demand, and determine the supply capacity (i.e., the amount of goods to be imported from suppliers) of that logistics network in the area where it will conduct business. However, consumer demand is uncertain. This poses a challenge for online retailers of agricultural products in making supply decisions. In addition, there are many business models that firms can construct, and how to choose the one that will maximize their profitability is also an important issue.

Research on the supply strategies and business model choices of online retail enterprises for agricultural products can reduce operational costs and enhance market responsiveness. This helps to optimize the supply chain structure of agricultural products and promotes the sustainable development of the agricultural product supply chain.

The literature focuses on the issues of the online retail of agricultural products, the purchase quantity of goods, and supply chain demand uncertainty; however, few in-depth studies have evaluated the various models for the online retail of agricultural products, and research on the supply strategy for operating a business under the premise of consumer demand uncertainty is lacking.

Therefore, this study is highly necessary. To solve the above problems, this paper establishes a model for an online retail supply strategy for agricultural products based on the above three models of online retail (community group buying, the prepositioned warehouse model, and a mixture of the two), taking into account the uncertainty of consumer demand and through the expected profit function of the three models. The model is then solved numerically to calculate the value of the supply capacity at the profit optimum. Based on the model expression, the optimal business model chosen and the effective interval of its supply strategy are determined. Finally, sensitivity analysis is used to make recommendations for online retailers of agricultural products.

In this study, Section 1 is the introduction, Section 2 is the literature review, Section 3 establishes a model for an online retail supply strategy for agricultural products, Section 4 numerically solves the mathematical model, Section 5 conducts numerical and sensitivity analyses by combining the data of Chinese firms, and Section 6 describes the conclusions, theoretical value, and managerial implications of this paper.

2. Literature Review

The research topics relevant to this paper include agricultural product online retail, commodity purchase quantities, and demand uncertainty. The following is a literature review of these three areas.

2.1. Agricultural Product Online Retail

Online retail for agricultural products has developed previously and has experienced various business model iterations, and there have been failures and successes in the exploration process. Farmigo is an innovative agricultural product sales platform in the U.S. On this platform, farmers can directly manage the sale and distribution of agricultural products. Tengwei et al. [5] argue that the Farmigo model pays attention to the production and marketing ends of the agricultural supply chain and reduces transaction costs. Rory et al. [6], through an analysis of the Amazon Fresh business model, argue that the unreasonable scope of distribution is one of the reasons for the demise of this fresh food business and summarize the operational capabilities necessary for fresh food e-commerce companies to participate in competition with offline shops. Galtier et al. [7] suggested that market information systems should be used to enhance the transparency and standardization of the online sales of agricultural products.

2.1.1. Community Group Buying

Community group buying is an e-commerce model that has emerged in recent years, and many scholars define community group buying based on online group buying. Kauffman et al. [8] argue that online group buying is a way to bring buying together on one online platform and, as long as these groups of consumers with the same intention and buying needs are large enough, they can take the initiative in the price game with sellers. Anand [9], on the other hand, argues from the seller’s perspective that online group buying is just a marketing tool for sellers to put consumers with purchase intentions together to stimulate consumers’ purchases and then achieve profitability by selling more at a lower price. According to Xue [10], community group buying gradually evolved from online group buying, which was initially a spontaneous act of some people in the community recommending goods to each other. With the continuous development of social tools and media on the internet, the addition of capital has given rise to a broader definition of community group buying. Huang [11] argues that community group buying is a community-based retailing approach that brings together people living in the same community to sell in a WeChat group, with obvious regionalization and localization characteristics. Community residents will also be willing to try the new purchase mode based on their trust in neighborhood referrals.

Community group buying is an agricultural product online retailing model that provides consumers with online shopping services for agricultural products through a three-level logistics network (regional distribution centers to grid warehouses to self-pickup stations). Community group buying adopts the next-day delivery model of ‘presale + self-pick-up’, and the platform recruits brokers (mostly housewives or convenience store owners), who operate work groups through social software to meet the needs of consumers in the community. The platform will cut off orders every night and purchase goods from suppliers, who will deposit goods with the regional distribution center (provincial warehouse) in advance. After the platform makes the purchase, the regional distribution center will sort the goods and transport them to grid warehouses (small distribution centers or freight stations) for ‘lightering’ and then transport them to self-pickup stations where brokers are located; finally, consumers will go to brokers to pick up the goods [12,13]. This article summarizes scholars’ research on the community group buying process and presents the operational model diagram as shown in Figure 1.

The existing research on community group buying focuses on supply chain collaboration and logistics network optimization. Some scholars have employed a two-level programming model to study the collaborative optimization of pricing and delivery routes for fresh agricultural products under the community group buying model [4]. Other researchers have constructed a logistics network model for fresh agricultural products under the community group buying model with the objective of minimizing costs, obtaining joint optimization results for location and routing considering direct supply from the production area [14].

2.1.2. Prepositioned Warehouse

A prepositioned warehouse is a logistics warehouse distribution model that has emerged in recent years. Compared with traditional e-commerce, prepositioned warehouses are small in scale and close to consumers. Liu [15] regards the prepositioned warehouse as a small or medium-sized warehousing and distribution center because it only undertakes warehousing and distribution functions. Xie [16] believes that the service objective of a prepositioned warehouse is directly for consumers because its small size and close proximity to customers generates lower costs than end stores and because it is easier to carry out site selection. At present, there are few theories regarding prepositioned warehouses, and some scholars believe that a prepositioned warehouse is actually a variant of a transshipment warehouse in the traditional logistics and distribution model [17].

A prepositioned warehouse can be regarded as a small warehouse and front-distribution center, and a regional distribution center needs to supply only a prepositioned warehouse. Once the consumer orders, the goods from the prepositioned warehouse are close to the consumer rather than arriving from the regional distribution center in the suburbs, and can support the consumer receiving the goods in a few hours. The platform regularly purchases goods from suppliers, and the regional distribution centers replenishes the goods according to a unified arrangement. There may be differences in the form of prepositioned warehouses [18]; some prepositioned warehouses only serve online transactions and do not generate offline commercial activities, while others combine offline stores with prepositioned warehouses, which can provide consumers with an omni-channel service of instant online delivery and offline in-store consumption. This article summarizes scholars’ research on the prepositioned warehouse process and presents the operational model diagram as shown in Figure 2.

Research on the application of prepositioned warehouses focuses on issues such as inventory, site selection, and routing. Feng [19] proposed an inventory strategy optimization plan for prepositioned warehouses based on Internet of Things information technology and supply chains, in conjunction with storage theory. Huang [20] studied the site selection, routing, and the joint optimization problem of both under the omnichannel model.

2.1.3. Community Group Buying Combined with Prepositioned Warehouses

With the development of prepositioned warehouses in practice, enterprises have found that high logistics costs, high storage requirements, and the high prices of “hourly delivery” goods have made it difficult for them to expand their potential customer base. Therefore, some enterprises have combined the business model of “community group buying” and “prepositioned warehouse” so that the types of commodities they operate can be expanded from the “hourly delivery” model to include “next-day delivery” products.

This model can effectively address key issues in the online sales process of fresh agricultural products, such as high delivery costs, significant losses, and difficulties with ensuring quality. The mixed model currently lacks mature theoretical research.

2.2. Commodity Purchase Quantity

Quantitative research on an online retail supply strategy for agricultural products is equivalent to addressing the problem of commodity purchase quantity; for example, in research on the material stockpiling problem, products are divided into mathematical planning methods and newsboy models.

Some scholars have used mathematical planning methods to study the stockpiling decisions of suppliers [21,22,23]. For example, using stochastic programming methods, Chang et al. [24] investigated the problems of warehouse location and inventory decision-making in response to a flood disaster. Using a multi-objective stochastic programming method, Mohammadi et al. [25] investigated how to determine the stockpile quantity of supplies with maximum expected demand coverage, minimum expected cost, and minimum difference in the level of service between nodes.

In addition, since the newsboy model is suitable for solving the problem of commodity purchasing quantity under uncertain demand, in recent years, some scholars have begun to apply the newsboy model to determine the reserve level of supplies [26,27]. For example, Campbell et al. [28] determined the supplier’s location decision and the optimal physical stockpile level based on the newsboy model. Chen et al. [29] studied the optimal physical stockpile decision of emergency supplies for nonprofit organizations based on the newsboy model by considering the uncertainty of emergency supply demand and the quantity of social donations.

2.3. Demand Uncertainty

The demand for an online retail model for agricultural products is characterized by uncertainty, timeliness, and phasing, and the study of a relevant supply strategy can draw on studies related to demand uncertainty in the field of inventory management. For example, Reimann [30] used the newsboy model to study the optimal physical and production capacity of mixed reserve decisions in commercial supply chains. On this basis, Reimann [31] further constructed a product delay strategy model for the selling season. Bicer et al. [32] investigated the stockpiling decision problem by building a dynamic planning model with capacity constraints and demand forecast updates. Garvey et al. [33] considered the chain of supply chain disruptions and risk propagation effects, constructed Bayesian networks with a newsboy model targeting risk severity, and obtained the optimal inventory and production decisions based on a measure of risk severity. Florian et al. [34] further investigated the optimal decision-making process for inventory and reserve capacity in a continuous multistage supply chain.

2.4. Comments

Currently, there is relatively little research on the supply strategy issues of online retail for agricultural products. The existing literature has focused on problems such as the online retail of agricultural products, commodity purchase quantities, and supply chain demand uncertainties, but there has been little in-depth discussion on various models for online retail of agricultural products. By reviewing the deficiencies of the literature, the following questions can be answered by researchers on the choice of online retail mode for agricultural products and decision-making regarding supply capacity:

(1)

There is a lack of research on supply strategies for agricultural e-commerce. Scholars have mainly concentrated on optimizing logistics networks [4] and the game theory among supply chain members [14,19,20].

(2)

Many articles have studied purchase quantity or stocking decisions through the newsboy model. However, very few articles have studied the issue of purchase quantity or supply decisions for the online retailing of agricultural products in the context of agricultural e-commerce.

(3)

There has been no strict classification of different models for agricultural e-commerce. Existing studies in agricultural e-commerce have focused on the perishable nature of agricultural products and have considered the impact of delivery time on consumers. However, there has been no classification of agricultural e-commerce based on differences in delivery times, leading to confusion in this field of research. For example, studies on the site selection problem of community group buying do not highlight the characteristics of next-day delivery for community group buying products, and changing the research object to prepositioned warehouses does not affect the research results.

(4)

Scholars have conducted preliminary research on business models such as community group buying and prepositioned warehouses, but currently, the research is more independent, and no consideration has been given to which model is more suitable for the enterprise.

Therefore, the integration of the research directions of online retail for agricultural products and commodity purchase quantities is very meaningful. This paper will study supply strategies for agricultural e-commerce by establishing an online retail supply strategy model for agricultural products, considering consumer demand uncertainty, while providing selection recommendations for each e-commerce model.

3. Model Building

3.1. Model Assumptions and Notation

The community group buying platform purchases goods from suppliers only after the order is cut off every night. The suppliers will store the goods in advance in the regional distribution centers belonging to the platform, and the goods management model is similar to a supplier-managed inventory. This business model saves inventory costs to a large extent and enables community group buying firms to sell goods at a lower price p₁. Community group buying’s asset-light operations and next-day delivery times give it a more abundant supply capacity r.

Prepositioned warehouses shorten delivery times by storing goods in advance in the prepositioned warehouse but also increase construction and operation costs. Due to the high freshness requirements of fresh produce, a prepositioned warehouse also requires a certain inventory holding cost h. Compared with the “next-day delivery” of community group buying, the fast delivery time of the prepositioned warehouse makes consumers accept that the firm sells goods at a higher price p₂, which is assumed to be p₂ ≥ p₁ in this paper. In addition, due to the limited storage capacity of the prepositioned warehouse, it can provide only a lower supply capacity s.

Some companies have combined the business models of “community group buying” and “prepositioned warehouse” to expand the types of goods handled from “hourly delivery” to “next-day delivery”. Simply put, consumers can choose to buy next-day delivery products when the demand for products in the prepositioned warehouse is not satisfied. In this paper, we assume that when consumers are faced with both “hourly delivery” and “next-day delivery” products, they will not be affected by the price and will prefer products with faster delivery times.

Regardless of the business model, the supply capacity determines the business scale, while the supply capacity is the embodiment of the level of logistics network construction and operation. If the unit construction and operation cost is e, then the cost for community group buying enterprises to have a logistics network with supply capacity r is e₁r, and the cost for prepositioned warehouse enterprises to have a logistics network with supply capacity s is e₂s. The construction and operation costs for prepositioned warehouses are generally higher than the costs of community group buying; this paper assumes that e₂ ≥ e₁.

The notation is defined in

Table 1. Description of Symbols—Decision Variables.

Decision Variables	Definition
r	Commodity supply capacity of community group buying business
s	Commodity supply capacity of prepositioned warehouse business

and

Table 2. Description of symbols and parameters.

Parameter	Definition
e1	Community group buying construction and operation cost
e2	Prepositioned warehouse construction and operation cost
c	Average procurement cost of commodities
p1	Average sale price of goods in community group buying business
h	Average holding cost of goods in prepositioned warehouse
p2	Average sale price of goods in prepositioned warehouse business
x	Stochastic demand from consumers
f(x)	Probability density function of demand
F(x)	Probability distribution function of demand

below:

The model assumptions are summarized as follows:

(1)

p₂ ≥ p₁;

(2)

e₂ ≥ e₁;

(3)

The sale price of goods in any business model is much greater than that of any form of cost in that business model;

(4)

Consumers, when confronted with goods from both the prepositioned warehouse business and the community group buying business, will prefer goods from the prepositioned warehouse.

3.2. Profit Function

An online retailer of agricultural products will build a logistics network according to a predetermined supply capacity, with a unit construction cost of e. After the completion of the logistics network, the online retailer of agricultural products starts its business operations, purchases goods at price c, and sells them at price p.

(1)

Profit function of the community group buying business

The study of the profit of community group buying businesses needs to consider the following two cases:

Case 1: When 0 ≤ x ≤ r, the community group’s supply capacity can meet demand, and x items are sold;

Case 2: When r < x, the community group’s supply capacity cannot meet demand, only r items can be sold, regardless of how large the demand is.

To summarize, considering the construction cost, the profit function of community group buying in each case can be written as:

$${\pi }_1^{*}\left(r\right)=\left\{\begin{array}{c}-e_{1}r+\left(p_1-c\right)x,\hspace{1em}0\le x\le r\\ -e_{1}r+\left(p_1-c\right)r,\hspace{1em}r<x\end{array}\right.$$

(1)

Taking the expectation for ${\pi }_1^{*}$ yields an expression for the profit function of the community group buying business:

$${\pi }_1\left(r\right)=E\left[{\pi }_1^{*}\left(r\right)\right]=-e_{1}r+{\int }_0^r\left(p_1-c\right)\mathit{xf}\left(x\right)\mathit{dx}+{\int }_r^{+\infty }\left(p_1-c\right)\mathit{rf}\left(x\right)\mathit{dx}$$

(2)

Profit function of prepositioned warehouse

The study of the profit of a prepositioned warehouse business needs to consider the following two cases:

Case 1: When 0 ≤ x ≤ s, the prepositioned warehouse’s supply capacity can meet demand and x items are sold, and the remaining (s − x) items incur holding costs;

Case 2: When s < x, the prepositioned warehouse’s supply capacity cannot meet demand, only s items can be sold, regardless of how large the demand is.

To summarize, considering the construction cost, the profit function of the prepositioned warehouse in each case can be written as follows:

$${\pi }_2^{*}\left(s\right)=\left\{\begin{array}{c}-e_{2}s+\left(p_2-c\right)x-h\left(s-x\right),\hspace{1em}0\le x\le s\\ -e_{2}s+\left(p_2-c\right)s,\hspace{1em}s<x\end{array}\right.$$

(2)

Taking the expectation for ${\pi }_2^{*}$ yields an expression for the profit function of the prepositioned warehouse business:

$${\pi }_2\left(s\right)=E\left[{\pi }_2^{*}\left(s\right)\right]=-e_{2}s+{\int }_0^s[\left(p_2-c\right)x-h\left(s-x\right)]f\left(x\right)\mathit{dx}+{\int }_s^{+\infty }\left(p_2-c\right)\mathit{sf}\left(x\right)\mathit{dx}$$

(3)

Profit function of the mixed model of community group buying and prepositioned warehouse

The study of the profit of the mixed model needs to consider the following three cases:

Case 1: When 0 ≤ x ≤ s, the prepositioned warehouse’s supply capacity can meet demand, x items are sold, and the remaining (s − x) items incur holding costs;

Case 2: When s < x ≤ s + r, the supply capacity of the prepositioned warehouse cannot satisfy the demand, and the excess demand is satisfied via community group buying; the prepositioned warehouse sells s items, and community group sells (x − s) items;

Case 3: When s + r < x, the supply capacity of both the prepositioned warehouse and the community group cannot satisfy the demand; no matter how large the demand is, the prepositioned warehouse can sell only s items, and community group can sell only r items.

To summarize, considering the construction costs, the profit function of the mixed model in each case can be written as follows:

$${\pi }_3^{*}\left(r,s\right)=\left\{\begin{array}{c}-e_{2}s-e_{1}r+\left(p_2-c\right)x-h\left(s-x\right),\hspace{1em}0\le x\le s\\ -e_{2}s-e_{1}r+\left(p_2-c\right)s+\left(p_1-c\right)\left(x-s\right),\hspace{1em}s<x\le s+r\\ -e_{2}s-e_{1}r+\left(p_2-c\right)s+\left(p_1-c\right)r,\hspace{1em}s+r<x\end{array}\right.$$

(3)

Taking the expectation for ${\pi }_3^{*}$ yields an expression for the profit function of the mixed model of community group buying and prepositioned warehouse:

$$\begin{gathered} {\pi }_3\left(r,s\right)=E\left[{\pi }_3^{*}\left(r,s\right)\right] \\ =-e_{2}s-e_{1}r+{\int }_0^s\left[\left(p_2-c\right)x-h\left(s-x\right)\right]f\left(x\right)\mathit{dx}+{\int }_s^{s+r}\left[\left(p_2-c\right)s+\left(p_1-c\right)\left(x-s\right)\right]f\left(x\right)\mathit{dx}+{\int }_{s+r}^{+\infty }\left[\left(p_2-c\right)s+\left(p_1-c\right)r\right]f\left(x\right)\mathit{dx} \end{gathered}$$

3.3. Online Retail Supply Strategy Model for Agricultural Products

Finding the maximum value of the profit π is equivalent to finding the minimum value of −π. It is useful to set Z = −π. Thus, the online retail supply strategy model for agricultural products is:

(1)

Community group buying

min Z₁(r)
st. r ≥ 0

(2)

Prepositioned warehouse

min Z₂(s)
st. s ≥ 0

(3)

Mixed model of community group buying and prepositioned warehouse

min Z₃(r,s)
st. s ≥ 0

r ≥ 0

4. Model Solution

It is possible to simplify the profit functions of the three online retail business models for agricultural products using the integral formula:

$$\int \mathit{xf}\left(x\right)\mathit{dx}=\mathit{xF}\left(x\right)-\int F\left(x\right)\mathit{dx}$$

where f(x) is the derivative of F(x). After simplification, the three profit functions are obtained:

$${\pi }_1\left(r\right)=-\left(p_1-c\right){\int }_0^{r}F\left(x\right)\mathit{dx}+\left(p_1-c-e_1\right)r$$

(4)

$${\pi }_2\left(s\right)=-\left(p_2-c+h\right){\int }_0^{s}F\left(x\right)\mathit{dx}+\left(p_2-c-e_2\right)s$$

(5)

$${\pi }_3\left(r,s\right)=-\left(p_2-c+h\right){\int }_0^{s}F\left(x\right)\mathit{dx}-\left(p_1-c\right){\int }_s^{s+r}F\left(x\right)\mathit{dx}+\left(p_2-c-e_2\right)s+\left(p_1-c-e_1\right)r$$

(6)

Next, the three online retail business models for agricultural products are solved separately:

4.1. Supply Strategy Model Solution for Community Group Buying

min Z₁(r)
st. r ≥ 0

The constraints are clearly convex.

Taking the first-order derivative with respect to r for Z₁ yields

$${\displaystyle \frac{d}{\mathit{dr}}}{Z}_1\left(r\right)=\left(p_1-c\right)F\left(r\right)-\left(p_1-c-e_1\right)$$

Taking the second-order derivative with respect to r for Z₁ yields

$${\displaystyle \frac{d^2}{{\mathit{dr}}^2}}{Z}_1\left(r\right)=\left(p_1-c\right)f\left(r\right)$$

Clearly, the second-order derivative of Z₁ with respect to r is greater than zero.

Theorem 1. 

Z₁ is a convex function of r.

According to Theorem 1, Z₁ has a minimum value of approximately r. The KKT conditions for the model Z₁

$$\begin{gathered} \left(p_1-c\right)F\left(r\right)-\left(p_1-c-e_1\right)-{\lambda }^r=0 \\ -r{\lambda }^r=0 \\ {\lambda }^r\ge 0 \\ -r\le 0 \end{gathered}$$

At this point, it is necessary to classify and discuss the following:

(1)

λ^r = 0. According to the expression of the KKT condition, it can be seen that −r < 0, i.e., to carry out community group buying business the optimal value of r is found to be

$$r=F^{-1}\left({\displaystyle \frac{p_1-c-e_1}{p_1-c}}\right)$$

(2)

r = 0. At this point, the KKT condition has no solution and is discarded.

Conclusion 1. 

Model Z₁ obtains the maximum profit for π₁ when it takes the minimum value of r. The optimal value of r is:

$$r=F^{-1}\left({\displaystyle \frac{p_1-c-e_1}{p_1-c}}\right)$$

4.2. Supply Strategy Model Solution for a Prepositioned Warehouse

min Z₂(s)
st. s ≥ 0

The constraints are clearly convex.

Taking the first-order derivative with respect to s for Z₂ yields

$${\displaystyle \frac{d}{\mathit{ds}}}{Z}_2\left(s\right)=\left(p_2-c+h\right)F\left(s\right)-\left(p_2-c-e_2\right)$$

Taking the second-order derivative with respect to s for Z₂ yields

$${\displaystyle \frac{d^2}{{\mathit{ds}}^2}}{Z}_2\left(s\right)=\left(p_2-c+h\right)f\left(s\right)$$

Clearly, the second-order derivative of Z₂ with respect to s is greater than zero.

Theorem 2. 

Z₂ is a convex function of s.

According to Theorem 2, Z₂ has a minimum value of approximately s. The KKT conditions for the model Z₂ are

$$\begin{gathered} \left(p_2-c+h\right)F\left(s\right)-\left(p_2-c-e_2\right)-{\lambda }^s=0 \\ -s{\lambda }^s=0 \\ {\lambda }^s\ge 0 \\ -s\le 0 \end{gathered}$$

At this point, it is necessary to classify and discuss the following:

(1)

λ^s = 0. According to the expression of the KKT condition, it can be seen that −s < 0, i.e., to carry out a prepositioned warehouse business the optimal value of s is found to be

$$s=F^{-1}\left({\displaystyle \frac{p_2-c-e_2}{p_2-c+h}}\right)$$

(2)

s = 0. At this point, the KKT condition has no solution and is discarded.

Conclusion 2. 

Model Z₂ obtains the maximum profit for π₂ when it takes the minimum value of s. The optimal value of s is:

$$s=F^{-1}\left({\displaystyle \frac{p_2-c-e_2}{p_2-c+h}}\right)$$

4.3. Supply Strategy Model Solution for the Mixed Model

min Z₃(r,s)
st. s ≥ 0

r ≥ 0

The constraints are clearly convex.

Taking the first-order partial derivatives with respect to (r,s) for model Z₃

$${\displaystyle \frac{d}{\mathit{dr}}}{Z}_3\left(s,r\right)=\left(p_1-c\right)F\left(s+r\right)-\left(p_1-c-e_1\right)$$

$${\displaystyle \frac{d}{\mathit{ds}}}{Z}_3\left(s,r\right)=\left(p_2-p_1+h\right)F\left(s\right)+\left(p_1-c\right)F\left(s+r\right)-\left(p_2-c-e_2\right)$$

Taking the second-order partial derivative with respect to (r,s) for model Z₃

$${\displaystyle \frac{d^2}{{\mathit{dr}}^2}}{Z}_3\left(s,r\right)=\left(p_1-c\right)f\left(s+r\right)$$

$${\displaystyle \frac{d^2}{\mathit{drds}}}{Z}_3\left(s,r\right)=\left(p_1-c\right)f\left(s+r\right)$$

$${\displaystyle \frac{d^2}{\mathit{dsdr}}}{Z}_3\left(s,r\right)=\left(p_1-c\right)f\left(s+r\right)$$

$${\displaystyle \frac{d^2}{{\mathit{ds}}^2}}{Z}_3\left(s,r\right)=\left(p_2-c+h\right)f\left(s\right)+\left(p_1-c\right)F\left(s+r\right)$$

It can be shown that all the sequential principal subequations of the Hessian matrix of Z₃ are greater than zero. Therefore, the Hessian matrix of Z₃ is a positive definite.

Theorem 3. 

Z₃ is a joint convex function of r,s.

According to Theorem 3, Z₃ has a minimum value of (r,s). The KKT conditions for the model Z₃ are

$$\begin{gathered} \left(p_1-c\right)F\left(s+r\right)-\left(p_1-c-e_1\right)-{\lambda }^r=0 \\ \left(p_2-p_1+h\right)F\left(s\right)+\left(p_1-c\right)F\left(s+r\right)-\left(p_2-c-e_2\right)-{\lambda }^s=0 \\ -r{\lambda }^r=0 \\ -s{\lambda }^s=0 \\ {\lambda }^r\ge 0 \\ {\lambda }^s\ge 0 \\ -r\le 0 \\ -s\le 0 \end{gathered}$$

At this point, it is necessary to classify and discuss the following:

(1)

λ^r = 0 and λ^s = 0.

According to the expression of the KKT condition, we can see that −r < 0 and −s < 0, i.e., there is a need to carry out both community group buying and establish a prepositioned warehouse. Finding the optimal values of r and s:

$$r=F^{-1}\left({\displaystyle \frac{p_1-c-e_1}{p_1-c}}\right)-F^{-1}\left({\displaystyle \frac{p_2-p_1-e_2+e_1}{p_2-p_1+h}}\right)$$

$$s=F^{-1}\left({\displaystyle \frac{p_2-p_1-e_2+e_1}{p_2-p_1+h}}\right)$$

It is worth noting that the basis for operating two businesses simultaneously is r > 0. Since the probability distribution function of demand, F(x), is a monotonically increasing function, the condition that two businesses can be operated at the same time is equivalent to F(s + r) > F(s):

$${\displaystyle \frac{p_1-c-e_1}{p_1-c}}>{\displaystyle \frac{p_2-p_1-e_2+e_1}{p_2-p_1+h}}$$

We can obtain

$$p_2-p_1<{\displaystyle \frac{h\left(p_1{-c-e}_1\right)+\left(p_1-c\right)\left(e_2-e_1\right)}{e_1}}$$

Let it be that p₂ − p₁ < β.

Another condition for operating two businesses at the same time is that s > 0, which is equivalent to F(s) > 0; that is,

$${\displaystyle \frac{p_2-p_1-e_2+e_1}{p_2-p_1+h}}>0$$

We can obtain

$$p_2-p_1>e_2-e_1$$

Let it be that p₂ − p₁ > α. It can be easily proven that α < β holds according to the model assumptions.

(2)

r = 0 and λ^s = 0.

According to the expression of the KKT condition, we can know that λ^r ≥ 0 and −s < 0, i.e., the supply capacity of community group buying is 0, and only the prepositioned warehouse business is carried out at this time. Finding the optimal values of r and s:

r = 0

$$s=F^{-1}\left({\displaystyle \frac{p_2-c-e_2}{p_2-c+h}}\right)$$

s is clearly larger than 0. From λ^r ≥ 0 and the KKT conditional expression, it follows that

$$\left(p_1-c\right)F\left(s+r\right)-\left(p_1-c-e_1\right)={\lambda }^r\ge 0$$

and r = 0, so that

$${\displaystyle \frac{p_2-c-e_2}{p_2-c+h}}\ge {\displaystyle \frac{p_1-c-e_1}{p_1-c}}$$

We can obtain

$$p_2-p_1\ge {\displaystyle \frac{h\left(p_1{-c-e}_1\right)+\left(p_1-c\right)\left(e_2-e_1\right)}{e_1}}$$

That is, p₂ − p₁ ≥ β.

(3)

λ^r = 0 and s = 0.

According to the expression of the KKT condition, we know that −r < 0 and λ^s ≥ 0, i.e., the supply capacity of the prepositioned warehouse is 0, and only the community group buying business is carried out at this time. Finding the optimal values of r and s:

$$r=F^{-1}\left({\displaystyle \frac{p_1-c-e_1}{p_1-c}}\right)$$

s = 0

r is clearly larger than 0. From λ^s ≥ 0 and the KKT conditional expression, it follows that

$$\left(p_2-p_1+h\right)F\left(s\right)+\left(p_1-c\right)F\left(s+r\right)-\left(p_2-c-e_2\right)={\lambda }^s\ge 0$$

and s = 0, so we can obtain

$$p_2-p_1\le { e}_2-e_1$$

That is, p₂ − p₁ ≤ α.

(4)

r = s = 0. At this point, the KKT condition has no solution and is discarded.

Conclusion 3. 

a. When α < p − p₁ < β, both the community group buying and prepositioned warehouse businesses make sense to carry out, and the optimal values of r and s are

$$r=F^{-1}\left({\displaystyle \frac{p_1-c-e_1}{p_1-c}}\right)-F^{-1}\left({\displaystyle \frac{p_2-p_1-e_2+e_1}{p_2-p_1+h}}\right)$$

$$s=F^{-1}\left({\displaystyle \frac{p_2-p_1-e_2+e_1}{p_2-p_1+h}}\right)$$

At this point, model Z3 takes the minimum value with respect to (r,s), and π₃ obtains the maximum profit;

b. When p₂ − p₁ ≥ β, the enterprise only carries out the business of the prepositioned warehouse, and the optimal values of r and s are

r = 0

$$s=F^{-1}\left({\displaystyle \frac{p_2-c-e_2}{p_2-c+h}}\right)$$

At this point, Z₃ is exactly equivalent to Z₂, and the optimal solution for s is also the same;

c. When p₂ − p₁ ≤ α, the enterprise only carries out the business of community group buying, and the optimal values of r and s are

$$r=F^{-1}\left({\displaystyle \frac{p_1-c-e_1}{p_1-c}}\right)$$

s = 0

At this point, Z₃ is exactly equivalent to Z₁, and the optimal solution for r is also the same.

Taken together, the above findings show that the value of the average sale price p₂ of prepositioned warehouse goods and the average sale price p₁ of community group buying goods have an effect on the decision of an enterprise to carry out different businesses. Figure 3 below shows the effect of the relationship between p₂ − p₁ and p₁ on the enterprise conducting the online retail business of agricultural products, with the minimum value of p₁ being taken as c + e₁ and the minimum value of p₂ − p₁ being taken as 0.

Figure 3 shows that when the value of p₂ − p₁ is less than α, the enterprise chooses to conduct the community group buying business. Because the construction and operation costs of the prepositioned warehouse are higher than those of community group buying, the prepositioned warehouse business does not earn more profit than the community group buying business when p₂ is very close to p₁. α is a constant.

When the value of p₂ − p₁ is (α, β), the enterprise chooses to carry out two businesses at the same time, and if the supply capacity of the prepositioned warehouse business is unable to satisfy consumer demand, this can be supplemented by the community group buying business. β is a linear function of p₁, with the slope determined by h, e₁, and e₂ together.

When the value of p₂ − p₁ is larger than β, the community group buying business cannot compete with the prepositioned warehouse, and there is no sense in carrying out the community group buying business.

5. Numerical Experiments

In this section, the authors use numerical experiments to determine the optimal supply strategies of different models of online retail logistics networks for agricultural products and how different values of model parameters affect their results.

Referring to Chen [35] and Zhang [36] for numerical simulations, we assume that the demand obeys a normal distribution. In this paper, we assume x~N(10,2). The cost parameters for the online retailer of agricultural products are shown in

Table 3. Parameter settings.

Parameters	Value
Community group buying construction and operation cost e1	500
Prepositioned warehouse construction and operation cost e2	1000
Average procurement cost of commodities c	2000
Average sale price of goods in community group buying business p1	3000
Average holding cost of goods in prepositioned warehouse h	1000
Average sale price of goods in prepositioned warehouse business p2	3700

below:

5.1. Results

To compare the various business models for online retailers of agricultural products, the optimal supply strategies and corresponding profits for the different models chosen are given in

Table 4. Optimal supply strategies for different online retail models of agricultural products.

Model	Optimal Supply Strategy	Profit
Community group buying (r1)	(10)	4202
Prepositioned warehouse (s2)	(8.7087)	5251
Mixed model (r3, s3)	(2.3737, 7.6263)	5531

below. The optimal supply strategy refers to the optimal quantity of goods (measured in thousands of units) required to achieve the highest profit for each business model on a daily basis. Profit indicates the optimal expected profit (measured in yuan) per day under that business model.

Table 4 shows that the profitability of the mixed model is optimal when p₂ − p₁ is in the interval (α, β). This is consistent with the formulation of Conclusion 3. The optimal supply strategy of the mixed model takes a smaller value of s₃ than does the prepared warehouse model s₂, and the value of r₃ can be seen as the difference between the community group buying models r₁ and s₃. This finding is in line with the findings for the decision variables in Conclusion 1, Conclusion 2, and Conclusion 3.

To further investigate the effect of the commodity price p₂ of the prepositioned warehouse on the results of the model, p₂ = 3000:100:5500 is set. In addition, 3000:100:5500 indicates that p₂ is increased from 3000 to 5500 at intervals of 100. Figure 4 below shows the effect of p₂ on the profit of the community group buying business model, the profit of the prepositioned warehouse business model, and the profit of the mixed business model.

It can be noted that when p₂ is smaller than p₁+α, the profit of the community group buying business model is optimal; the mixed model only carries out the community group buying business, and the two are completely equivalent. When p₂ is larger than p₁ + β, the profit of the prepositioned warehouse business model is optimal; the mixed model only carries out the prepositioned warehouse business, and the two are completely equivalent. When p₂ takes the value of (p₁ + α, p₁ + β), the profit of the mixed model is optimal, and the community group buying business and the prepositioned warehouse business are carried out at the same time. This result reaffirms Conclusion 3. It is worth noting that, as the value of p₂ increases, the difference between the mixed model’s profit and the prepositioned warehouse’s profit becomes less pronounced.

5.2. Sensitivity Analysis

To investigate how cost-related parameters affect the profitability of different business models for agricultural products of online retailers, this paper conducts sensitivity analyses on the community group buying construction and operation cost e₁, the prepositioned warehouse construction and operation cost e₂, the procurement cost of commodities c, and the holding cost of goods in a prepositioned warehouse h. Figure 5, Figure 6, Figure 7 and Figure 8 below show the results of the sensitivity analyses for varying the different cost parameters.

To facilitate the comparison of the impacts of different cost parameters, this paper takes the values set in Table 2 as the base and sets the range of variation for each parameter between 0.8 times the parameter value and 1.2 times the parameter value.

(1)

Community group buying construction and operating cost e₁

As shown in Figure 5 below, e₁ does not have any relationship with the prepositioned warehouse business model and does not affect its profit. With the increase in e₁, the profit of the community group buying model and mixed model decreases, but the mixed model is less influenced than the community group buying model is, and the profit of the mixed model gradually converges to the prepositioned warehouse model.

Figure 5. Effect of community group buying construction and operating costs on model profits.

Figure 5. Effect of community group buying construction and operating costs on model profits.

(2)

Prepositioned warehouse construction and operating cost e₂

As shown in Figure 6 below, e₂ does not have any relationship with the community group buying business model and does not affect its profit. With the increase in e₂, the profits of the prepositioned warehouse model and mixed model decrease, but the mixed model is less influenced than the c prepositioned warehouse model is, and the profit of the mixed model gradually converges to that of the community group buying model.

Figure 6. Effect of prepositioned warehouse construction and operating cost on model profits.

Figure 6. Effect of prepositioned warehouse construction and operating cost on model profits.

(3)

Procurement cost of commodities c

As shown in Figure 7 below, c has an effect on the profits of all three models. As c increases, the profits of the three models decrease, but the decrease in the prepositioned warehouse model is slightly smaller, gradually approaching the profit curve of the mixed model.

Figure 7. Effect of the procurement cost of commodities on model profits.

Figure 7. Effect of the procurement cost of commodities on model profits.

(4)

Holding cost of goods in prepositioned warehouse h

As shown in Figure 8 below, h does not have any relationship with the community group buying business model and does not affect its profits. As h increases, the profits of the prepositioned warehouse model and the mixed model decrease. In terms of slope, the overall effect is small, and the mixed model is less influenced than the prepositioned warehouse model is.

Figure 8. Effect of holding cost on model profits.

Figure 8. Effect of holding cost on model profits.

6. Discussion and Conclusions

6.1. Discussion

This paper establishes a commodity supply strategy model for different modes of the online retail of agricultural products and verifies the conclusions drawn from the model via numerical analyses. When the difference between commodity price p₂ of the prepositioned warehouse and commodity price p₁ of community group buying is less than α, the profit of community group buying is optimal; when the difference between p₂ and p₁ is greater than β, the profit of the prepositioned warehouse is optimal; and when the difference between p₂ and p₁ is within the interval (α, β), the profit of the mixed model with both community group buying and the positioned warehouse is optimal.

Numerical analysis shows that the online retailer of agricultural products chooses to carry out different business models based on the value of the commodity price p₂ of the prepositioned warehouse to maximize profits. For example, when α = 500, β = 2000, and p₁ = 3000, if the commodity price p₂ of the prepositioned warehouse is 3700, the enterprise chooses to carry out both community group buying and prepositioned warehouse businesses. The supply of the group buying business is 2.3737, and the supply of the prepositioned warehouse business is 7.6263. The profit of the mixed model is 5531, which is significantly greater than the profit of 4202 for the community group buying model and 5251 for the prepositioned warehouse model. If the value of p₂ is adjusted, when p₂ is less than 3500, the profit of the community group buying model is the largest; when p₂ is more than 5000, the profit of the prepositioned warehouse model is the largest.

The price of goods largely depends on the purchasing power of consumers, thus obtaining managerial insights (1): In economically underdeveloped areas where consumers have low purchasing power and the difference between p₂ and p₁ is small, enterprises may consider carrying out the community group buying business; in economically developed areas where consumers have strong purchasing power and the difference between p₂ and p₁ is large, enterprises may consider carrying out the business of prepositioned warehouses; and in areas of average economic development where consumers have normal purchasing power and the difference between p₂ and p₁ is moderate, enterprises may consider carrying out both businesses at the same time.

By analyzing the supply strategy expressions for the three business models, we find that the four cost-related parameters of community group buying construction and operation cost e₁, prepositioned warehouse construction and operation cost e₂, procurement cost of commodities c, and the holding cost of goods in a prepositioned warehouse h have an effect on the values of α and β, which in turn affects the business choices of the online retailers of agricultural products.

Therefore, managerial insights (2) are obtained: Before an enterprise conducts a business, it has to determine the values of α and β and then determine the business to be conducted and the supply strategy based on the p₁ and p₂ situation in the market.

The paper also conducts a sensitivity analysis of the four cost parameters mentioned above and finds that an increase in the values of all these parameters leads to a decrease in the profitability of the business model associated with them. However, the holding cost h of the prepositioned warehouse has a much smaller influence on profits than the other three parameters. This situation can be explained by the fact that e₁, e₂, and c have an impact on all supply and demand scenarios (oversupply and undersupply) of the corresponding business model, whereas h has an impact only when there is an oversupply of the prepositioned warehouse business.

Thus, managerial insights (3) are gained: Among the four cost parameters mentioned above, enterprises must focus on controlling the average procurement cost of commodities c. Depending on the business model carried out by the enterprise, attention should be given to the construction and operation costs e₁ or/and e₂. The importance of the holding cost h is ranked after the previous three.

6.2. Research Limitation and Outlook

This paper has discussed the issue of supply strategies for online retailers of agricultural products and achieved some results; however, it still has several limitations. Future research can start from the following directions:

(1)

In this paper, for simplicity, it is assumed in the model that the demand for commodities is a random variable obeying a certain kind of normal distribution. In future research, the number of commodity types can increase, and different parameters and distribution functions can be used.

(2)

In this paper, three business models were selected according to the actual situation in China. In future research, other online retailing models for agricultural products can be discussed and added to the model.

6.3. Conclusions

The online retailing of agricultural products is a gradually emerging form of online shopping. In practice, different business models for the online retail of agricultural products need to be discussed separately. This paper argues that supply capacity determines business scale and that an appropriate supply strategy can guide agricultural product online retailers to maximize profits. By reviewing practices in China, this paper summarizes three models for the online retail of agricultural products: community group buying, prepositioned warehouses, and a ‘mixed’ model in which the first two are carried out simultaneously.

This article integrates the three main business models for agricultural product e-commerce in China. Based on the uncertainty of demand, it establishes an expected profit function regarding the supply quantity of the logistics network, providing theoretical references for the supply strategy and business model selection of e-commerce in the agricultural product supply chain.

In the process of analysis, this paper takes the opposite of the expected profit function as the objective and proves that the objective functions of the three models are all convex functions of the supply capacity of the business. The optimal supply strategy and the expression for each business model are then derived. Next, the intervals for enterprises to choose the profit-optimal business model are given and visually demonstrated through graphs.

Finally, through numerical experiments, the optimal supply strategy for the online retail model of agricultural products is verified, as is how different values of the model parameters affect the profitability of the three business models. These findings lead to managerial insights:

(1)

In economically underdeveloped regions, it is appropriate for enterprises to conduct a community group buying business; in economically developed regions, it is appropriate for enterprises to conduct a prepositioned warehouse business; and in regions with average economic development, it is appropriate for enterprises to conduct both businesses.

(2)

The enterprise needs to determine the interval of the profit-optimal business model through each cost parameter and then formulate the business and supply strategy to be carried out according to the commodity price situation in the market.

(3)

To increase profits, enterprises need to focus on controlling the average procurement costs of commodities and pay attention to the construction and operating costs of the proposed business.