Optimal Financing Strategy in a Dual-Channel Supply Chain with Agricultural Product

Abstract

This study models a two-stage agricultural supply chain consisting of a financially constrained manufacturer of agricultural products and a financially stable retailer. We examine two supply chain structures: traditional and dual channel. Our analysis centers on the effects of consumer green preferences, consumer sensitivity to the freshness of agricultural products, and substitution rate between green and non-green agricultural products on the profitability of supply chain members. The purpose of this work is to study the optimal financing strategy for companies producing both regular and organic products simultaneously. We analyze optimal financing strategies for the manufacturer using three models: bank financing, internal debt financing, and internal equity financing. Our results indicate that in both traditional and dual-channel supply chains, increased consumer green preferences or greater sensitivity to the freshness of agricultural products improve supply chain profitability, while a higher substitution rate between green and non-green products reduces profits. Additionally, the manufacturer prefers internal debt financing when consumer environmental awareness is low. Conversely, as consumer environmental awareness increases, internal equity financing becomes more profitable. These findings offer valuable insights for agricultural product manufacturers facing financial constraints, assisting them in selecting the most appropriate financing model.

1. Introduction

Increased environmental awareness, driven by melting icebergs, rising sea levels, and frequent typhoons, has led to a surge in consumer demand for green products. This heightened consciousness is shifting more individuals toward eco-friendly purchases and raising expectations for product sustainability. Consequently, major companies like H&M, Marks & Spencer, and Levi’s have implemented advanced emission reduction technologies to lower carbon footprints and enhance product greenness [1]. However, producing green products requires substantial investment in research and development, resulting in higher retail prices compared to conventional products. Additionally, consumers are seeking greater product personalization and supply chain flexibility. Due to the slower development pace of small and medium-sized agricultural product manufacturers, these enterprises often produce both organic and ordinary products to maintain profitability.

Fresh agricultural products play a crucial role in agriculture and are essential to daily life worldwide. The global focus on developing supply chains for fresh agricultural products underscores their significance. Due to the short lifecycle and stringent freshness requirements, members of the supply chain incur preservation costs to maintain product quality. As living standards improve and health awareness increases, there is growing emphasis on the freshness of agricultural products. In recent years, capital giants have successively seized the fresh food market, adopting a full chain postproduction preservation approach to further increase sales volume and expand market share.

Traditionally, essential agricultural products have been purchased through offline channels, such as supermarkets and local markets. However, with the advent of the mobile internet era, manufacturers are not only utilizing traditional retailers but also leveraging online stores to sell directly to consumers, aiming to expand market share and increase profits. The introduction of online direct sales channels not only enhances market penetration but also introduces new value transfers for enterprises. The COVID-19 pandemic in 2020 further accelerated the shift toward online purchasing of agricultural products, due to lockdowns and widespread home isolation. The convenience of online shopping has led manufacturers to offer a diverse range of products through digital channels, catering to consumer needs and exploring emerging markets.

This study’s aim is to fill the research gap by maximizing the expected total profit of a green supply chain with a financially constrained agricultural product manufacturer and a financially robust retailer and two types of agricultural products. In this research, the demand for products depends on product prices, consumer green preferences, consumer sensitivity to the freshness of agricultural products, substitution rate between green and non-green agricultural products, and efforts to maintain product freshness. The model’s optimal decision variables, derived from a manufacturer-leadership Stackelberg game, were identified through a decentralized model. Based on this, an analysis of the financing decision-making domain for the agricultural product manufacturer was conducted.

The following questions are achieved as the key objectives of this research:

(1)

Which financing model is working best for maximizing the profits of the manufacturer producing two products simultaneously?

(2)

Will financing decisions differ between the two operating models of the agricultural product manufacturer?

(3)

Under two different operating models, how do consumer green preferences, consumer sensitivity to the freshness of agricultural products, and substitution rates between green and non-green agricultural products affect the profits of the manufacturer and the retailer?

(4)

How do decision variables interact and affect the financing decision domain of the manufacturer?

The remainder of this paper is organized as follows. Section 2 incorporates a survey on related research. Section 3 discusses two supply chain models: only opening retail channels and opening “retail + online channels”, and derived equilibrium strategies for supply chain members under three financing models. Section 4 performs numerical analysis, analyzes the impact of three important parameters on the profits of supply chain members, and plots sensitivity analysis and decision domains. Section 5 provides a real-life study case on Arla Foods. Section 6 presents the managerial insights. Finally, research conclusions and a few future research directions are presented in Section 7.

2. Research Overview

Herein, a brief literature review is carried out towards four main directions: (i) green supply chain, (ii) preservation of fresh products, (iii) dual-channel supply chain, and (iv) supply chain finance.

2.1. Green Supply Chain

With small and medium-sized enterprises starting to produce green products and consumers gradually increasing their environmental awareness, domestic and foreign scholars have begun to study green supply chains. Ghosh et al. [2] studied the impact of consumer green sensitivity coefficient on supply chain member decisions under different scenarios such as manufacturer led, retailer led, and Nash equilibrium in a two-stage green supply chain. Swami et al. [3] considered the coordination problem between retailers and manufacturers in vertical green supply chains and found that the ratio of optimal greening efforts invested by retailers and manufacturers is equal to the ratio of their green sensitivity ratio and greening cost ratio. Ji et al. [4] studied the optimal decision problem of a dual-channel supply chain and obtained the optimal emission reduction level, taking into account consumer green preferences and sales efforts. Wang et al. [5] considered the carbon reduction problem in dual-channel supply chains based on carbon emission systems and consumer low-carbon preferences. They established profit models for manufacturers and retailers and found the optimal direct and retail prices through a Stackelberg game. And they analyzed the impact of consumer low-carbon preferences on supply chain decisions. Yang et al. [6] analyzed supply chain carbon reduction and incentive mechanisms with social and consumer low-carbon preferences, established two types of supply chain models: decentralized and centralized, and compared supply chain decisions with and without social preferences. Finally, coordination was carried out through unilateral payment contracts. Hong et al. [7] analyzed the emission reduction choices of green supply chains under the influence of consumer environmental awareness and carbon taxes, established supply chain profits models under decentralized and centralized modes, and carried out the coordination of revenue sharing, cost sharing, and revenue and cost sharing. Hong et al. [8] proposed a dynamic pricing decision model for new and remanufactured products of a manufacturer, taking into account the environmental needs of consumers. Mishra et al. [9] considered decision elements such as joint pricing, dynamic investment in environmental costs, dynamic investment in replenishment costs, dynamic investment in preservation technology costs, and optimal replenishment time and constructed a non-instantaneous deteriorating product replenishment model. Barman et al. [10] developed a multi-objective supply chain inventory management approach that accounts for deteriorating products and imperfect quality production within neutral environments. Various carbon reduction policies, including carbon tax, carbon quota trading, carbon quota offsetting, and green technology, have been implemented to mitigate the impact of carbon emissions.

2.2. Preservation of Fresh Products

Due to the perishable nature of fresh agricultural products, supply chain members need to consider efforts and costs to maintain the freshness of products. A large number of scholars have conducted research on the preservation of fresh products. Chen et al. [11] first studied the shipping integration problem in the supply chain of perishable products by integrating preservation efforts, and the study proved that fresh investment has a positive impact on costs. Yu et al. [12] constructed a decay function to solve the network design problem of a dual-channel supply chain for fresh agricultural products under information uncertainty. Liu et al. [13] studied the impact of preservation efforts on inventory control, but did not consider the coordination problem of the supply chain system. Yang et al. [14] considered the level of preservation effort investment, then compared and analyzed the optimal pricing and preservation decision-making problems of single-channel, dual-channel, and online to offline (O2O) models under a supplier-led scenario. They found that the preservation effort level is optimal under centralized decision making, while the O2O model can bring more profits to retailers under decentralized decision making. Wang et al. [15] simultaneously considered green efforts and preservation efforts and constructed a green fresh agricultural product supply chain decision-making and coordination model. They found that adding a cost-sharing contract can make the optimal level of green efforts, retailer profits, and farmer profits superior to decentralized decision making. Liu et al. [16] modeled the value-added services of fresh e-commerce platforms and studied the coordination of the fresh supply chain when suppliers maintain freshness and e-commerce platforms provide value-added services.

2.3. Dual-Channel Supply Chain

With the continuous advancement of the Internet and the global spread of COVID-19 in recent years, an increasing number of consumers have shifted to online shopping channels. This shift has also piqued scholarly interest in dual-channel supply chains, leading to extensive research in this area. Yang et al. [17] investigated the effects of product promotion within a dual-channel supply chain, where manufacturers and retailers utilize online and physical retail stores, respectively. Modak et al. [18] examined a dual-channel supply chain by incorporating stochastic demand with delivery time dependencies. Ghosh et al. [19] analyzed a two-level dual-channel supply chain model, considering emission-sensitive stochastic demand under government-imposed total quantity controls and trading regulations, as well as consumer preferences for low-carbon options. Huo et al. [20] explored pricing strategies in dual-channel supply chains, focusing on consumer preferences for fairness and low-carbon advertising. Wang et al. [21] investigated pricing strategies in dual-channel supply chains with an emphasis on the channel preferences of risk-averse retailers and consumers. Xu et al. [22] analyzed pricing and sales efforts within a dual-channel supply chain, incorporating channel preferences and revenue-sharing contracts. Barman et al. [23] investigated a dual-channel green supply chain model that incorporates dual sales channels, carbon reduction rates, and online delivery cycles, using these factors as marketing strategies to encourage increased customer purchases. Ghosh et al. [24] examined the influence of customer channel preferences in a stochastic demand environment, exploring the impact of retailers’ cooperative advertising and manufacturers’ direct online services on the channel’s best decisions and coordination.

2.4. Supply Chain Finance

Many scholars have conducted research on the comparison of external and internal financing in supply chain finance. Yang et al. [25] studied the financing equilibrium decision of a two-stage supply chain with one supplier and two retailers with limited funds. They found that as competition intensity increases, the supplier may consider merging with one retailer. By establishing an evolutionary model of the equilibrium situation, the conditions under which the supplier may only provide trade credit to one retailer and the other retailer can only use external financing were determined. And they conducted sensitivity analysis on the capital structure and competition intensity of the retailer. Tang et al. [26] studied unreliable suppliers obtaining production financing through purchase order financing and buyer direct financing. They found that when manufacturers and banks have symmetric and asymmetric information, manufacturers and suppliers have their own preferences for the two financing strategies. Cao et al. [27] considered a supply chain consisting of a supplier and a manufacturer dependent on carbon emissions, where financially constrained manufacturers can choose between internal financing (supplier) and external financing (bank). They found that regardless of whether carbon reduction investment is considered or not, trade credit financing of a supplier is a unique financing equilibrium for manufacturers. Zhao et al. [28] studied a supply chain constrained by funds, in which a retailer provides advance payment discount financing to a supplier. Zhen et al. [29] found that manufacturers with financial constraints can alleviate financial pressure through third-party platforms, banks, and retail credit financing and obtained the optimal financing strategies for manufacturers under three financing models. Yan et al. [30] considered a dual-channel supply chain consisting of a financially constrained supplier and an online retailer providing financing. By analyzing the issue of price competition in the supply chain, they found that online retailer financing is a value-added service of online retailers, and financing is beneficial for both online retailers and suppliers.

Currently, much scholarly research focuses on optimal decision-making problems where either a single manufacturer exclusively produces green products or two manufacturers each specialize in different product types. However, in real economic and social situations, manufacturers, particularly small and medium-sized enterprises, often face financial constraints that hinder a complete transition from producing solely ordinary products to exclusively organic ones. This study’s aim is to fill the research gap by exploring the optimal financing strategies faced by a manufacturer producing both conventional and organic products simultaneously. In this research, the demand for products is influenced by consumer green preferences, consumer sensitivity to the freshness of agricultural products, and substitution rates between green and non-green agricultural products. Concurrently, in the digital age, there has been a growing interest among scholars in examining online sales channels. We conduct a comparative analysis between traditional retail channels and the “retail + online channel” sales model. Lastly, we analyze three distinct financing models: bank financing, internal debt financing, and internal equity financing.

Table 1. A brief literature survey.

Author(s)	Green Supply Chains	Maintain the Freshness of Products	External Financing	Internal Financing	Dual-Channel Supply Chain
Ghosh et al. [2]	√
Swami et al. [3]	√
Ji et al. [4]	√				√
Yang et al. [25]			√
Wang et al. [5]	√				√
Yang et al. [6]	√
Chen et al. [11]		√
Yu et al. [12]					√
Tang et al. [26]			√
Yang et al. [17]	√				√
Hong et al. [7]	√
Liu et al. [13]		√
Yang et al. [14]		√			√
Cao et al. [27]	√		√	√
Zhao et al. [28]				√
Modak et al. [18]					√
Hong et al. [8]	√
Mishra et al. [9]	√
Wang et al. [15]	√	√
Zhen et al. [29]				√	√
Yan et al. [30]				√	√
Ghosh et al. [19]	√				√
Liu et al. [16]		√
Huo et al. [20]	√				√
Wang et al. [21]					√
Xu et al. [22]				√	√
Barman et al. [10]	√
Barman et al. [23]	√				√
Ghosh et al. [24]					√
This paper	√	√	√	√	√

refers to the difference between the key contributions of the present work and the contributions of several existing works are involved the present work.

The main contributions of our research are as follows:

(1)

We develop a supply chain model that enables a single agricultural product manufacturer to produce both organic and ordinary products concurrently. This contrasts with studies focusing on a single manufacturer that exclusively produces green products or two manufacturers each specializing in different product types. Our findings offer theoretical guidance for small and medium-sized enterprises to make production decisions in the process of transitioning from ordinary production to organic production.

(2)

We conduct a comparative analysis of the traditional retail channel sales model and the “retail + online channels” sales model, examining their respective strengths and weaknesses. Additionally, we investigate the optimal selection of sales models across varying economic landscapes. Our findings offer a scientific foundation for agricultural product manufacturers contemplating the expansion of online channels for selling their products while bearing the cost of maintaining freshness.

(3)

We explore how consumer green preferences, consumer sensitivity to the freshness of agricultural products, and substitution rate between green and non-green agricultural products influence demand and optimal decision making within the supply chain. Our sensitivity analysis reveals that profits for supply chain members correlate positively with consumer green preferences and their sensitivity to the freshness of agricultural products and negatively with substitution rate between green and non-green agricultural products. Importantly, this correlation persists regardless of whether online channels are involved.

(4)

We investigate three distinct financing models: bank financing, internal debt financing, and internal equity financing. Through comparisons between external and internal financing, and among different types of internal financing, we analyze the financing decision-making processes among agricultural product manufacturers operating under two distinct supply chain models. Our findings offer valuable insights to agricultural product manufacturers facing financial constraints, aiding them in selecting the most suitable financing models.

3. Model Building

3.1. Basic Assumptions

Firstly, we establish a two-stage agricultural supply chain comprising a financially constrained agricultural product manufacturer, denoted as $M$, and a financially robust retailer, denoted as $R$. The manufacturer supplies two types of agricultural products—organic and ordinary—to the retailer, with substitutability between these products within the same cycle. In this supply chain framework, the manufacturer acts as the leader, setting the wholesale prices for the agricultural products, followed by the retailer, who determines the selling prices based on these wholesale prices. We consider two operational models for the agricultural product manufacturer: (1) the agricultural product manufacturer only opens retail channels, and the manufacturer invests in green technology to develop organic agricultural products, while the retailer invests in preservation efforts to ensure the freshness of agricultural products, referred to hereafter as the “Tradition_” mode. (2) The agricultural product manufacturer establishes “retail + online channels”, where it simultaneously invests in green technology to develop organic agricultural products as well as preservation efforts to ensure the freshness of agricultural products, referred to hereafter as the “Dual_” mode. To explore different financing models for the manufacturer, we introduce three financing mechanisms: bank financing (BF), internal debt financing (IDF), and internal equity financing (IEF). In order to focus on profit maximization strategies without considering risk aversion or risk preference factors, we assume both the manufacturer and the retailer are risk-neutral entities driven by profit maximization. The description of the model parameters in the text is shown in

Table 2. Meaning of model parameters.

Symbol	Description
Parameters
$q$	Total amount of market demand for agricultural products (unit)
$\rho$	Market share of organic agricultural products $\left(0\le \rho \le 1\right)$
$\beta$	Price elasticity of products $\left(\beta >0\right)$ (unit/CNY)
$k$	Substitution rate between green and non-green agricultural products $\left(0\le k\le 1\right)$
$K$	Self-owned initial capital of the agricultural product manufacturer (CNY)
$c_1$	The unit production cost of organic agricultural products (CNY/unit)
$c_2$	The unit production cost of ordinary agricultural products (CNY/unit)
$s$	Cost coefficient of maintaining freshness effort $\left(s>0\right)$
$u$	Green cost coefficient of organic agricultural products $\left(u>0\right)$
$\gamma$	Consumer sensitivity to the freshness of agricultural products $\left(\gamma >0\right)$
$\theta$	Consumer green preference coefficient $\left(\theta >0\right)$
$\tau$	Market share of consumer demand in online channels
$r_1$	The loan interest rate for bank financing $\left(0<r_1\le 1\right)$
$r_2$	The loan interest rate for internal debt financing $\left(0<r_2\le 1\right)$
$b$	The proportion of dividends received by retailers in internal equity financing
${\pi }_R$	Retailer’s profits (CNY)
${\pi }_M$	Profits of agricultural product manufacturer (CNY)
Decision variables
$p_1$	Wholesale price of organic agricultural products from manufacturer (CNY/unit)
$p_2$	Wholesale price of ordinary agricultural products from manufacturer $\left(p_1>p_2\right)$ (CNY/unit)
$p_3$	The selling price of organic agricultural products (CNY/unit)
$p_4$	The selling price of ordinary agricultural products $\left(0<c_2<c_1<p_4<p_3\right)$ (CNY/unit)
$e$	Level of maintaining freshness effort
$g$	Greenness of organic agricultural products

. In addition, we make the following assumptions:

Assumptions 1.

In this agricultural product supply chain, the demand for products is shaped by several key factors: organic agricultural product price $p_3$, ordinary agricultural product price $p_4$, the greenness of organic agricultural products $g$ , the substitution rate between green and non-green agricultural products $k$ (based on findings from Christopher et al. [31]), and efforts to maintain product freshness $e$. Swami et al. [3] inform our understanding of “greenness” in this context. The demand for organic agricultural products $D_1$ and the demand for ordinary agricultural products $D_2$ are as follows:

$$D_1=\rho q-\beta p_3+k\beta \left(p_4-p_3\right)+\gamma e+\theta g$$

(1)

$$D_2=\left(1-\rho \right)q-\beta p_4+k\beta \left(p_3-p_4\right)+\gamma e-\theta g$$

(2)

where  $\rho$  represents the market share of organic agricultural products.  $q$  represents the total amount of market demand for agricultural products.  $\beta$  represents the price elasticity of products.  $\gamma$  represents the consumer sensitivity to the freshness of agricultural products.  $\theta$  represents the consumer green preference coefficient.

Assumptions 2.

In this article, based on varying degrees of consumer green preferences, we generally set $\theta \in \left[0,{\theta }_{\max }\right]$, and the specific value of ${\theta }_{\max }$ does not significantly impact our research findings and conclusions.

Assumptions 3.

For the production of organic agricultural products, the agricultural product manufacturer needs to invest in green research and development costs. According to the research of Poyago [32], the investment of research and development for organic agricultural products is ${\displaystyle \frac{1}{2}}u{g}^2$, where $u$ represents the green cost coefficient of organic agricultural products.

Assumptions 4.

We assume equal consumer sensitivity to freshness for both organic and ordinary agricultural products, as well as for both offline and online channels. Yu et al. [33] propose that maintaining freshness in agricultural products requires a certain effort level and the cost of maintaining freshness effort is assumed to be ${\displaystyle \frac{1}{2}}s{e}^2$, where $s$ represents the cost coefficient of maintaining freshness effort.

Assumptions 5.

Due to financial constraints encountered during the transition from traditional to organic production, agricultural product manufacturers must select appropriate financing solutions to address the issue of insufficient funds. We assume that the agricultural product manufacturer’s own capital is $K$, which is insufficient to produce the required agricultural products.

Figure 1, Figure 2 and Figure 3 illustrate the decision-making process for agricultural product manufacturers considering bank financing, internal debt financing, and internal equity financing. Within the Stackelberg game framework, both the manufacturer and the retailer aim to maximize their profits. As the leader in this game, the manufacturer makes decisions in the initial stage. The manufacturer sets the wholesale price ($p_1$, $p_2$) and the greenness of organic products ($g$). Based on the manufacturer’s decision, the retailer observes these choices and subsequently sets the optimal retail price ($p_3$, $p_4$) to maximize their profits.

3.2. Traditional Channel Agricultural Product Supply Chain

In the traditional channel agricultural product supply chain structure, the agricultural product manufacturer produces both organic and ordinary agricultural products, which are subsequently sold through the retailer. The traditional channel supply chain structure is shown in Figure 4.

In the traditional channel agricultural product supply chain, when the agricultural product manufacturer lacks sufficient self-owned capital to produce the required quantity of agricultural products, the self-owned capital $K_T$ must fulfill the following condition:

$$K_T<c_1{D}_1+c_2{D}_2+{\displaystyle \frac{1}{2}}u{g}^2$$

(3)

where $c_1$ represents the unit production cost of organic agricultural products, and $c_2$ represents the unit production cost of ordinary agricultural products.

Thus, the amount of loans that the agricultural product manufacturer needs to obtain from banks or the retailer is:

$$L_T=c_1{D}_1+c_2{D}_2+{\displaystyle \frac{1}{2}}u{g}^2-K_T$$

(4)

3.2.1. Bank Financing (Tradition_BF)

In the model for bank financing decisions, we assume the funding provider to be a typical commercial bank. Our focus is on assessing the influence of bank financing within the supply chain context. Therefore, we do not account for scenarios where banks decline loans based on the qualifications of agricultural product manufacturers. Following the acquisition of bank financing, agricultural product manufacturers produce goods and subsequently supply them to retailers in pursuit of maximizing profits.

Under the bank financing decision model, after financing, the total profits of the agricultural product manufacturer $M$ are:

$${\pi }_{M,T\_BF}=\left(p_1-c_1\right)D_1+\left(p_2-c_2\right)D_2-{\displaystyle \frac{1}{2}}u{g}^2-L_T{r}_1$$

(5)

where $r_1$ represents the loan interest rate for bank financing.

The total profits of the retailer $R$ are:

$${\pi }_{R,T\_BF}=\left(p_3-p_1\right)D_1+\left(p_4-p_2\right)D_2-{\displaystyle \frac{1}{2}}s{e}^2$$

(6)

Proposition 1.

Under bank financing, the optimal sales prices and wholesale prices for organic and ordinary agricultural products in the traditional channel agricultural product supply chain, the optimal greenness of organic agricultural products, and the optimal level of maintaining freshness effort by the retailer are:

$$p_{1,T\_BF}^{*}={\displaystyle \frac{M_1+F_1+G_2}{4\beta \left(Y_1-{\theta }^2\right)}}$$

(7)

$$p_{2,T\_BF}^{*}={\displaystyle \frac{M_1+F_2+G_1+4\beta u\left(1-2\rho \right)R_{1}q}{4\beta \left(Y_1-{\theta }^2\right)}}$$

(8)

$$g_{T\_BF}^{*}={\displaystyle \frac{\theta \left(\left(2\rho -1\right)q+\beta \left(1+2k\right)R_1\left(c_2-c_1\right)\right)}{2\left(Y_1-{\theta }^2\right)}}$$

(9)

$$p_{3,T\_BF}^{*}={\displaystyle \frac{N_1+I_1-J_2}{8\beta \left(Y_1-{\theta }^2\right)A_1}}$$

(10)

$$p_{4,T\_BF}^{*}={\displaystyle \frac{N_1+I_2-J_1+12\beta u\left(1-2\rho \right)R_1{A}_{1}q}{8\beta \left(Y_1-{\theta }^2\right)A_1}}$$

(11)

$$e_{T\_FB}^{\ast }={\displaystyle \frac{\gamma \left(q-\beta R_1\left(c_1+c_2\right)\right)}{4A_1}}$$

(12)

We record the maximum profits of the manufacturer and the retailer as  ${\pi }_{M,T\_BF}^{\ast }$  and  ${\pi }_{R,T\_BF}^{\ast }$, respectively, then

(1) 

${\displaystyle \frac{\partial {\pi }_{M,T\_BF}^{\ast }}{\partial \theta }}>0$,${\displaystyle \frac{\partial {\pi }_{M,T\_BF}^{\ast }}{\partial k}}<0$,${\displaystyle \frac{\partial {\pi }_{M,T\_BF}^{\ast }}{\partial \gamma }}>0$,${\displaystyle \frac{\partial {\pi }_{R,T\_BF}^{\ast }}{\partial \gamma }}>0$,

(2) 

When  $u>{\displaystyle \frac{{\theta }^2}{2\beta \left(1+r_1\right)\left(1+2k\right)}}$,${\displaystyle \frac{\partial {\pi }_{R,T\_BF}^{\ast }}{\partial \theta }}>0$  and  ${\displaystyle \frac{\partial {\pi }_{R,T\_BF}^{\ast }}{\partial k}}<0$,

where

$A_1=\beta s-{\gamma }^2$, $A_2=\left(2{\gamma }^2-3\beta s\right){\theta }^2$, $A_2=\left(6{\gamma }^2-5\beta s\right)\beta {\theta }^2$, $A_4=2\beta s-3{\gamma }^2$, $R_1=1+r_1$,

$Y_1=2\beta u\left(1+2k\right)R_1$, $M_1=\left(4\beta u\left(k+\rho \right)R_1-{\theta }^2\right)q$, $F_1=\left(4{\beta }^{2}u\left(1+2k\right)R_1^2-3\beta {\theta }^2{R}_1\right)c_1$,

$F_2=\left(4{\beta }^{2}u\left(1+2k\right)R_1^2-3\beta {\theta }^2{R}_1\right)c_2$, $G_1=\beta {\theta }^2{R}_1{c}_1$, $G_2=\beta {\theta }^2{R}_1{c}_2$, $N_1=\left(A_2+{\gamma }^2{Y}_1+12\beta u\left(k+\rho \right)R_1{A}_1\right)q$,

$I_1=R_1\left(A_3+\beta A_4{Y}_1\right)c_1$, $I_2=R_1\left(A_3+\beta A_4{Y}_1\right)c_2$, $J_1=\beta R_1\left(A_2+{\gamma }^2{Y}_1\right)c_1$, $J_2=\beta R_1\left(A_2+{\gamma }^2{Y}_1\right)c_2$.

Proposition 1 indicates that in the traditional channel agricultural product supply chain model, when the agricultural product manufacturer secures adequate production financing through bank loans, under certain conditions, the profits of both the manufacturer and the retailer correlate positively with consumer green preferences. As consumer demand for greener organic agricultural products rises, the manufacturer responds by increasing green investments, thereby producing organic products with higher greenness. At the same time, consumers increase their purchases of organic agricultural products and reduce their purchases of ordinary agricultural products. The increased profits of organic agricultural products are enough to compensate for the reduced profits of ordinary agricultural products, so the total profits of supply chain members increase. In economically advanced regions with high per capita GDP, consumers generally possess substantial purchasing power. This financial capacity enables them to select higher-priced, environmentally friendly products. Consumers in developed regions often place greater emphasis on environmental protection and sustainable development. Consequently, demand for organic products is higher in these markets. Manufacturers and retailers can capture a larger market share and increase profits by offering organic products that meet these demands. Additionally, higher production costs are positively correlated with consumer green preferences, as elevated costs are often indicative of superior product quality or greater environmental investments, which can appeal to consumers who favor organic products. In other words, when the production costs of organic products are high and these products align with consumers’ green preferences, consumers are more inclined to pay premium prices to support environmentally friendly production.

Moreover, Proposition 1 indicates a negative correlation between the profits of both the manufacturer and the retailer and the substitution rate between green and non-green agricultural products. As competition intensifies between two types of agricultural products, consumers favor lower-priced ordinary agricultural products more, leading to an increase in sales. At the same time, the sales of organic agricultural products have decreased. However, the profits brought by the increase in ordinary agricultural product sales are not enough to compensate for the losses caused by the decrease in organic agricultural product sales and the research and development investment in organic agricultural products. So, the profits for supply chain members decrease. In economically advanced regions with a profound understanding of environmental issues, a high substitution rate between green and non-green products can lead to the rapid replacement of non-green products by green alternatives. This substitution effect may result in a decline in the sales of non-green products, consequently diminishing their profitability. Therefore, it resulted in an overall decrease in total profits. Additionally, high production costs for green products can result in elevated market prices, which may reduce consumer willingness to purchase and lower the substitution rate between green and non-green products.

Proposition 1 also indicates that the profits of both the manufacturer and the retailer are positively correlated with consumer sensitivity to the freshness of agricultural products. As consumers become more sensitive to the freshness of agricultural products, the agricultural manufacturer needs to increase the cost of maintaining freshness to improve the freshness of agricultural products and the prices of products. Nonetheless, heightened consumer demand for these fresher products drives increased overall sales, thereby enhancing the profits for supply chain members. Concrete proof can be seen in Appendix A.

3.2.2. Internal Debt Financing (Tradition_IDF)

In the model for internal debt financing decisions, we assume the funding provider is the retailer.

Under the internal debt financing decision model, after financing, the total profits of the agricultural product manufacturer $M$ are:

$${\pi }_{M,T\_IDF}=\left(p_1-c_1\right)D_1+\left(p_2-c_2\right)D_2-{\displaystyle \frac{1}{2}}u{g}^2-L_T{r}_2$$

(13)

where $r_2$ represents the loan interest rate for internal debt financing.

The total profits of the retailer $R$ are:

$${\pi }_{R,T\_IDF}=\left(p_3-p_1\right)D_1+\left(p_4-p_2\right)D_2-{\displaystyle \frac{1}{2}}s{e}^2+L_T{r}_2$$

(14)

Proposition 2.

Under internal debt financing, the optimal sales prices and wholesale prices for organic and ordinary agricultural products in the traditional channel agricultural product supply chain, the optimal greenness of organic agricultural products, and the optimal level of maintaining freshness effort by the retailer are:

$$p_{1,T\_IDF}^{\ast }={\displaystyle \frac{M_2+F_3+G_4}{4\beta \left(Y_2-{\theta }^2\right)}}$$

(15)

$$p_{2,T\_IDF}^{\ast }={\displaystyle \frac{M_2+F_4+G_3+4\beta u\left(1-2\rho \right)R_{2}q}{4\beta \left(Y_2-{\theta }^2\right)}}$$

(16)

$$g_{T\_IDF}^{\ast }={\displaystyle \frac{\theta \left(\left(2\rho -1\right)q+\beta \left(1+2k\right)\left(c_2-c_1\right)\right)}{2\left(Y_2-{\theta }^2\right)}}$$

(17)

$$p_{3,T\_IDF}^{\ast }={\displaystyle \frac{N_2+I_3-J_4}{8\beta \left(Y_2-{\theta }^2\right)A_2}}$$

(18)

$$p_{4,T\_IDF}^{\ast }={\displaystyle \frac{N_2+I_4-J_3+12\beta u\left(1-2\rho \right)A_1{R}_{2}q}{8\beta \left(Y_2-{\theta }^2\right)A_2}}$$

(19)

$$e_{T\_IDF}^{\ast }={\displaystyle \frac{\gamma \left(q-\beta \left(c_1+c_2\right)\right)}{4A_1}}$$

(20)

We record the maximum profits of the manufacturer and the retailer as  ${\pi }_{M,T\_IDF}^{\ast }$  and  ${\pi }_{R,T\_IDF}^{\ast }$  , respectively, then

(1) 

${\displaystyle \frac{\partial {\pi }_{M,T\_IDF}^{\ast }}{\partial \theta }}>0$  ,  ${\displaystyle \frac{\partial {\pi }_{M,T\_IDF}^{\ast }}{\partial k}}<0$  ,  ${\displaystyle \frac{\partial {\pi }_{M,T\_IDF}^{\ast }}{\partial \gamma }}>0$  ,  ${\displaystyle \frac{\partial {\pi }_{R,T\_IDF}^{\ast }}{\partial \gamma }}>0$  ,

(2) 

When  $u>{\displaystyle \frac{{\theta }^2}{2\beta \left(1+r_2\right)\left(1+2k\right)}}$,${\displaystyle \frac{\partial {\pi }_{R,T\_IDF}^{\ast }}{\partial \theta }}>0$  and  ${\displaystyle \frac{\partial {\pi }_{R,T\_IDF}^{\ast }}{\partial k}}<0$,

where

$R_2=1+r_2$, $Y_2=2\beta u\left(1+2k\right)R_2$, $M_2=\left(4\beta u\left(k+\rho \right)R_2-{\theta }^2\right)q$,

$F_3=\left(4{\beta }^{2}u\left(1+2k\right)\left(2r_2^2+3r_2+1\right)+\beta {\theta }^2\left(4r_2-3\right)\right)c_1$, $F_4=\left(4{\beta }^{2}u\left(1+2k\right)\left(2r_2^2+3r_2+1\right)+\beta {\theta }^2\left(4r_2-3\right)\right)c_2$,

$G_3=\beta {\theta }^2{c}_1$, $G_4=\beta {\theta }^2{c}_2$, $N_2=\left(A_2+{\gamma }^2{Y}_2+12\beta u\left(k+\rho \right)A_1{R}_2\right)q$, $I_3=\left(A_3+\beta A_4{Y}_2\right)c_1$,

$I_4=\left(A_3+\beta A_4{Y}_2\right)c_2$, $J_3=\beta \left(A_2+{\gamma }^2{Y}_2\right)c_1$, $J_4=\beta \left(A_2+{\gamma }^2{Y}_2\right)c_2$.

Proposition 2 indicates that within the traditional channel agricultural product supply chain model, when the agricultural product manufacturer secures adequate production costs through internal debt financing, under certain conditions, a result similar to Proposition 1 can obtained. We observe that the profits of both the manufacturer and the retailer exhibit positive correlations with consumer green preferences, while displaying negative correlations with the substitution rate between green and non-green agricultural products. Additionally, the profits of both the manufacturer and the retailer show positive correlations with consumer sensitivity to the freshness of agricultural products. Concrete proof can be seen in Appendix B.

3.2.3. Internal Equity Financing (Tradition_IEF)

In the model for internal equity financing decisions, we assume that the funding provider is the retailer. Specifically, the retailer offers financial support to the agricultural product manufacturer and subsequently receives dividends at the end of the period, determined by their shareholding ratio. However, the retailer does not engage in the agricultural product manufacturer’s production and operational decision-making processes.

Under the internal equity financing decision model, after financing, the total profits of the agricultural product manufacturer $M$ are:

$${\pi }_{M,T\_IEF}=\left(1-b\right)\left[\left(p_1-c_1\right)D_1+\left(p_2-c_2\right)D_2\right]-{\displaystyle \frac{1}{2}}u{g}^2$$

(21)

where $b$ represents the proportion of dividends received by retailers in internal equity financing.

The total profits of the retailer $R$ are:

$${\pi }_{R,T\_IEF}=\left(p_3-p_1\right)D_1+\left(p_4-p_2\right)D_2-{\displaystyle \frac{1}{2}}s{e}^2+b\left[\left(p_1-c_1\right)D_1+\left(p_2-c_2\right)D_2\right]$$

(22)

Proposition 3.

Under internal equity financing, the optimal sales prices and wholesale prices for organic and ordinary agricultural products in the traditional channel agricultural product supply chain, the optimal greenness of organic agricultural products, and the optimal level of maintaining freshness effort by the retailer are:

$$p_{1,T\_IEF}^{\ast }={\displaystyle \frac{M_3+F_5+G_4}{4\beta \left(1-b\right)\left(A_5-{\theta }^2\right)}}$$

(23)

$$p_{2,T\_IEF}^{\ast }={\displaystyle \frac{M_3+F_6+G_3+4\beta u\left(1-2\rho \right)q}{4\beta \left(1-b\right)\left(A_5-{\theta }^2\right)}}$$

(24)

$$g_{T\_IEF}^{\ast }={\displaystyle \frac{\theta \left(\left(2\rho -1\right)q+\beta \left(1+2k\right)\left(c_2-c_1\right)\right)}{2\left(A_5-{\theta }^2\right)}}$$

(25)

$$p_{3,T\_IEF}^{\ast }={\displaystyle \frac{N_3+I_5-J_6}{8\beta \left(A_5-{\theta }^2\right)A_1}}$$

(26)

$$p_{4,T\_IEF}^{\ast }={\displaystyle \frac{N_3+I_6-J_5+12\beta u\left(1-2\rho \right)A_{1}q}{8\beta \left(A_5-{\theta }^2\right)A_1}}$$

(27)

$$e_{T\_IEF}^{\ast }={\displaystyle \frac{\gamma \left(q-\beta \left(c_1+c_2\right)\right)}{4A_1}}$$

(28)

We record the maximum profits of the manufacturer and the retailer as  ${\pi }_{M,T\_IEF}^{\ast }$  and  ${\pi }_{R,T\_IEF}^{\ast }$, respectively, then

(1) 

${\displaystyle \frac{\partial {\pi }_{M,T\_IEF}^{\ast }}{\partial \theta }}>0$,${\displaystyle \frac{\partial {\pi }_{M,T\_IEF}^{\ast }}{\partial k}}<0$,${\displaystyle \frac{\partial {\pi }_{M,T\_IEF}^{\ast }}{\partial \gamma }}>0$,${\displaystyle \frac{\partial {\pi }_{R,T\_IEF}^{\ast }}{\partial \gamma }}>0$,

(2) 

When  $u>{\displaystyle \frac{{\theta }^2}{2\beta \left(1+2k\right)}}$  ,  ${\displaystyle \frac{\partial {\pi }_{R,T\_IEF}^{\ast }}{\partial \theta }}>0$  and  ${\displaystyle \frac{\partial {\pi }_{R,T\_IEF}^{\ast }}{\partial k}}<0$,

where

$A_5=2\beta u\left(1+2k\right)$,  $M_3=\left(4\beta u\left(k+\rho \right)-{\theta }^2\right)q$,  $F_5=\left(4{\beta }^{2}u\left(1+2k\right)\left(1-b\right)+\beta {\theta }^2\left(4b-3\right)\right)c_1$,

$F_6=\left(4{\beta }^{2}u\left(1+2k\right)\left(1-b\right)+\beta {\theta }^2\left(4b-3\right)\right)c_2$,  $N_3=\left(A_2+{\gamma }^2{A}_5+12\beta u\left(k+\rho \right)A_1\right)q$,  $I_5=\left(A_3+\beta A_4{A}_5\right)c_1$,

$I_6=\left(A_3+\beta A_4{A}_5\right)c_2$, $J_5=\beta \left(A_2+{\gamma }^2{A}_5\right)c_1$, $J_6=\beta \left(A_2+{\gamma }^2{A}_5\right)c_2$.

Proposition 3 indicates that within the traditional channel agricultural product supply chain model, when the agricultural product manufacturer secures adequate production costs through internal equity financing, under certain conditions, a result similar to Proposition 1 can obtained. We observe that the profits of both the manufacturer and the retailer exhibit positive correlations with consumer green preferences, while displaying negative correlations with the substitution rate between green and non-green agricultural products. Additionally, the profits of both the manufacturer and the retailer show positive correlations with consumer sensitivity to the freshness of agricultural products. Concrete proof can be seen in Appendix C.

3.3. Dual-Channel Agricultural Product Supply Chain

In the dual-channel agricultural product supply chain structure consisting of “retail + online channels”, we assume homogeneity of products sold through these channels. The agricultural manufacturer distributes two types of agricultural products through both retailers and online platforms. The dual-channel supply chain structure is shown in Figure 5.

In the dual-channel supply chain model, consumer channel preference coefficients $\tau$ influence demand distribution across different channels [34]. The demands for organic and ordinary agricultural products in offline and online channels are specified as follows:

$$D_{1n}=\left(1-\tau \right)\left(\rho q-\beta p_3+k\beta \left(p_4-p_3\right)+\gamma e+\theta g\right)$$

(29)

$$D_{1f}=\tau \left(\rho q-\beta p_3+k\beta \left(p_4-p_3\right)+\gamma e+\theta g\right)$$

(30)

$$D_{2n}=\left(1-\tau \right)\left(\left(1-\rho \right)q-\beta p_4+k\beta \left(p_3-p_4\right)+\gamma e-\theta g\right)$$

(31)

$$D_{2f}=\tau \left(\left(1-\rho \right)q-\beta p_4+k\beta \left(p_3-p_4\right)+\gamma e-\theta g\right)$$

(32)

In the dual-channel agricultural product supply chain, when the agricultural product manufacturer lacks sufficient self-owned capital to produce the required quantity of agricultural products, the self-owned capital $K_D$ must fulfill the following condition:

$$K_D<c_1\left(D_{1n}+D_{1f}\right)+c_2\left(D_{2n}+D_{2f}\right)+{\displaystyle \frac{1}{2}}u{g}^2+{\displaystyle \frac{1}{2}}s{e}^2$$

(33)

Thus, the amount of loans that the agricultural product manufacturer needs to obtain from banks or the retailer is:

$$L_D=c_1\left(D_{1n}+D_{1f}\right)+c_2\left(D_{2n}+D_{2f}\right)+{\displaystyle \frac{1}{2}}u{g}^2+{\displaystyle \frac{1}{2}}s{e}^2-K_D$$

(34)

3.3.1. Bank Financing (Dual_BF)

Under the bank financing decision model, after financing, the total profits of the agricultural product manufacturer $M$ are:

$${\pi }_{M,D\_BF}=\left(p_3-c_1\right)D_{1f}+\left(p_1-c_1\right)D_{1n}+\left(p_4-c_2\right)D_{2f}+\left(p_2-c_2\right)D_{2n}-{\displaystyle \frac{1}{2}}u{g}^2-{\displaystyle \frac{1}{2}}s{e}^2-L_D{r}_1$$

(35)

The total profits of the retailer $R$ are:

$${\pi }_{R,D\_BF}=\left(p_3-w_1\right)D_{1n}+\left(p_4-w_2\right)D_{2n}$$

(36)

Proposition 4.

Under bank financing, the optimal sales prices and wholesale prices for organic and ordinary agricultural products in the dual-channel agricultural product supply chain, the optimal greenness of organic agricultural products, and the optimal level of maintaining freshness effort by the agricultural product manufacturer are:

$$p_{1,D\_BF}^{\ast }=R_1\left({\displaystyle \frac{M_4+F_7+G_6+\left(\tau -1\right)\left(2\rho -1\right)u{\gamma }^{2}q}{2\left({\gamma }^2+s{Y}_3\right)\left({\theta }^2+Y_3{A}_7\right)}}\right)$$

(37)

$$p_{2,D\_BF}^{\ast }=R_1\left({\displaystyle \frac{M_4+F_8+G_5+\left(\tau -1\right)\left(1-2\rho \right)\left(u{\gamma }^2+2us{Y}_3\right)q}{2\left({\gamma }^2+s{Y}_3\right)\left({\theta }^2+Y_3{A}_7\right)}}\right)$$

(38)

$$g_{D\_BF}^{\ast }={\displaystyle \frac{\theta \left(\left(2\rho -1\right)q-\beta \left(1+2k\right)R_1\left(c_2-c_1\right)\right)}{-2\left({\theta }^2+Y_3{A}_7\right)}}$$

(39)

$$e_{D\_BF}^{\ast }={\displaystyle \frac{\gamma \left(q-\beta R_1\left(c_2+c_1\right)\right)}{-2\left({\gamma }^2+s{Y}_3\right)}}$$

(40)

$$p_{3,D\_BF}^{\ast }=R_1\left({\displaystyle \frac{N_4+I_7+J_8+A_6\left(2\rho -1\right)u{\gamma }^{2}q}{4\left({\gamma }^2+s{Y}_3\right)\left({\theta }^2+Y_3{A}_7\right)}}\right)$$

(41)

$$p_{4,D\_BF}^{\ast }=R_1\left({\displaystyle \frac{N_4+I_8+J_7+A_6\left(1-2\rho \right)\left(u{\gamma }^2+2us{Y}_3\right)q}{4\left({\gamma }^2+s{Y}_3\right)\left({\theta }^2+Y_3{A}_7\right)}}\right)$$

(42)

We record the maximum profits of the manufacturer and the retailer as  ${\pi }_{M,D\_BF}^{\ast }$  and  ${\pi }_{R,D\_BF}^{\ast }$, respectively, then

(1) 

${\displaystyle \frac{\partial {\pi }_{M,D\_BF}^{\ast }}{\partial \theta }}>0$  ,  ${\displaystyle \frac{\partial {\pi }_{M,D\_BF}^{\ast }}{\partial k}}<0$  ,  ${\displaystyle \frac{\partial {\pi }_{M,D\_BF}^{\ast }}{\partial \gamma }}>0$  ,

(2) 

When  $u>{\displaystyle \frac{{\theta }^2}{\beta u\left(1+2k\right)\left(1+r_1\right)\left(2-\tau \right)}}$  ,  ${\displaystyle \frac{\partial {\pi }_{R,D\_BF}^{\ast }}{\partial \theta }}>0$  and  ${\displaystyle \frac{\partial {\pi }_{R,D\_BF}^{\ast }}{\partial k}}<0$,

(3) 

When  $s>{\displaystyle \frac{{\gamma }^2}{\beta \left(1+r_1\right)\left(2-\tau \right)}}$,  ${\displaystyle \frac{\partial {\pi }_{R,D\_BF}^{\ast }}{\partial \gamma }}>0$,

where

$A_6=2\tau -3$,  $A_7=\left(1+2k\right)u$,  $Y_3=\beta \left(\tau -2\right)R_1$,  $Y_4=\beta \left(\tau -3\right)R_1$,  $Y_5=\beta \left(2\tau -5\right)R_1$,

$M_4=\left(\tau -1\right)\left(s{\theta }^2+2us\left(k+\rho \right)Y_3\right)q$,  $F_7=\left(\left(s{Y}_4+2{\gamma }^2\right){\theta }^2+A_7\left({\gamma }^2{Y}_4-2\beta s{R}_1{Y}_3\right)\right)c_1$,

$F_8=\left(\left(s{Y}_4+2{\gamma }^2\right){\theta }^2+A_7\left({\gamma }^2{Y}_4-2\beta s{R}_1{Y}_3\right)\right)c_2$,  $G_5=\left(\left(\tau -1\right)\beta R_1\left({\gamma }^2{A}_7-s{\theta }^2\right)\right)c_1$,

$G_6=\left(\left(\tau -1\right)\beta R_1\left({\gamma }^2{A}_7-s{\theta }^2\right)\right)c_2$,  $N_4=A_6\left(s{\theta }^2+2us\left(k+\rho \right)Y_3\right)q$,

$I_7=\left(\left(s{Y}_5+4{\gamma }^2\right){\theta }^2+A_7\left({\gamma }^2{Y}_5-2\beta s{R}_1{Y}_3\right)\right)c_1$,  $I_8=\left(\left(s{Y}_5+4{\gamma }^2\right){\theta }^2+A_7\left({\gamma }^2{Y}_5-2\beta s{R}_1{Y}_3\right)\right)c_2$,

$J_7=\beta R_1{A}_6\left({\gamma }^2{A}_7-s{\theta }^2\right)c_1$, $J_8=\beta R_1{A}_6\left({\gamma }^2{A}_7-s{\theta }^2\right)c_2$.

Proposition 4 indicates that within the dual-channel agricultural product supply chain model, when the agricultural product manufacturer secures adequate production costs through bank financing, under certain conditions, a result similar to Proposition 1 can obtained. We observe that the profits of both the manufacturer and the retailer exhibit positive correlations with consumer green preferences, while displaying negative correlations with the substitution rate between green and non-green agricultural products. Additionally, the profits of both the manufacturer and the retailer show positive correlations with consumer sensitivity to the freshness of agricultural products. Concrete proof can be seen in Appendix D.

3.3.2. Internal Debt Financing (Dual_IDF)

Under the internal debt financing decision model, after financing, the total profits of the agricultural product manufacturer $M$ are:

$${\pi }_{M,D\_IDF}=\left(p_3-c_1\right)D_{1f}+\left(p_1-c_1\right)D_{1n}+\left(p_4-c_2\right)D_{2f}+\left(p_2-c_2\right)D_{2n}-{\displaystyle \frac{1}{2}}u{g}^2-{\displaystyle \frac{1}{2}}s{e}^2-L_D{r}_2$$

(43)

The total profits of the retailer $R$ are:

$${\pi }_{R,D\_IDF}=\left(p_3-w_1\right)D_{1n}+\left(p_4-w_2\right)D_{2n}+L_D{r}_2$$

(44)

Proposition 5.

Under internal debt financing, the optimal sales prices and wholesale prices for organic and ordinary agricultural products in the dual-channel agricultural product supply chain, the optimal greenness of organic agricultural products, and the optimal level of maintaining freshness effort by the agricultural product manufacturer are:

$$p_{1,D\_IDF}^{\ast }={\displaystyle \frac{M_5+F_9+G_8+Y_{10}\left(2\rho -1\right){\gamma }^{2}uq}{2\left(\tau -1\right)\left({\theta }^2-u\left(1+2k\right)\left(b\tau -\tau +2\right)Y_8\right)\left(s{Y}_8+{\gamma }^2\right)}}$$

(45)

$$p_{2,D\_IDF}^{\ast }={\displaystyle \frac{M_5+F_{10}+G_7+Y_{10}\left(1-2\rho \right)\left({\gamma }^{2}u+2su{Y}_8\right)q}{2\left(\tau -1\right)\left({\theta }^2-u\left(1+2k\right)\left(b\tau -\tau +2\right)Y_8\right)\left(s{Y}_8+{\gamma }^2\right)}}$$

(46)

$$g_{D\_IDF}^{\ast }={\displaystyle \frac{\theta \left(\left(2\rho -1\right)q+\beta \left(1+2k\right)\left(c_2-c_1\right)\right)}{2\left(u\left(1+2k\right)\left(b\tau -\tau +2\right)Y_8-{\theta }^2\right)}}$$

(47)

$$e_{D\_IDF}^{\ast }={\displaystyle \frac{\gamma \left(q-\beta \left(c_2+c_1\right)\right)}{-2\left(s{Y}_8+{\gamma }^2\right)}}$$

(48)

$$p_{3,D\_IDF}^{\ast }={\displaystyle \frac{N_5+I_9+J_{10}+Y_6\left(2\rho -1\right){\gamma }^{2}uq}{4\left({\theta }^2-u\left(1+2k\right)\left(b\tau -\tau +2\right)Y_8\right)\left(s{Y}_8+{\gamma }^2\right)}}$$

(49)

$$p_{4,D\_IDF}^{\ast }={\displaystyle \frac{N_5+I_{10}+J_9+Y_6\left(1-2\rho \right)\left({\gamma }^{2}u+2su{Y}_8\right)q}{4\left({\theta }^2-u\left(1+2k\right)\left(b\tau -\tau +2\right)Y_8\right)\left(s{Y}_8+{\gamma }^2\right)}}$$

(50)

We record the maximum profits of the manufacturer and the retailer as  ${\pi }_{M,D\_IDF}^{\ast }$  and  ${\pi }_{R,D\_IDF}^{\ast }$, respectively, then

(1) 

${\displaystyle \frac{\partial {\pi }_{M,D\_IDF}^{\ast }}{\partial \theta }}>0$,  ${\displaystyle \frac{\partial {\pi }_{M,D\_IDF}^{\ast }}{\partial k}}<0$,  ${\displaystyle \frac{\partial {\pi }_{M,D\_IDF}^{\ast }}{\partial \gamma }}>0$,

(2) 

When  $u>{\displaystyle \frac{{\theta }^2}{\beta \left(1+2k\right)\left(1+r_2\right)\left(2-\tau \right)}}$,  ${\displaystyle \frac{\partial {\pi }_{R,D\_IDF}^{\ast }}{\partial \theta }}>0$  and  ${\displaystyle \frac{\partial {\pi }_{R,D\_IDF}^{\ast }}{\partial k}}<0$,

(3) 

When  $s>{\displaystyle \frac{{\gamma }^2}{\beta \left(1+r_2\right)\left(2-\tau \right)}}$,  ${\displaystyle \frac{\partial {\pi }_{R,D\_IDF}^{\ast }}{\partial \gamma }}>0$,

where

$A_8=\beta {\gamma }^{2}u\left(1+2k\right)-\beta s{\theta }^2$,  $A_9=s{\theta }^2+{\gamma }^{2}u\left(1+2k\right)$,  $R_3=2{\gamma }^2{\theta }^2\left(\tau -r_2-1\right)$,  $Y_6=\left(2\tau -3\right)R_2$,

$Y_7=\beta \left(\tau -1\right)R_2$,  $Y_8=\beta \left(\tau -2\right)R_2$,  $Y_9=\beta \left(2\tau -5\right)R_2$,  $Y_{10}={\left(\tau -1\right)}^2{R}_2$,  $M_5=Y_{10}\left(s{\theta }^2+2su\left(k+\rho \right)Y_8\right)q$,

$F_9=\left(R_3+\left(\left(\tau -3\right)Y_7-2r_2{Y}_8\right)A_9-2su\left(1+2k\right)Y_8\left(Y_7+Y_8{r}_2\right)\right)c_1$,

$F_{10}=\left(R_3+\left(\left(\tau -3\right)Y_7-2r_2{Y}_8\right)A_9-2su\left(1+2k\right)Y_8\left(Y_7+Y_8{r}_2\right)\right)c_2$,  $G_7=Y_{10}{A}_8{c}_1$,  $G_8=Y_{10}{A}_8{c}_2$,

$N_5=Y_6\left(s{\theta }^2+2su\left(k+\rho \right)Y_8\right)q$,  $I_9=\left(4{\gamma }^2{\theta }^2+Y_9{A}_9-\left(1+2k\right)\beta su{R}_2{Y}_8\right)c_1$,

$I_{10}=\left(4{\gamma }^2{\theta }^2+Y_9{A}_9-\left(1+2k\right)\beta su{R}_2{Y}_8\right)c_2$, $J_9=Y_6{A}_8{c}_1$, $J_{10}=Y_6{A}_8{c}_2$.

Proposition 5 indicates that within the dual-channel agricultural product supply chain model, when the agricultural product manufacturer secures adequate production costs through internal debt financing, under certain conditions, a result similar to Proposition 1 can obtained. We observe that the profits of both the manufacturer and the retailer exhibit positive correlations with consumer green preferences, while displaying negative correlations with the substitution rate between green and non-green agricultural products. Additionally, the profits of both the manufacturer and the retailer show positive correlations with consumer sensitivity to the freshness of agricultural products. Concrete proof can be seen in Appendix E.

3.3.3. Internal Equity Financing (Dual_IEF)

Under the internal equity financing decision model, after financing, the total profits of the agricultural product manufacturer $M$ are:

$${\pi }_{M,D\_IEF}=\left(1-b\right)[\left(p_3-c_1\right)D_{1f}+\left(p_1-c_1\right)D_{1n}+\left(p_4-c_2\right)D_{2f}+\left(p_2-c_2\right)D_{2n}]-{\displaystyle \frac{1}{2}}u{g}^2-{\displaystyle \frac{1}{2}}s{e}^2$$

(51)

The total profits of the retailer $R$ are:

$${\pi }_{R,D\_IEF}=\left(p_3-p_1\right)D_{1n}+\left(p_4-p_2\right)D_{2n}+b[\left(p_3-c_1\right)D_{1f}+\left(p_1-c_1\right)D_{1n}+\left(p_4-c_2\right)D_{2f}+\left(p_2-c_2\right)D_{2n}]$$

(52)

Proposition 6.

Under internal equity financing, the optimal sales prices and wholesale prices for organic and ordinary agricultural products in the dual-channel agricultural product supply chain, the optimal greenness of organic agricultural products, and the optimal level of maintaining freshness effort by the agricultural product manufacturer are:

$$p_{1,D\_IEF}^{\ast }={\displaystyle \frac{M_6+F_{11}+G_{10}-{\gamma }^{2}u\left(2\rho -1\right)B_{3}q}{2\left(b-1\right)\left(\tau -1\right)\left(s{B}_1-{\gamma }^2\right)\left(u\left(1+2k\right)B_1-{\theta }^2\right)}}$$

(53)

$$p_{2,D\_IEF}^{\ast }={\displaystyle \frac{M_6+F_{12}+G_9+\left(1-2\rho \right)\left(\beta su{B}_5-{\gamma }^{2}u{B}_3\right)q}{2\left(b-1\right)\left(\tau -1\right)\left(s{B}_1-{\gamma }^2\right)\left(u\left(1+2k\right)B_1-{\theta }^2\right)}}$$

(54)

$$g_{D\_IEF}^{\ast }={\displaystyle \frac{\theta \left(\left(2\rho -1\right)q-\beta \left(1+2k\right)\left(c_2-c_1\right)\right)}{2\left(u\left(1+2k\right)B_1-{\theta }^2\right)}}$$

(55)

$$e_{D\_IEF}^{\ast }={\displaystyle \frac{\gamma \left(q-\beta \left(c_2+c_1\right)\right)}{2\left(s{B}_1-{\gamma }^2\right)}}$$

(56)

$$p_{3,D\_IEF}^{\ast }={\displaystyle \frac{N_6+I_{11}+J_{12}+B_2\left(1-4\rho \right)u{\gamma }^{2}q}{4\left(s{B}_1-{\gamma }^2\right)\left(u\left(1+2k\right)B_1-{\theta }^2\right)}}$$

(57)

$$p_{4,D\_IEF}^{\ast }={\displaystyle \frac{N_6+I_{12}+J_{11}+B_2\left(\left(4\rho -1\right)u{\gamma }^2+2us\left(1-2\rho \right)B_1\right)q}{4\left(s{B}_1-{\gamma }^2\right)\left(u\left(1+2k\right)B_1-{\theta }^2\right)}}$$

(58)

We record the maximum profits of the manufacturer and the retailer as  ${\pi }_{M,D\_IEF}^{\ast }$  and  ${\pi }_{R,D\_IEF}^{\ast }$, respectively, then

(1) 

${\displaystyle \frac{\partial {\pi }_{M,D\_IEF}^{\ast }}{\partial \theta }}>0$,${\displaystyle \frac{\partial {\pi }_{M,D\_IEF}^{\ast }}{\partial k}}<0$,${\displaystyle \frac{\partial {\pi }_{M,D\_IEF}^{\ast }}{\partial \gamma }}>0$,

(2) 

When  $u>{\displaystyle \frac{{\theta }^2}{\beta \left(1+2k\right)\left(b\tau -\tau +2\right)}}$,${\displaystyle \frac{\partial {\pi }_{R,D\_IEF}^{\ast }}{\partial \theta }}>0$  and  ${\displaystyle \frac{\partial {\pi }_{R,D\_IEF}^{\ast }}{\partial k}}<0$,

(3) 

When  $s>{\displaystyle \frac{{\gamma }^2}{\beta \left(b\tau -\tau +2\right)}}$,${\displaystyle \frac{\partial {\pi }_{R,D\_IEF}^{\ast }}{\partial \gamma }}>0$,

where

$B_1=\beta \left(b\tau -\tau +2\right)$,  $B_2=2b\tau -2\tau +3$,  $B_3=\tau \left(b-1\right)\left(b\tau -\tau +2\right)+1$,  $B_4=\left(\tau -2\right)\left(b-1\right)\left(b\tau -\tau +2\right)+1$,

$B_5=2\tau \left(b-1\right)\left({\left(b\tau -\tau +2\right)}^2+1\right)+4$,  $B_6=-\left(2\left(1+2k\right)\left(\left(b-1\right){\left(b\tau -\tau +2\right)}^2+\tau \right)+2\right)$,

$M_6=\left(\beta su\left(k+\rho \right)B_5-s{\theta }^2{B}_3\right)q$,

$F_{11}=\left(2{\gamma }^2{\theta }^2\left(b-1\right)\left(\tau -1\right)-\beta B_4\left(s{\theta }^2+{\gamma }^{2}u\left(1+2k\right)\right)-8bsu{\theta }^2+{\beta }^{2}su{B}_6\right)c_1$,

$F_{12}=\left(2{\gamma }^2{\theta }^2\left(b-1\right)\left(\tau -1\right)-\beta B_4\left(s{\theta }^2+{\gamma }^{2}u\left(1+2k\right)\right)-8bsu{\theta }^2+{\beta }^{2}su{B}_6\right)c_2$,

$G_9=\beta B_3\left(s{\theta }^2-{\gamma }^{2}u\left(1+2k\right)\right)c_1$,  $G_{10}=\beta B_3\left(s{\theta }^2-{\gamma }^{2}u\left(1+2k\right)\right)c_2$,  $N_6=B_2\left(2us\left(k+\rho \right)B_1-s{\theta }^2\right)q$,

$I_{11}=\left(\left(4{\gamma }^2-\beta s\left(B_2+2\right)\right){\theta }^2+\beta u\left(1+2k\right)\left(2s{B}_1-{\gamma }^2\left(B_2+2\right)\right)\right)c_1$,

$I_{12}=\left(\left(4{\gamma }^2-\beta s\left(B_2+2\right)\right){\theta }^2+\beta u\left(1+2k\right)\left(2s{B}_1-{\gamma }^2\left(B_2+2\right)\right)\right)c_2$,  $J_{11}=\beta B_2\left(s{\theta }^2-{\gamma }^{2}u\left(1+2k\right)\right)c_1$,

$J_{12}=\beta B_2\left(s{\theta }^2-{\gamma }^{2}u\left(1+2k\right)\right)c_2$.

Proposition 6 indicates that within the dual-channel agricultural product supply chain model, when the agricultural product manufacturer secures adequate production costs through internal equity financing, under certain conditions, a result similar to Proposition 1 can obtained. We observe that the profits of both the manufacturer and the retailer exhibit positive correlations with consumer green preferences, while displaying negative correlations with the substitution rate between green and non-green agricultural products. Additionally, the profits of both the manufacturer and the retailer show positive correlations with consumer sensitivity to the freshness of agricultural products. Concrete proof can be seen in Appendix F.

In summary, when considering factors such as the level of economic and sustainable development and per capita gross domestic product, Propositions 1 through 6 are self-explaining, irrespective of the channel type—whether traditional or dual-channel—or the type of financing model.

4. Numerical Analysis

Under three financing models—bank financing, internal debt financing, and internal equity financing—we aim to explain how profits of the agricultural product manufacturer and the retailer in two types of supply chains are affected by consumer green preferences, consumer sensitivity to the freshness of agricultural products, and the substitution rate between green and non-green agricultural products. We will investigate the correlations among these variables and describe the distribution of decision domains by assigning specific parameter values based on our earlier assumptions. The parameter values are determined based on a combination of [35]. The following basic parameters are set in this paper: $q=1000$, $K=800$, $\beta =5$, $\rho =0.65$, $c_1=9$, $c_2=8$, $u=7$, $s=7$, $\tau =0.55$, $b=0.015$, $r_1=0.035$, $r_2=0.032$. When studying consumer green preferences, in order to eliminate the influence of substitution rate between green and non-green agricultural products and consumer sensitivity to the freshness of agricultural products, both are taken as intermediate values, i.e., $k=0.5$, $\gamma =0.5$. When analyzing the substitution rate between green and non-green agricultural products, due to the low green preference of consumers in the current market, we assign a lower value to consumer green preferences while keeping consumer sensitivity to the freshness of agricultural products at a moderate level, i.e., $\theta =2$, $\gamma =0.5$. Similarly, when examining the consumer sensitivity to the freshness of agricultural products as an influencing factor, we set $\theta =2$, $k=0.5$.

4.1. Sensitivity Analysis

4.1.1. The Impact of Consumer Green Preferences on the Profits of Manufacturer and Retailer

From Figure 6, in both the traditional channel agricultural product supply chain model and the dual-channel agricultural product supply chain model, the profits of the agricultural product manufacturer are observed to be directly influenced by consumer preferences for green products, regardless of whether it engages in bank financing, internal debt financing, or internal equity financing. As consumer awareness of environmental protection grows, the greenness and demand for organic agricultural products increase significantly, leading to a corresponding decline in sales of ordinary agricultural products. Additionally, the price of organic products rises with heightened environmental consciousness among consumers, while the price of ordinary products tends to decrease. Consequently, profits from organic agricultural products increase while profits from ordinary agricultural products decrease. However, the increase in profits from organic products outweighs the decrease in profits from ordinary products, resulting in an overall profit increase for the agricultural product manufacturer as consumer green preferences rise. This conclusion similarly applies to the retailer. Figure 7 illustrates that in both supply chain models, the retailer experiences a positive correlation between its profits and consumer green preferences across all three financing models. This relationship aligns with Propositions 1–6.

Examining the graphs in Figure 6 reveals that when consumers exhibit weak environmental awareness, both the traditional and dual-channel models of agricultural product supply chains indicate that the agricultural product manufacturer achieves maximum profits by opting for internal debt financing. During this phase, the manufacturer incurs relatively low green costs, making a financing model with a fixed, low-interest rate conducive to maximizing profits. However, when consumers reach a certain level of environmental awareness, the agricultural product manufacturer must produce sufficiently green organic products to meet consumer demands, thereby increasing the associated green costs. Consequently, choosing internal equity financing allows the manufacturer to share green costs with retailers, resulting in higher profits.

4.1.2. The Impact of Substitution Rate between Green and Non-Green Agricultural Products on the Profits of Manufacturer and Retailer

Figure 8 and Figure 9 illustrate that in both the traditional and dual-channel agricultural product supply chain models, the profits of both the agricultural product manufacturer and the retailer vary inversely with the substitution rate between green and non-green agricultural products across three financing decision models. As competition between two types of agricultural products intensifies, consumers increasingly opt for ordinary agricultural products at lower prices. Sales of ordinary agricultural products have notably risen, accompanied by an increase in their selling price. Organic agricultural products have lost their competitive edge, resulting in decreased sales and reduced greenness of products. Nevertheless, the profits from increased sales of ordinary agricultural products and reduced green costs fail to offset the losses incurred by decreased sales of organic agricultural products. Consequently, the total profits of both the agricultural product manufacturer and the retailer are declining. This relationship aligns with Propositions 1–6.

In Figure 8, the profits of the agricultural product manufacturer vary due to the setting of the loan interest rates of bank financing and the dividend ratios of the retailer. Specifically, in Figure 8a, opting for internal debt financing yields higher profits compared to choosing bank financing. Conversely, in Figure 8b, the opposite holds true. Importantly, altering the ratio between these parameters modifies the profit size accordingly.

4.1.3. The Impact of Consumer Sensitivity to the Freshness of Agricultural Products on the Profits of Manufacturer and Retailer

From Figure 10 and Figure 11, it is evident that in both the traditional channel agricultural product supply chain model and the dual-channel agricultural product supply chain model, the profits of both the agricultural product manufacturer and the retailer correlate directly with consumer sensitivity to the freshness of agricultural products across three types of financing decision models. As consumer sensitivity to agricultural product freshness increases, the manufacturer or the retailer enhances efforts to maintain freshness, thereby boosting sales of both organic and ordinary agricultural products. Consequently, prices for both types of agricultural products rise, and the increased profits for the manufacturer or the retailer sufficiently offset the costs incurred in enhancing product freshness. Consequently, total profits for both parties increase. This relationship also aligns with Propositions 1–6. In Figure 10b, variations in the setting of loan interest rates for bank financing and dividend ratios for retailers cause the profits of the agricultural product manufacturer to intersect under the Dual_BF and Dual_IEF when consumer sensitivity to agricultural product freshness intensifies.

4.1.4. The Impact of Green Cost Coefficient of Organic Agricultural Products on the Profits of Manufacturer and Retailer

Figure 12 and Figure 13 illustrate that, in both the traditional and dual-channel agricultural product supply chain models, the profits of agricultural product suppliers and retailers are inversely proportional to the green cost coefficient of organic agricultural products across the three financing decision models. A higher green cost coefficient generally indicates a greater investment in environmental protection during production. As the green cost coefficient rises, agricultural product manufacturers facing financial constraints will reduce their green investments per unit of capital, leading to a decrease in product greenness. Simultaneously, an increase in the green cost coefficient directly raises the cost of green production. Although higher green production costs might be partially mitigated by market premiums or waste reduction, overall profits tend to decline.

4.1.5. The Impact of Cost Coefficient of Maintaining Freshness Effort on the Profits of Manufacturer and Retailer

Figure 14 and Figure 15 demonstrate that, within both the traditional and dual channel agricultural product supply chain models, the profits of agricultural product suppliers and retailers exhibit an inverse relationship with the cost coefficient of maintaining freshness effort across the three financing decision models. A higher cost coefficient of maintaining freshness effort typically necessitates increased investment in production costs to sustain product freshness. For instance, employing advanced refrigeration technology and high-quality packaging materials can substantially prolong the shelf life of products. While enhanced freshness may facilitate higher market prices for agricultural products, these price increases often fail to offset the elevated preservation costs, leading to a reduction in overall profits for both suppliers and retailers.

4.1.6. The Impact of Consumer Green Preferences and Consumer Sensitivity to the Freshness of Agricultural Products on the Profits of Supply Chain Members in a Dual-Channel Supply Chain

Figure 16 and Figure 17 illustrate that the profits of supply chain members increase as consumer green preferences and their sensitivity to the freshness of agricultural products rise. Under the combined effect of both, the growth trajectory of supply chain members’ profits is non-planar, which is different from the case of single-factor effects. Additionally, it can also be seen that, under the dual-factor effect, the profits of supply chain members are bounded and have a maximum value at a given parameter value. Notably, consumer green preferences have a more substantial impact on profits compared to their sensitivity to the freshness of agricultural products. Therefore, it is advisable for supply chain members to prioritize enhancing green marketing initiatives to boost consumers’ environmental awareness and, consequently, improve profitability.

4.2. Decision Domain

According to Figure 6a, Figure 8a, and Figure 10a, in the traditional channel supply chain, the agricultural product manufacturer consistently achieves maximum profits by opting for internal debt financing when consumer environmental awareness is relatively weak. This is because internal debt financing offers lower interest rates, enabling the agricultural product manufacturer to raise larger funds for producing high-greenness, environmentally friendly organic products and set higher product prices to maximize profits.

Below, we examine the decision-making process of the agricultural product manufacturer concerning financing models in the dual-channel supply chain. In this section, we analyze the decision-making domain of the agricultural product manufacturer within the setting ${\theta }_{\max }=15$.

In Figure 18, the solid line indicates that the profits of the agricultural product manufacturer are equal under Dual_BF and Dual_IEF, and the dashed line indicates that the profits of the agricultural product manufacturer are equal under Dual_IDF and Dual_IEF. Each line divides the graph into two regions, which we can analyze based on Figure 6 in two distinct scenarios. In scenario one, concerning bank financing and internal equity financing, the manufacturer in Region I typically opts for bank financing, whereas those in Regions II and III lean towards internal equity financing. This preference arises because, with low consumer environmental awareness, the agricultural product manufacturer requires minimal financing to produce organic goods in demand. The manufacturer opting for bank financing with fixed, low-interest rates will achieve higher profits. Conversely, high consumer environmental awareness prompts the manufacturer to raise green costs for greener organic products, necessitating increased financing. At this time, the agricultural product manufacturer chooses internal equity financing and shares production costs with the retailer to obtain higher profits. In scenario two, regarding internal debt financing and internal equity financing, the manufacturers in Regions I and II lean towards internal debt financing, whereas that in Region III prefers internal equity financing. Likewise, with low consumer environmental awareness, the manufacturer requires less financing, resulting in higher profits for those choosing Dual_IDF over Dual_IEF. Conversely, the agricultural product manufacturer opting for Dual_IDF may experience lower profits compared to those selecting Dual_IEF when consumers have a high awareness of environmental protection.

Comparing the two scenarios, the advantage of internal equity financing over bank financing is greater than that of internal debt financing. The decision domain of internal equity financing in the former not only encompasses the decision domain in the latter (Region III), but also introduces a new favorable region (Region II). This difference arises from the lower loan interest rate of internal debt financing compared to bank financing. Given identical consumer green preferences, the agricultural product manufacturer generates higher profits under internal debt financing than under bank financing. Consequently, in the second scenario, the manufacturer opts for internal equity financing only when consumer green preferences are relatively higher. Additionally, according to Figure 18, as consumer sensitivity to the freshness of agricultural products increases, consumer green preferences decrease when the agricultural product manufacturer achieves equal profits under Dual_BF and Dual_IEF, as well as under Dual_IDF and Dual_IEF. This occurs because, with heightened consumer demand for freshness in agricultural products, the manufacturer or the retailer incurs higher costs to ensure product freshness meets expectations. Simultaneously, both types of products experience an increase in sales volume and selling price, resulting in sufficient profit growth to offset the higher costs. Ultimately, the manufacturer experiences an increase in profits. The intersection point, where the manufacturer achieves equal profits under Dual_BF and Dual_IEF, as well as under Dual_IDF and Dual_IEF, moves towards decreasing consumer green preferences.

In Figure 19, similar to Figure 18, the solid line denotes equal profits of the agricultural product manufacturer under Dual_BF and Dual_IEF, while the dashed line denotes equal profits under Dual_IDF and Dual_IEF. Each line partitions the graph into two regions, analyzed across two scenarios akin to Figure 18. As observed in Figure 19, the substitution rate between green and non-green agricultural products positively correlates with consumer green preferences when the manufacturer achieves equal profits under Dual_BF and Dual_IEF and similarly under Dual_IDF and Dual_IEF. This trend emerges because heightened competition between two types of agricultural product diminishes the advantage of organic products, leading to reduced sales prices and volumes. Although sales prices and volumes of ordinary agricultural products may rise, the resultant profits increase fails to offset losses, thereby decreasing the manufacturer profits overall. Consequently, the intersection point where profits of the manufacturer equalize under Dual_BF and Dual_IEF, as well as under Dual_IDF and Dual_IEF, moves towards an increase in consumer green preferences.

The meanings conveyed by solid and dashed lines in Figure 20, along with the corresponding analysis results for each region, closely resemble those depicted in Figure 18 and Figure 19. Upon examining Figure 20, as the price elasticity of products increases, consumer green preferences initially rise and then decline when the agricultural product manufacturer achieves equal profits under Dual_BF and Dual_IEF, as well as under Dual_IDF and Dual_IEF. This occurs because when the price elasticity of products is low, heightened consumer price sensitivity prompts the manufacturer to decrease their investment in green costs. Consequently, prices of both two types of agricultural product decrease significantly, organic product sales decline, and ordinary product sales increase. However, the resulting profits increase does not offset losses, leading to reduced profits for the agricultural product manufacturer. Conversely, when the price elasticity of products is high, the manufacturer continues reducing green investments as consumers become more sensitive to product prices. In order to ensure no loss, sales prices of both types of agricultural product decrease marginally, leading to decreased sales and subsequently lower profits for the agricultural product manufacturer. In summary, the point of intersection where the manufacturer achieves equal profits under Dual_BF and Dual_IEF, as well as under Dual_IDF and Dual_IEF, moves towards higher consumer green preferences. However, as consumer price sensitivity reaches a critical level, this intersection moves towards lower consumer green preferences.

5. Case Study

Arla Foods, an internationally renowned dairy cooperative headquartered in Denmark, operates globally and ranks among the world’s largest dairy companies. The company offers a diverse product line, including conventional dairy products such as milk, yogurt, cheese, and butter, which are produced using traditional agricultural models and standardized production techniques. Additionally, Arla Foods produces organic dairy products, including organic milk, yogurt, and cheese. These organic products adhere to EU organic standards, excluding the use of synthetic pesticides and fertilizers, and uphold stringent animal welfare standards.

5.1. Production Background

The rationale behind Arla Foods’ simultaneous production of conventional and organic dairy products is rooted in market demand and strategic objectives. Arla Foods began integrating organic dairy products into its portfolio in the early 2000s, with a notable expansion of this product line occurring around 2005. Conventional dairy products fulfill traditional market needs by ensuring a stable supply and offering a broad range of options. In contrast, organic dairy products address a growing consumer base concerned with health and sustainability. This dual approach allows the company to broaden its market reach while adaptively responding to shifts in consumer preferences and promoting environmentally sustainable production practices.

5.2. Production Plan

Arla Foods in Denmark has implemented several strategic measures to simultaneously produce both regular and organic dairy products. First, the company has set up dedicated production lines and facilities to ensure that organic dairy products are entirely separate from regular ones, avoiding cross-contamination. Second, Arla Foods is investing in organic farms to secure a stable supply of organic milk. Additionally, the company is focused on obtaining organic certification and conducting market research to better understand consumer preferences. Following this, Arla Foods has developed a specialized marketing and promotion strategy for its organic products. Finally, Arla Foods is committed to environmentally friendly and sustainable production practices to minimize its environmental impact. For a detailed chronology of Arla Foods’ development, please consult

Table 3. Detailed chronology of Arla Foods’ development.

Year	Decision Making and Planning
2000	During this period, Arla Foods concentrated on the potential of the organic dairy market and commenced preliminary research and testing of organic products.
2005	Arla Foods has formally introduced its organic dairy product line. Subsequently, the company initiated the gradual development of distinct production lines and facilities to support the manufacture of organic dairy products.
2007	Arla Foods has augmented its investment in organic farms and broadened its market promotion and sales strategies for organic dairy products. This is reflected in heightened advertising expenditures and enhanced consumer awareness of organic products.
2010	Arla Foods has continued in expanding its organic product line and bolstering marketing and consumer education efforts to drive sales. Concurrently, the company is optimizing production processes, enhancing the sustainability of its organic products, and ensuring adherence to the latest environmental standards.
2015	Arla Foods has enhanced its production processes, expanded its market share in organic products, and consistently updated its certifications and standards to sustain its competitiveness in the organic dairy sector.

.

5.3. Production Effect

According to

Table 4. Financing Cash Flow Ratio for Arla Foods from 2007 to 2023.

Year	2007	2008	2009	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021	2022	2023
Financing Cash Flow Ratio	$1.56$	$0.71$	$-1.09$	$1.63$	$3.83$	$7.7$	$-5.86$	$-46.5$	$39.1$	$-41.6$	$2.89$	$-5.79$	$-2.06$	$5.86$	$10.31$	$26.9$	$-14.8$

and Figure 21, in more than half of the 17 years from 2017 to 2023, Arla Foods’ financing cash flow ratio exceeded 1, indicating that financing played a crucial role in its development of organic products. The financing cash flow ratio in 2010 increased compared to the previous year, indicating that Arla Foods had intensified its financing activities to expand its organic product line and enhance marketing and consumer education. Consequently, Arla Foods’ annual profits exhibited an upward trend over the subsequent four years. The company has demonstrated strong profitability and maintained sufficient cash flow to support its operations and expansion, leading to a reduction in its financing activities. In 2015, Arla Foods further optimized its production processes by substantially increasing its financing activities. Figure 21 also reveals that, in the short term, financing may adversely impact profits. However, over the long term, if financing is allocated to effective investment and growth, profits may experience substantial increases. During this period, Arla Foods’ annual profit increased by 3.2 times, reaching approximately EUR 399 million in 2023. Arla Foods’ experience indicates that companies engaged in the simultaneous production of both conventional and organic products may face funding shortages during significant reform and innovation initiatives. In these situations, it becomes essential for companies to enhance their financing activities to secure adequate investment for innovation.

In the long term, Arla Foods has experienced significant profit growth. However, in the short term, increased financing activities may temporarily reduce the company’s annual profits. Nevertheless, as enterprises achieve technological innovations and enhance the greenness and freshness of their organic products, both enterprise and retailer profits will rise with the increased unit price of organic products, thereby improving the overall profitability of the supply chain. Concurrently, attention must be paid to cultivating consumers’ green preferences. If consumer awareness of environmental protection is insufficient, higher prices for organic products may lead to reduced purchases and, consequently, lower supply chain profits. In the long run, as the proportion of environmentally conscious consumers grows, the demand for organic products will increase, thereby enhancing annual enterprise profits. Higher profits will, in turn, encourage greater investment in innovation and green technologies, benefiting the supply chain through economies of scale. Ultimately, this creates a virtuous economic cycle that fosters the growth of corporate profits. These observations align with the actual performance of Arla Foods.

6. Managerial Insights

To enhance financing and improve overall output efficiency in the green supply chain, the development of the green supply chain can be advanced through the following strategies.

6.1. The Perspective of Green Development

Agricultural product manufacturers can concurrently adopt internal and external strategies to achieve mutual benefits. Internally, manufacturers should prioritize enhancing the production technology of organic agricultural products to elevate their environmental sustainability. Externally, they can engage in comprehensive market research to comprehend consumer preferences towards green products, analyze audience demographics for different agricultural types, and effectively capture and quantify consumer insights. Additionally, manufacturers can enhance environmental awareness among consumers through targeted green promotion efforts. At the same time, agricultural product manufacturers can bolster their capacity for producing organic agricultural products through innovations like constructing solar greenhouses, selecting high-quality varieties, and employing effective water and fertilizer management. This enhancement aims to strengthen the competitive edge of organic agricultural products while minimizing their substitutability with ordinary alternatives.

6.2. The Perspective of Supply Chain Financing Innovation

Banks and retailers can integrate quantitative metrics concerning manufacturers into the loan interest rate determination process. For instance, they can assess the proficiency of agricultural product manufacturers in producing organic goods. Enhanced product greenness can facilitate manufacturers’ access to funding. Moreover, in the context of opting for internal financing, concerning the mutually beneficial aspects of internal equity financing, retailers can encourage agricultural product manufacturers to prefer this option by lowering the dividend ratio.

6.3. The Perspective of Government Regulation

Effective green subsidy policies can accelerate the development of green technologies of enterprises. Subsidies to manufacturers can be provided through direct support of organic production costs. The government can provide subsidies to manufacturers in two ways. On the one hand, subsidies to manufacturers can be provided through direct support of organic production costs. On the other hand, the government provides subsidies based on the greenness of the green products produced by manufacturers. Higher greenness standards in products correlate with increased subsidy allocations to manufacturers. Additionally, subsidies can be provided to consumers purchasing green products, through influencing product pricing directly.

7. Conclusions with Future Studies

In the current era of green and sustainable development, the burgeoning consumer preference for eco-friendly products has prompted an increasing number of enterprises to incorporate green products into their product lines. This coexistence of conventional and eco-friendly products, each serving distinct consumer needs, exemplifies the trajectory of green economic growth. Certain agricultural product manufacturers, facing slower growth rates, opt to produce both organic and ordinary products concurrently. To investigate this scenario, we examine a two-stage supply chain where the agricultural manufacturer produces both two types of products, partnering with the retailer under the leadership of the manufacturer. We achieved optimal outcomes in both the traditional and dual-channel supply chain models. Our analysis examined the impact of consumer green preferences, consumer sensitivity to the freshness of agricultural products, and substitution rate between green and non-green agricultural products on the profits of supply chain members. Additionally, we thoroughly reviewed financing strategies available to agricultural manufacturers, including bank financing, internal debt financing, and internal equity financing. We analyzed how the interaction of decision variables influences the financing decisions of manufacturers.

This study performs a comprehensive analysis of manufacturers’ financing decisions, addressing the research gap related to firms that produce both conventional and organic products simultaneously. It also aids manufacturers in selecting financing models that maximize profits, optimize decision-making processes, and mitigate the adverse effects of financing on profitability. The main conclusions are as follows:

(1)

In both traditional channel and dual-channel supply chain models, consumer green preferences positively influence the profits of the agricultural product manufacturer and the retailer, irrespective of the financing model chosen. As consumer awareness of environmental protection grows, they demonstrate a willingness to pay premium prices for organic agricultural products. The agricultural product manufacturer achieves higher profits through internal debt financing when consumer green preferences are relatively low. When consumer green preferences reach a certain height, the agricultural product manufacturer achieves higher profits through internal equity financing.

(2)

In traditional channel supply chain and dual-channel supply chain models, regardless of the financing model chosen by the agricultural product manufacturer, the substitution rate between green and non-green agricultural products has a detrimental impact on the profits of both the manufacturer and the retailer. As competition intensifies between these two types of products, organic agricultural products lose their competitive edge, resulting in decreased sales volumes and lower selling prices. While sales volumes and selling prices of ordinary agricultural products may increase, the resulting profits gains are insufficient to offset these losses. Consequently, the total profits of the agricultural product manufacturer decrease.

(3)

In traditional channel supply chain and dual-channel supply chain models, irrespective of the financing model chosen by the agricultural product manufacturer, consumer sensitivity to the freshness of agricultural products positively impacts the profits of both the manufacturer and the retailer. With increasing consumer sensitivity to the freshness of agricultural products, the agricultural product manufacturer or the retailer increases their investments in maintaining freshness. Simultaneously, the selling price and sales volume of products also increase. The resulting increase in profits compensates for the investments made in freshness maintenance costs. Ultimately, this leads to increased profits for both the agricultural product manufacturer and the retailer.

(4)

Given that bank financing typically incurs higher interest rates compared to internal debt financing, when choosing between these two financing models, the agricultural product manufacturer consistently achieves greater profits by opting for internal debt financing. In the dual-channel supply chain model, choosing between bank financing and internal equity financing, as well as internal debt financing and internal equity financing, the manufacturer is inclined to select internal equity financing when consumers have relatively high green preferences. The advantage of internal equity financing is greater in the former than in the latter.

(5)

In the dual-channel supply chain model, the consumer green preference coefficient is inversely related to the consumer sensitivity to the freshness of agricultural products and directly related to the substitution rate between green and non-green agricultural products when the agricultural product manufacturer’s profits are equal under bank financing versus internal equity financing and under internal debt financing versus internal equity financing. Additionally, this coefficient exhibits a direct relationship with the price elasticity of products when the price elasticity of products is relatively low and an inverse relationship when it is relatively high.

Here are two main limitations in this study. First, in the actual economic environment, there are often differences in sales prices between online and offline channels. Second, consumers in offline channels have the advantage of assessing product freshness through visual and tactile inspection, which generally leads to higher sensitivity to freshness compared to online channels. The model that we are currently constructing cannot accurately depict real economic problems. In future research, we will use this research result as a basis to further explore relevant issues. The specific research directions are as follows:

(1)

We will examine the pricing disparities of agricultural products between online and offline sales channels. In the actual economic environment, differing operational costs between these channels often lead to distinct pricing strategies. Online channels entail logistics expenses for manufacturers to ensure rapid and pristine delivery of agricultural products, contrasting with offline channels where retailers manage operational costs like rent.

(2)

We will examine variations in consumer sensitivity to the freshness of agricultural products between online and offline retail environments. In the actual economic and social context, consumers have the advantage of tactile inspection, enabling them to assess freshness more comprehensively compared to online platforms. Consequently, retailers in offline stores must put in more efforts to maintain the freshness of agricultural products, thereby incurring higher expenses of maintaining freshness.

(3)

Our future research will incorporate an analysis of government subsidies, green credit policies, and carbon emission trading prices. Government subsidies alleviate pressure on enterprises to manufacture environmentally friendly products, fostering engagement in environmental protection and pollution reduction activities. Green credit policies incentivize enterprises to enhance their green production technologies and mitigate environmental violations. Elevated carbon emission trading prices similarly motivate enterprises to advance technology, conserve energy, and reduce carbon emissions. These factors collectively exert a substantial influence on the sustainable development practices of enterprises. Hence, this research direction merits critical attention in future investigations.