# Fresh Food Dual-Channel Supply Chain Considering Consumers’ Low-Carbon and Freshness Preferences

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

- (1)
- What are the optimal sales price and carbon emission reduction decisions in a fresh food dual-channel supply chain?
- (2)
- What are the effects of the low carbon preference coefficient of consumers, freshness level, and channel preference coefficient on the optimal decision and profit of supply chain members?
- (3)
- From the perspective of the producer and retailer, what is the difference between the best decision and profit for different dual-channel sales models?

## 2. Literature Review

#### 2.1. Consumer Preference

#### 2.2. Fresh Food Supply Chain Decision Making

#### 2.3. Multi-Channel Supply Chain

#### 2.4. Research Gap

## 3. Problem Description, Notations, and Assumptions

**Assumption**

**1.**

**Assumption**

**2.**

**Assumption**

**3.**

**Assumption**

**4.**

**Assumption**

**5.**

## 4. The Models

#### 4.1. Retailer Dual-Channel Model

**Proposition**

**1.**

**Corollary**

**1.**

**Corollary**

**2.**

#### 4.2. Producer Dual-Channel Model

**Proposition**

**2.**

**Corollary**

**3.**

**Corollary**

**4.**

**Corollary**

**5.**

- (1)
- $\frac{\partial {e}^{2*}}{\partial \phi}<0$,$\frac{\partial {w}^{2*}}{\partial \phi}<0$;
- (2)
- When$\frac{2{\gamma}^{2}}{3}<h<2{\gamma}^{2}$,$\frac{\partial {p}^{2*}}{\partial \phi}<0$,$\left|\frac{\partial {p}^{2*}}{\partial \phi}\right|<\left|\frac{\partial {w}^{2*}}{\partial \phi}\right|$; when$h>2{\gamma}^{2}$,$\frac{\partial {p}^{2*}}{\partial \phi}>0$;
- (3)
- $\frac{\partial {D}^{2*}}{\partial \phi}0$,$\frac{\partial {\prod}_{p}^{2*}}{\partial \phi}0$,$\frac{\partial {\prod}_{sc}^{2*}}{\partial \phi}<0$;
- (4)
- When$\frac{2{\gamma}^{2}}{3}<h<{\gamma}^{2}$,$\frac{\partial {\prod}_{r}^{2*}}{\partial \phi}<0$; when$h{\gamma}^{2}$,$\frac{\partial {\prod}_{r}^{2*}}{\partial \phi}>0$,$\left|\frac{\partial {\prod}_{p}^{2*}}{\partial \phi}\right|<\left|\frac{\partial {\prod}_{r}^{2*}}{\partial \phi}\right|.$

- (1)
- The producer’s carbon emission reduction and wholesale price decrease with the increase of the consumers’ purchase preference for the retailer’s offline channel ($\phi $). When $\phi $ is small, the online demand of the producer is larger, and the producer can obtain larger profits. The increasing profits will also stimulate the producer to carry out carbon emissions reduction to further increase market demand and profit. With the relatively high cost of carbon emission reduction, the wholesale price is also high. With the increase of $\phi $, the online demand of the producer decreases, and the motivation for carbon emission reduction is lacking. Therefore, the wholesale price also decreases.
- (2)
- When the carbon emissions reduction investment cost coefficient ($h$) is less than a threshold value, the sales price decreases with the increase of $\phi $, because the wholesale price is decreasing. In addition, the rate of change of the wholesale price is greater than that of the sales price. As a result, when $h$ is greater than a threshold, the sales price increases as $\phi $ increases.
- (3)
- The market demand decreases with the increase of $\phi $, because the carbon emissions reduction decreases with the increase of $\phi $. The producer’s profit decreases with the increase of $\phi $. This is because with the increase of $\phi $, the offline sales channel of the retailer occupies a larger market demand, leading to the decrease of the producer’s profit.
- (4)
- When $h$ is small, the retailer’s profit decreases with the increase of $\phi $. Under these circumstances, the producer’s profit also decreases, so the profit of the whole supply chain decreases. When $h$ is large, the retailer’s profit increases with the increase of $\phi $. The sales price and market demand jointly affect the retailer’s profit and eventually lead to the increase of the profit. In this case, the reduction rate of the producer’s profit is greater than the increase rate of the retailer’s profit, and the profit of the whole supply chain decreases.

#### 4.3. Mixed Dual-Channel Model

**Proposition**

**3.**

**Corollary**

**6.**

**Corollary**

**7.**

**Corollary**

**8.**

- (1)
- $\frac{\partial {e}^{3*}}{\partial \phi}<0$,$\frac{\partial {w}^{3*}}{\partial \phi}<0$;$\frac{\partial {e}^{3*}}{\partial \varphi}0$,$\frac{\partial {w}^{3*}}{\partial \varphi}<0$;
- (2)
- When$\frac{9{\gamma}^{2}}{10}<h<3{\gamma}^{2}$,$\frac{\partial {p}^{3*}}{\partial \phi}0$,$\frac{\partial {p}^{3*}}{\partial \varphi}<0$and$\left|\frac{\partial {p}^{3*}}{\partial \phi}\right|<\left|\frac{\partial {w}^{3*}}{\partial \phi}\right|$,$\left|\frac{\partial {p}^{3*}}{\partial \varphi}\right|<\left|\frac{\partial {w}^{3*}}{\partial \varphi}\right|$; When$h>3{\gamma}^{2}$,$\frac{\partial {p}^{3*}}{\partial \phi}0$,$\frac{\partial {p}^{3*}}{\partial \varphi}0$;
- (3)
- $\frac{\partial {D}^{3*}}{\partial \phi}<0$,$\frac{\partial {\prod}_{p}^{3*}}{\partial \phi}<0$,$\frac{\partial {\prod}_{sc}^{3*}}{\partial \phi}<0$;$\frac{\partial {D}^{3*}}{\partial \varphi}<0$,$\frac{\partial {\prod}_{p}^{3*}}{\partial \varphi}<0$,$\frac{\partial {\prod}_{sc}^{3*}}{\partial \varphi}<0$;
- (4)
- When$\frac{9{\gamma}^{2}}{10}<h<\frac{3{\gamma}^{2}}{2}$,$\frac{\partial {\prod}_{r}^{3*}}{\partial \phi}<0$,$\frac{\partial {\prod}_{r}^{3*}}{\partial \varphi}0$; when$h\frac{3{\gamma}^{2}}{2}$,$\frac{\partial {\prod}_{r}^{3*}}{\partial \phi}>0$,$\frac{\partial {\prod}_{r}^{3*}}{\partial \varphi}>0$, and$\left|\frac{\partial {\prod}_{p}^{3*}}{\partial \phi}\right|<\left|\frac{\partial {\prod}_{r}^{3*}}{\partial \phi}\right|$,$\left|\frac{\partial {\prod}_{p}^{3*}}{\partial \varphi}\right|<\left|\frac{\partial {\prod}_{r}^{3*}}{\partial \varphi}\right|.$

## 5. Comparison

**Proposition**

**4.**

**Proposition**

**5.**

**Proposition**

**6.**

**Proposition**

**7.**

- (1)
- a: When${\phi}_{r-13}^{*}\u03f5\left[\mathit{max}\left(0,{\phi}_{3},{\phi}_{5}\right),\mathit{min}\left({\phi}_{1},{\phi}_{4},1\right)\right]$,${\phi}_{r-13}^{*}$exist. If$\mathit{max}\left(0,{\phi}_{3},{\phi}_{5}\right)\le \phi \le {\phi}_{r-13}^{*}$, then${\prod}_{r}^{1*}{\prod}_{r}^{3*}$; if${\phi}_{r-13}^{*}<\phi \le min\left({\phi}_{1},{\phi}_{4},1\right)$,${\prod}_{r}^{1*}<{\prod}_{r}^{3*}$;b: When${\phi}_{r-13}^{*}>\mathit{min}\left({\phi}_{1},{\phi}_{4},1\right)$,${\phi}_{r-13}^{*}$does not exist, in this case,${\prod}_{r}^{1*}>{\prod}_{r}^{3*}$.Here, when$\phi ={\phi}_{r-13}^{*}$,${\prod}_{r}^{1*}={\prod}_{r}^{3*}$.
- (2)
- a: When${\phi}_{r-23}^{*}\u03f5\left[\mathit{max}\left(0,{\phi}_{2},{\phi}_{3},{\phi}_{5}\right),\mathit{min}\left({\phi}_{1},{\phi}_{4},1\right)\right]$,${\phi}_{r-23}^{*}$exists. If$\mathit{max}\left(0,{\phi}_{2},{\phi}_{3},{\phi}_{5}\right)\le \phi \le {\phi}_{r-23}^{*}$,${\prod}_{r}^{2*}<{\prod}_{r}^{3*}$; if${\phi}_{r-23}^{*}<\phi \le min\left({\phi}_{1},{\phi}_{4},1\right)$,${\prod}_{r}^{2*}>{\prod}_{r}^{3*}$;b: When${\phi}_{r-23}^{*}>\mathit{min}\left({\phi}_{1},{\phi}_{4},1\right)$,${\phi}_{r-23}^{*}$does not exist, in this case,${\prod}_{r}^{2*}<{\prod}_{r}^{3*}$.Here, when$\phi ={\phi}_{r-23}^{*}$,${\prod}_{r}^{2*}={\prod}_{r}^{3*}$.

**Proposition**

**8.**

- (1)
- a: When${\phi}_{p-13}^{*}\u03f5[\mathit{max}\left(0,{\phi}_{3},{\phi}_{5}\right),min\left({\phi}_{1},{\phi}_{4},1\right)$],${\phi}_{p-13}^{*}$exists. If$\mathit{max}\left(0,{\phi}_{3},{\phi}_{5}\right)\le \phi \le {\phi}_{p-13}^{*}$,${\prod}_{p}^{1*}<{\prod}_{p}^{3*}$; if${\phi}_{p-13}^{*}<\phi <min\left({\phi}_{1},{\phi}_{4},1\right)$,${\prod}_{p}^{1*}>{\prod}_{p}^{3*}$;b: When${\phi}_{p-13}^{*}>\mathit{min}\left({\phi}_{1},{\phi}_{4},1\right)$,${\phi}_{p-13}^{*}$does not exist, in this case,${\prod}_{p}^{1*}<{\prod}_{p}^{3*}$.Here, when$\phi ={\phi}_{p-13}^{*}$,${\prod}_{p}^{1*}={\prod}_{p}^{3*}$.
- (2)
- a: When${\phi}_{p-23}^{*}\u03f5\left[\mathit{max}\left(0,{\phi}_{2},{\phi}_{3},{\phi}_{5}\right),\mathit{min}\left({\phi}_{1},{\phi}_{4},1\right)\right]$,${\phi}_{p-23}^{*}$exists. If$\mathit{max}\left(0,{\phi}_{2},{\phi}_{3},{\phi}_{5}\right)\le \phi \le {\phi}_{p-23}^{*}$,${\prod}_{p}^{2*}>{\prod}_{p}^{3*}$; if${\phi}_{p-23}^{*}<\phi \le min\left({\phi}_{1},{\phi}_{4},1\right)$,${\prod}_{p}^{2*}<{\prod}_{p}^{3*}$;b: When${\phi}_{p-23}^{*}>\mathit{min}\left({\phi}_{1},{\phi}_{4},1\right)$,${\phi}_{p-23}^{*}$does not exist, in this case,${\prod}_{p}^{2*}>{\prod}_{p}^{3*}$.Here, when$\phi ={\phi}_{p-23}^{*}$,${\prod}_{p}^{2*}={\prod}_{p}^{3*}$.

## 6. Numerical Analysis

#### 6.1. Impact of $\phi $

#### 6.2. Impact of $\gamma $

#### 6.3. Impact of $\theta $

## 7. Managerial Implication

- (1)
- Since the freshness of fresh food has an important impact on the profit of members of the supply chain, and the loss of fresh food in the circulation process is the most important factor affecting its freshness, enterprises in the supply chain should try to control the circulation loss of fresh food and improve the freshness of food. On the one hand, enterprises can improve technical equipment by putting in special refrigerated transport vehicles and cold storage facilities to improve the level of specialization and standardization. Then, enterprises could ensure that the temperature control of the fresh food supply chain is under control and keep products efficient and high quality on their way into the sales market. On the other hand, enterprises can strengthen staff training, teach them to operate in accordance with the cold chain standard, and reduce the loss in the circulation process of fresh food by human reason.
- (2)
- Consumers’ low-carbon preference for fresh food makes both manufacturers and retailers more profitable. Therefore, enterprises in the supply chain should understand the preferences of consumers and make corresponding measures to reduce emissions in a timely manner. Enterprises can take measures such as increasing the use of clean energy, reducing the use or recycling of packaged products to meet consumers’ low-carbon preferences, and improve the profits of the supply chain. In addition, in order to further enhance consumers’ preference for low carbon and achieve the goal of low-carbon emission reduction, the government can advocate and promote the whole society’s low-carbon consumption by popularizing environmental protection knowledge and providing subsidies for low-carbon consumption.
- (3)
- In production dual-channel and mixed dual-channel models, the change of consumers’ channel preference will also have an impact on supply chain members. This requires supply chain enterprises to timely understand consumers’ channel preferences by means of market research or big data analysis, so as to adjust market supply and channel selection strategies in a timely manner and enhance their competitiveness.
- (4)
- Supply chain members can consider transforming single dual-channel supply chain model to mixed dual-channel supply chain model to increase the profit of the whole supply chain. Enterprises can judge whether to open mixed dual channels according to the carbon emission reduction investment cost coefficient and consumers’ purchasing preference for offline sales channels of retailers and then make profit maximization decisions.

## 8. Conclusions

- (1)
- We explore the impacts of the low-carbon preference coefficient of consumers and freshness level on the three dual-channel supply chains. We find that a higher low-carbon preference coefficient of consumers and freshness level can increase the sales price, producer’s carbon emission reduction, market demand, retailer’s profit, producer’s profit, and supply chain’s profit. Therefore, enterprises in the supply chain should understand the preferences of consumers and take corresponding measures in a timely manner to reduce carbon emissions and keep the freshness of fresh food, which will improve the profits of the supply chain.
- (2)
- The impact of the consumers’ purchasing preferences on the three dual-channel supply chains is investigated. In the producer dual-channel model and the mixed dual-channel model, the increase of the consumers’ purchasing preferences for the retailer’s offline channel or the consumers’ purchasing preferences for the retailer’s online channel will reduce the wholesale price, carbon emission reduction, market demand, producer’s profit, and supply chain’s profit. The value of the carbon emission reduction investment cost coefficient decides the relationship between the sales price and the consumers’ purchasing preference for the retailer’s offline channel or the consumers’ purchasing preference for the retailer’s online channel. It also decides how the retailer’s profit changes with the consumers’ purchasing preference for the retailer’s offline channel or the consumers’ purchasing preference for the retailer’s online channel.
- (3)
- The comparison of the optimal decision, market demand, and profit in the three dual-channel models need to be determined according to the value of the consumers’ purchasing preference for the retailer’s offline channel. Therefore, if the supply chain members want to add an online channel on a single dual-channel supply chain to improve the profit, it can be specifically judged according to the value of consumers’ purchasing preference for the retailer’s offline channel.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Proof of Proposition**

**1.**

**Proof of Corollary**

**1.**

- (1)
- $\frac{\partial {p}^{1*}}{\partial \gamma}=\frac{3h\gamma \left(a+2\theta \right)}{2{\left(-2h+{\gamma}^{2}\right)}^{2}}>0$, $\frac{\partial {w}^{1*}}{\partial \gamma}=\frac{h\gamma \left(a+2\theta \right)}{{\left(-2h+{\gamma}^{2}\right)}^{2}}>0$, $\frac{\partial {e}^{1*}}{\partial \gamma}=\frac{\left(2h+{\gamma}^{2}\right)\left(a+2\theta \right)}{2{\left(-2h+{\gamma}^{2}\right)}^{2}}>0$;
- (2)
- $\frac{\partial {\mathrm{D}}^{1*}}{\partial \gamma}=\frac{h\gamma \left(a+2\theta \right)}{{\left(-2h+{\gamma}^{2}\right)}^{2}}>0$;
- (3)
- $\text{}\frac{\partial {\prod}_{p}^{1*}}{\partial \gamma}=\frac{h\gamma {\left(a+2\theta \right)}^{2}}{4{\left(-2h+{\gamma}^{2}\right)}^{2}}0$, $\frac{\partial {\prod}_{r}^{1*}}{\partial \gamma}=\frac{{h}^{2}\gamma {\left(a+2\theta \right)}^{2}}{2{\left(2h-{\gamma}^{2}\right)}^{3}}<0$, $\frac{\partial {\prod}_{sc}^{1*}}{\partial \gamma}=\frac{h\gamma \left(4h-{\gamma}^{2}\right){\left(a+2\theta \right)}^{2}}{4{\left(2h-{\gamma}^{2}\right)}^{3}}>0$. □

**Proof of Corollary**

**2.**

- (1)
- $\frac{\partial {p}^{1*}}{\partial \theta}=\frac{3h}{4h-2{\gamma}^{2}}>0$, $\frac{\partial {w}^{1*}}{\partial \theta}=\frac{\gamma}{2h-{\gamma}^{2}}>0$,$\frac{\partial {e}^{1*}}{\partial \theta}=\frac{h}{2h-{\gamma}^{2}}>0$;
- (2)
- $\frac{\partial {\mathrm{D}}^{1*}}{\partial \theta}=\frac{h}{2h-{\gamma}^{2}}>0$;
- (3)
- $\frac{\partial {\prod}_{p}^{1*}}{\partial \theta}=\frac{h\left(a+2\theta \right)}{4h-2{\gamma}^{2}}>0$, $\frac{\partial {\prod}_{r}^{1*}}{\partial \theta}=\frac{{h}^{2}\left(a+2\theta \right)}{2{\left(-2h+{\gamma}^{2}\right)}^{2}}>0$, $\frac{\partial {\prod}_{sc}^{1*}}{\partial \theta}=\frac{h\left(3h-{\gamma}^{2}\right)\left(a+2\theta \right)}{2{\left(-2h+{\gamma}^{2}\right)}^{2}}>0$. □

**Proof of Proposition**

**2.**

**Proof of Corollary**

**3.**

- (1)
- $\frac{\partial {p}^{2*}}{\partial \gamma}=\frac{8h\gamma \left[a\left(1-\phi \right)+\theta \right]}{{\left(3h-2{\gamma}^{2}\right)}^{2}}>0$, $\frac{\partial {e}^{2*}}{\partial \gamma}=\frac{2\left(3h+2{\gamma}^{2}\right)\left[a\left(1-\phi \right)+\theta \right]}{{\left(3h-2{\gamma}^{2}\right)}^{2}}>0$, $\frac{\partial {w}^{2*}}{\partial \gamma}=\frac{4h\gamma \left[a\left(1-\phi \right)+\theta \right]}{{\left(3h-2{\gamma}^{2}\right)}^{2}}>0$;
- (2)
- $\frac{\partial {D}^{2*}}{\partial \gamma}=\frac{8h\gamma \left[a\left(1-\phi \right)+\theta \right]}{{\left(3h-2{\gamma}^{2}\right)}^{2}}>0$;
- (3)
- $\frac{\partial {\prod}_{r}^{2*}}{\partial \gamma}=\frac{4h\gamma \left[a\left(1-\phi \right)+\theta \right]\left[2h\theta +2a{\gamma}^{2}\left(1-2\phi \right)+ah\left(4\phi -1\right)\right]}{{\left(3h-2{\gamma}^{2}\right)}^{3}}$.

**Proof of Corollary**

**4.**

- (1)
- $\frac{\partial {p}^{2*}}{\partial \theta}=\frac{2h}{3h-2{\gamma}^{2}}>0$, $\frac{\partial {e}^{2*}}{\partial \theta}=\frac{2\gamma}{3h-2{\gamma}^{2}}>0$, $\frac{\partial {w}^{2*}}{\partial \theta}=\frac{h}{3h-2{\gamma}^{2}}>0$;
- (2)
- $\frac{\partial {\mathrm{D}}^{2*}}{\partial \theta}=\frac{2h}{3h-2{\gamma}^{2}}>0$;
- (3)
- $\frac{\partial {\prod}_{r}^{2*}}{\partial \theta}=\frac{h\left[2h\theta +2a{\gamma}^{2}\left(1-2\phi \right)+ah\left(-1+4\phi \right)\right]}{{\left(3h-2{\gamma}^{2}\right)}^{2}}>0$, $\frac{\partial {\prod}_{p}^{2*}}{\partial \theta}=\frac{2h\left[a\right(1-\phi )+\theta ]}{3h-2{\gamma}^{2}}>0$, $\frac{\partial {\prod}_{sc}^{2*}}{\partial \theta}=\frac{\partial {\prod}_{r}^{2*}}{\partial \theta}+\frac{\partial {\prod}_{p}^{2*}}{\partial \theta}>0$. □

**Proof of Corollary**

**5.**

- (1)
- $\frac{\partial {e}^{2*}}{\partial \phi}=\frac{-2a\gamma}{3h-2{\gamma}^{2}}<0$, $\frac{\partial {w}^{2*}}{\partial \phi}=\frac{-ah}{3h-2{\gamma}^{2}}<0$;
- (2)
- $\frac{\partial {p}^{2*}}{\partial \phi}=\frac{a\left(h-2{\gamma}^{2}\right)}{3h-2{\gamma}^{2}}$, when $h>2{\gamma}^{2}$,$\text{}\frac{\partial {p}^{2*}}{\partial \phi}0$; We know$\text{}\frac{2{\gamma}^{2}}{3}h$, so when $\frac{2{\gamma}^{2}}{3}<h<2{\gamma}^{2}$, $\frac{\partial {p}^{2*}}{\partial \phi}<0$;
- (3)
- $\frac{\partial {\mathrm{D}}^{2*}}{\partial \phi}=-\frac{2ah}{3h-2{\gamma}^{2}}<0$; $\frac{\partial {\prod}_{p}^{2*}}{\partial \phi}=\frac{-a\left[2h\theta +2a{\gamma}^{2}\left(1-2\phi \right)+ah\left(4\phi -1\right)\right]}{3h-2{\gamma}^{2}}$, $2h\theta +ah\left(4\phi -1\right)+2a{\gamma}^{2}\left(1-2\phi \right)>0\to \frac{\partial {\prod}_{p}^{2*}}{\partial \phi}<0$; Similarly, $\frac{\partial {\prod}_{sc}^{2*}}{\partial \phi}=\frac{-ah\left[2h\theta +2a{\gamma}^{2}\left(1-2\phi \right)+ah\left(4\phi -1\right)\right]}{{\left(3h-2{\gamma}^{2}\right)}^{2}}<0$;
- (4)
- $\frac{\partial {\prod}_{r}^{2*}}{\partial \phi}=\frac{2a\left(h-{\gamma}^{2}\right)\left[2h\theta +2a{\gamma}^{2}\left(1-2\phi \right)+ah\left(4\phi -1\right)\right]}{{\left(3h-2{\gamma}^{2}\right)}^{2}}$, $2h\theta +2a{\gamma}^{2}\left(1-2\phi \right)+ah\left(4\phi -1\right)>0\to \mathrm{When}\text{}h{\gamma}^{2}$, $\frac{\partial {\prod}_{r}^{2*}}{\partial \phi}>0$; when $\frac{2{\gamma}^{2}}{3}<h<{\gamma}^{2}$, $\frac{\partial {\prod}_{r}^{2*}}{\partial \phi}<0$. □

**Proof of Proposition**

**3.**

**Proof of Corollary**

**6.**

- (1)
- $\text{}\frac{\partial {p}^{3*}}{\partial \gamma}=\frac{14h\gamma \left[9\theta +a\left(7-6\sigma \right)\right]}{{\left(10h-9{\gamma}^{2}\right)}^{2}}$, $\frac{\partial {e}^{3*}}{\partial \gamma}=\frac{\left(10h+9{\gamma}^{2}\right)\left[9\theta +a\left(7-6\sigma \right)\right]}{{\left(10h-9{\gamma}^{2}\right)}^{2}}$, $\frac{\partial {w}^{3*}}{\partial \gamma}=\frac{8h\gamma \left[9\theta +a\left(7-6\sigma \right)\right]}{{\left(10h-9{\gamma}^{2}\right)}^{2}}$ . We know $0<\phi <1$; thus $\phi <\frac{6a\left(1-\varphi \right)+a+9\theta}{6a\left(1-\varphi \right)}=1+\frac{a+9\theta}{6a\left(1-\varphi \right)}\to 9\theta +a\left(7-6\sigma \right)>0$($\mathsf{\sigma}=\phi +\varphi -\phi \varphi $), and we can deduce $\frac{\partial {p}^{3*}}{\partial \gamma}>0$, $\frac{\partial {e}^{3*}}{\partial \gamma}>0$,$\text{}\frac{\partial {w}^{3*}}{\partial \gamma}0$;
- (2)
- $\frac{\partial {D}^{3*}}{\partial \gamma}=\frac{18h\gamma \left[9\theta +a\left(7-6\sigma \right)\right]}{{\left(10h-9{\gamma}^{2}\right)}^{2}}>0$;
- (3)
- $\frac{\partial {\prod}_{r}^{3*}}{\partial \gamma}=\frac{12h\gamma \left[9\theta +a\left(7-6\sigma \right)\right]\left[6h\theta +3a{\gamma}^{2}\left(2-3\sigma \right)+ah\left(6\sigma -2\right)\right]}{{\left(10h-9{\gamma}^{2}\right)}^{3}}>0$, From Proposition 3, we have $6h\theta +3a{\gamma}^{2}\left(2-3\mathsf{\sigma}\right)+ah\left(6\sigma -2\right)>0$, then $\frac{\partial {\prod}_{r}^{3*}}{\partial \gamma}>0$; $\frac{\partial {\prod}_{p}^{3*}}{\partial \gamma}=\frac{h\gamma {\left[9\theta +a\left(7-6\sigma \right)\right]}^{2}}{{\left(10h-9{\gamma}^{2}\right)}^{2}}>0$;$\text{}\frac{\partial {\prod}_{sc}^{3*}}{\partial \gamma}=\frac{\partial {\prod}_{r}^{3*}}{\partial \gamma}+\frac{\partial {\prod}_{p}^{3*}}{\partial \gamma}0$. □

**Proof of Corollary**

**7.**

- (1)
- $\frac{\partial {p}^{3*}}{\partial \theta}=\frac{7h}{10h-9{\gamma}^{2}}>0$, $\frac{\partial {e}^{3*}}{\partial \theta}=\frac{9\gamma}{10h-9{\gamma}^{2}}>0$,$\text{}\frac{\partial {w}^{3*}}{\partial \theta}=\frac{4h}{10h-9{\gamma}^{2}}0$;
- (2)
- $\frac{\partial {\mathrm{D}}^{3*}}{\partial \theta}=\frac{9h}{10h-9{\gamma}^{2}}>0$;
- (3)
- $\frac{\partial {\prod}_{r}^{3*}}{\partial \theta}=\frac{6h\left[6h\theta +3a{\gamma}^{2}\left(2-3\sigma \right)+2ah\left(3\sigma -1\right)\right]}{{\left(10h-9{\gamma}^{2}\right)}^{2}}$, From Proposition 3, we have $6h\theta +3a{\gamma}^{2}\left(2-3\sigma \right)+ah\left(6\sigma -2\right)>0$, then $\frac{\partial {\prod}_{r}^{3*}}{\partial \theta}>0$; $\frac{\partial {\prod}_{p}^{3*}}{\partial \theta}=\frac{9h\theta -ah\left(6\sigma -7\right)}{10h-9{\gamma}^{2}}>0$; $\frac{\partial {\prod}_{sc}^{3*}}{\partial \theta}=\frac{\partial {\prod}_{p}^{3*}}{\partial \theta}+\frac{\partial {\prod}_{r}^{3*}}{\partial \theta}>0$. □

**Proof of Corollary**

**8.**

- (1)
- $\frac{\partial {e}^{3*}}{\partial \phi}=\frac{6a\gamma \left(\varphi -1\right)}{10h-9{\gamma}^{2}}<0$, $\frac{\partial {w}^{3*}}{\partial \phi}=\frac{a\left(2h+3{\gamma}^{2}\right)\left(\varphi -1\right)}{2\left(10h-9{\gamma}^{2}\right)}<0$; $\frac{\partial {e}^{3*}}{\partial \varphi}=\frac{6a\gamma \left(\phi -1\right)}{10h-9{\gamma}^{2}}<0$, $\frac{\partial {w}^{3*}}{\partial \varphi}=\frac{a\left(2h+3{\gamma}^{2}\right)\left(\phi -1\right)}{2\left(10h-9{\gamma}^{2}\right)}<0$;
- (2)
- $\frac{\partial {p}^{3*}}{\partial \phi}=\frac{2a\left(h-3{\gamma}^{2}\right)\left(1-\varphi \right)}{10h-9{\gamma}^{2}}$, $\frac{\partial {p}^{3*}}{\partial \varphi}=\frac{2a\left(h-3{\gamma}^{2}\right)\left(1-\phi \right)}{10h-9{\gamma}^{2}}$. When $h>3{\gamma}^{2}$, we have $\frac{\partial {p}^{3*}}{\partial \phi}>0$, $\frac{\partial {p}^{3*}}{\partial \varphi}>0$; Because $\frac{9{\gamma}^{2}}{10}<h$, thus when $\frac{9{\gamma}^{2}}{10}<h<3{\gamma}^{2}$, we have $\frac{\partial {p}^{3*}}{\partial \phi}<0$, $\frac{\partial {p}^{3*}}{\partial \varphi}<0$;
- (3)
- $\frac{\partial {\mathrm{D}}^{3*}}{\partial \phi}=\frac{6ah\left(\varphi -1\right)}{10h-9{\gamma}^{2}}<0$; $\frac{\partial {\mathrm{D}}^{3*}}{\partial \varphi}=\frac{6ah\left(\phi -1\right)}{10h-9{\gamma}^{2}}<0$.$\frac{\partial {\prod}_{p}^{3*}}{\partial \phi}=-\frac{a\left(\varphi -1\right)\left[-6h\theta +ah\left(2+6\varphi \left(-1+\phi \right)-6\phi \right)+3a{\gamma}^{2}\left(-2-3\varphi \left(\phi -1\right)+3\phi \right)\right]}{10h-9{\gamma}^{2}}$,$\frac{\partial {\prod}_{p}^{3d*}}{\partial \phi}=-\frac{a\left(\phi -1\right)\left[-6h\theta +ah\left(2+6\varphi \left(-1+\phi \right)-6\phi \right)+3a{\gamma}^{2}\left(-2-3\varphi \left(\phi -1\right)+3\phi \right)\right]}{10h-9{\gamma}^{2}}\text{}$.

- (4)
- $\frac{\partial {\prod}_{r}^{3*}}{\partial \phi}=\frac{3a\left(2h-3{\gamma}^{2}\right)\left(\varphi -1\right)\left[-6h\theta +ah\left(2+6\varphi \left(-1+\phi \right)-6\phi \right)+3a{\gamma}^{2}\left(-2-3\varphi \left(-1+\phi \right)+3\phi \right)\right]}{{\left(10h-9{\gamma}^{2}\right)}^{2}}$, $\frac{\partial {\prod}_{r}^{3*}}{\partial \varphi}=\frac{3a\left(2h-3{\gamma}^{2}\right)\left(\phi -1\right)\left[-6h\theta +ah\left(2+6\varphi \left(-1+\phi \right)-6\phi \right)+3a{\gamma}^{2}\left(-2-3\varphi \left(-1+\phi \right)+3\phi \right)\right]}{{\left(10h-9{\gamma}^{2}\right)}^{2}}$. From Proposition 3, we have $6h\theta +3a{\gamma}^{2}\left[2+3\varphi \left(\phi -1\right)-3\phi \right]+ah\left[6\phi -2-6\varphi \left(\phi -1\right)\right]>0$, so when $h>\frac{3{\gamma}^{2}}{2}$, then $\frac{\partial {\prod}_{r}^{3*}}{\partial \phi}>0$, $\frac{\partial {\prod}_{r}^{3*}}{\partial \varphi}>0$; when $\frac{9{\gamma}^{2}}{10}<h<\frac{3{\gamma}^{2}}{2}$, then $\frac{\partial {\prod}_{r}^{3*}}{\partial \phi}<0$, $\frac{\partial {\prod}_{r}^{3*}}{\partial \varphi}<0$. □

**Proof of Proposition**

**4.**

**Proof of Proposition**

**5.**

**Proof of Proposition**

**6.**

**Proof of Proposition**

**7.**

- (1)
- Let ${\prod}_{r}^{1*}-{\prod}_{r}^{3*}=0$, we get that${\phi}_{1}^{*}=\frac{2h\theta \left(2h+3{\gamma}^{2}\right)+a\left[h{\gamma}^{2}\left(37-48\varphi \right)+6{\gamma}^{4}\left(3\varphi -2\right)+6{h}^{2}\left(4\varphi -3\right)\right]}{6a\left(2h-3{\gamma}^{2}\right)\left(2h-{\gamma}^{2}\right)\left(\varphi -1\right)}$${\phi}_{2}^{*}=\frac{2h\theta \left(22h-15{\gamma}^{2}\right)+a\left[h{\gamma}^{2}\left(19-48\varphi \right)+6{\gamma}^{4}\left(3\varphi -2\right)+{h}^{2}\left(2+24\varphi \right)\right]}{6a\left(2h-3{\gamma}^{2}\right)\left(2h-{\gamma}^{2}\right)\left(\varphi -1\right)}$${\phi}_{1}^{*}-{\phi}_{2}^{*}=\frac{h\left(10h-9{\gamma}^{2}\right)\left(a+2\theta \right)}{3a\left(2h-3{\gamma}^{2}\right)\left(2h-{\gamma}^{2}\right)\left(1-\varphi \right)}<0$, we have ${\phi}_{1}^{*}>{\phi}_{2}^{*}$.

- (2)
- Same as above. □

**Proof of Proposition**

**8.**

## References

- Dominici, A.; Boncinelli, F.; Gerini, F.; Marone, E. Determinants of online food purchasing: The impact of socio-demographic and situational factors. J. Retail. Consum. Serv.
**2021**, 60, 102473. [Google Scholar] [CrossRef] - Wang, Z.; Yao, D.Q.; Yue, X. E-business system investment for fresh agricultural food industry in China. Ann. Oper. Res.
**2017**, 257, 379–394. [Google Scholar] [CrossRef] - He, B.; Gan, X.; Yuan, K. Entry of online presale of fresh produce: A competitive analysis. Eur. J. Oper. Res.
**2019**, 272, 339–351. [Google Scholar] [CrossRef] - Cang, Y.M.; Wang, D.C. A comparative study on the online shopping willingness of fresh agricultural products between experienced consumers and potential consumers. Sustain. Comput. Inform. Syst.
**2020**, 30, 100493. [Google Scholar] - Cai, G. Channel Selection and Coordination in Dual-Channel Supply Chains. J. Retail.
**2010**, 86, 22–36. [Google Scholar] [CrossRef] - Ji, J.; Zhang, Z.; Yang, L. Comparisons of initial carbon allowance allocation rules in an O2O retail supply chain with the cap-and-trade regulation. Int. J. Prod. Econ.
**2017**, 187, 68–84. [Google Scholar] [CrossRef] - Chen, J.; Liang, L.; Yao, D.-Q.; Sun, S. Price and quality decisions in dual-channel supply chains. Eur. J. Oper. Res.
**2017**, 259, 935–948. [Google Scholar] [CrossRef] - Yang, L.; Tang, R. Comparisons of sales modes for a fresh product supply chain with freshness-keeping effort. Transp. Res. Part E Logist. Transp. Rev.
**2019**, 125, 425–448. [Google Scholar] [CrossRef] - Liu, C.; Chen, W.; Zhou, Q.; Mu, J. Modelling dynamic freshness-keeping effort over a finite time horizon in a two-echelon online fresh product supply chain. Eur. J. Oper. Res.
**2020**, in press. [Google Scholar] - Yang, L.; Tang, R.; Chen, K. Call, put and bidirectional option contracts in agricultural supply chains with sales effort. Appl. Math. Model.
**2017**, 47, 1–16. [Google Scholar] [CrossRef] - Liao, Z.; Zhu, X.; Shi, J. Case study on initial allocation of Shanghai carbon emission trading based on Shapley value. J. Clean. Prod.
**2015**, 103, 338–344. [Google Scholar] [CrossRef] - Hicks, R.L. Can Eco-Labels Tune a Market? Evidence from Dolphin-Safe Labeling. J. Environ. Econ. Manag.
**2002**, 43, 339–359. [Google Scholar] - Song, M. Low-carbon production with low-carbon premium in cap-and-trade regulation. J. Clean. Prod.
**2016**, 134, 652–662. [Google Scholar] - Du, S.; Zhu, J.; Jiao, H.; Ye, W. Game-theoretical analysis for supply chain with consumer preference to low carbon. Int. J. Prod. Res.
**2014**, 53, 3753–3768. [Google Scholar] [CrossRef] - Liu, B.; Li, T.; Tsai, S.-B. Low Carbon Strategy Analysis of Competing Supply Chains with Different Power Structures. Sustainability
**2017**, 9, 835. [Google Scholar] - Ghosh, D.; Shah, J. Supply chain analysis under green sensitive consumer demand and cost sharing contract. Int. J. Prod. Econ.
**2015**, 164, 319–329. [Google Scholar] [CrossRef] - Seyfang, G. Community action for sustainable housing: Building a low-carbon future. Energy Policy
**2010**, 38, 7624–7633. [Google Scholar] [CrossRef] [Green Version] - Zhou, Y.; Bao, M.; Chen, X.; Xu, X. Co-op advertising and emission reduction cost sharing contracts and coordination in low-carbon supply chain based on fairness concerns. J. Clean. Prod.
**2016**, 133, 402–413. [Google Scholar] [CrossRef] - Liu, M.L.; Li, Z.H.; Anwar, S.; Zhang, Y. Supply chain carbon emission reductions and coordination when consumers have a strong preference for low-carbon products. Environ. Sci. Pollut. Res.
**2021**, 28, 19969–19983. [Google Scholar] [CrossRef] - Xiaoyan, W.; Minggao, X.; Lu, X. Analysis of Carbon Emission Reduction in a Dual-Channel Supply Chain with Cap-And-Trade Regulation and Low-Carbon Preference. Sustainability
**2018**, 10, 580. [Google Scholar] [CrossRef] [Green Version] - Zhang, Z.; Yu, L. Dynamic Optimization and Coordination of Cooperative Emission Reduction in a Dual-Channel Supply Chain Considering Reference Low-Carbon Effect and Low-Carbon Goodwill. Int. J. Environ. Res. Public Health
**2021**, 18, 539. [Google Scholar] [CrossRef] [PubMed] - Cai, X.; Chen, J.; Xiao, Y.; Xu, X.; Yu, G. Fresh-product supply chain management with logistics outsourcing. Omega
**2013**, 41, 752–765. [Google Scholar] [CrossRef] - Herbon, A. Dynamic pricing vs. acquiring information on consumers’ heterogeneous sensitivity to product freshness. Int. J. Prod. Res.
**2013**, 52, 918–933. [Google Scholar] [CrossRef] - Zhang, K.; Ma, M. Differential Game Model of a Fresh Dual-Channel Supply Chain under Different Return Modes. IEEE Access
**2021**, 9, 8888–8901. [Google Scholar] [CrossRef] - Ma, X.; Wang, S.; Islam, S.M.N.; Liu, X. Coordinating a three-echelon fresh agricultural products supply chain considering freshness-keeping effort with asymmetric information. Appl. Math. Model.
**2019**, 67, 337–356. [Google Scholar] [CrossRef] - Zhu, Q.; Li, X.; Zhao, S. Cost-sharing models for green product production and marketing in a food supply chain. Ind. Manag. Data Syst.
**2018**, 118, 654–682. [Google Scholar] [CrossRef] - Feng, L.; Chan, Y.L.; Cárdenas-Barrón, L.E. Pricing and lot-sizing polices for perishable goods when the demand depends on selling price, displayed stocks, and expiration date. Int. J. Prod. Econ.
**2017**, 185, 11–20. [Google Scholar] [CrossRef] - Hsu, P.H.; Wee, H.M.; Teng, H.M. Preservation technology investment for deteriorating inventory. Int. J. Prod. Econ.
**2010**, 124, 387–393. [Google Scholar] [CrossRef] - Dye, C.Y.; Hsieh, T.P. An optimal replenishment policy for deteriorating items with effective investment in preservation technology. Eur. J. Oper. Res.
**2012**, 218, 106–112. [Google Scholar] [CrossRef] - Zhang, J.; Liu, G.; Zhang, Q.; Bai, Z. Coordinating a supply chain for deteriorating items with a revenue sharing and cooperative investment contract. Omega
**2015**, 56, 37–49. [Google Scholar] [CrossRef] - Liang, X.; Jiang, Q. Pricing strategy of manufacturer in dual-channel considering competition between online retailers and offline retailers. Control.Decision
**2019**, 34, 1501–1513. [Google Scholar] - Chen, Y.C.; Fang, S.-C.; Wen, U.-P. Pricing policies for substitutable products in a supply chain with Internet and traditional channels. Eur. J. Oper. Res.
**2013**, 224, 542–551. [Google Scholar] [CrossRef] - Peng, G.; Tian, X.; Chen, Q. Online Cooperative Promotion and Cost Sharing Policy under Supply Chain Competition. Math. Probl. Eng.
**2016**, 2016, 1–11. [Google Scholar] - Keen, C.; Wetzels, M.; De Ruyter, K.; Feinberg, R. E-tailers versus retailers. J. Bus. Res.
**2004**, 57, 685–695. [Google Scholar] [CrossRef] - Khouja, M.; Park, S.; Cai, G. Channel selection and pricing in the presence of retail-captive consumers. Int. J. Prod. Econ.
**2010**, 125, 84–95. [Google Scholar] [CrossRef] - Wang, Q.; Zhao, D.; He, L. Contracting emission reduction for supply chains considering market low-carbon preference. J. Clean. Prod.
**2016**, 120, 72–84. [Google Scholar] [CrossRef] - Taleizadeh, A.A.; Alizadeh-Basban, N.; Sarker, B.R. Coordinated contracts in a two-echelon green supply chain considering pricing strategy. Comput. Ind. Eng.
**2018**, 124, 249–275. [Google Scholar] [CrossRef] - Yu, B.; Wang, J.; Lu, X.; Yang, H. Collaboration in a low-carbon supply chain with reference emission and cost learning effects: Cost sharing versus revenue sharing strategies. J. Clean. Prod.
**2020**, 250, 119460. [Google Scholar] [CrossRef] - Guo, C.R.; Chen, G.Y. Price Competition and Equilibrium Analysis in Supply Chain with Double Hybrid Distribution Channels. Chin. J. Manag. Sci.
**2009**, 17, 65–71. [Google Scholar] - Basiri, Z.; Heydari, J. A mathematical model for green supply chain coordination with substitutable products. J. Clean. Prod.
**2017**, 145, 232–249. [Google Scholar] [CrossRef] [Green Version] - Fujiwara, O.; Perera, U.L.J.S.R. EOQ models for continuously deteriorating products using linear and exponential penalty costs. Eur. J. Oper. Res.
**1993**, 70, 104–114. [Google Scholar] [CrossRef] - Zhang, L.; Wang, J.; You, J. Consumer environmental awareness and channel coordination with two substitutable products. Eur. J. Oper. Res.
**2015**, 241, 63–73. [Google Scholar] [CrossRef] - Wang, S.Y.; Choi, S.H. Pareto-efficient coordination of the contract-based MTO supply chain under flexible cap-and-trade emission constraint. J. Clean. Prod.
**2020**, 250, 119571. [Google Scholar] [CrossRef] - Yang, L.; Zhang, Q.; Zhang, Z.Y. Channel selection and carbon emissions reduction policies in supply chains with the cap-and-trade scheme. J. Manag. Sci. China
**2017**, 20, 75–87. [Google Scholar] - Li, B.; Zhu, M.; Jiang, Y.; Li, Z. Pricing policies of a competitive dual-channel green supply chain. J. Clean. Prod.
**2016**, 112, 2029–2042. [Google Scholar] [CrossRef] - Xie, Q.H.; Huang, P.Q. A Quantity Discount Model for Coordination of Internet-based Hybrid Channels. Syst. Eng. Theory Pract.
**2007**, 8, 1–11. [Google Scholar] - Ranjan, A.; Jha, J.K. Pricing and coordination strategies of a dual-channel supply chain considering green quality and sales effort. J. Clean. Prod.
**2019**, 218, 409–424. [Google Scholar] [CrossRef] - Svanes, E.; Aronsson, A.K.S. Carbon footprint of a Cavendish banana supply chain. Int. J. Life Cycle Assess.
**2013**, 18, 1450–1464. [Google Scholar] [CrossRef] - Li, T.; Zhang, R.; Zhao, S.; Liu, B. Low carbon strategy analysis under revenue-sharing and cost-sharing contracts. J. Clean. Prod.
**2019**, 212, 1462–1477. [Google Scholar] [CrossRef] - Yang, H.; Chen, W. Retailer-driven carbon emission abatement with consumer environmental awareness and carbon tax: Revenue-sharing versus Cost-sharing. Omega
**2018**, 78, 179–191. [Google Scholar] [CrossRef]

Classification Method | The Specific Classification | Reference |
---|---|---|

Channel structure | (1) Pure online sales channels (2) Pure offline sales channels (3) Retailer dual-channel (retailer online sales + offline sales) (4) Supplier dual-channel (supplier online sales + retailer offline sales) (5) Mixed dual-channel (supplier online sales + retailer online and offline sales) | Cai et al. [5] Ji et al. [6] Chen et al. [7] Yang et al. [8] |

Channel control subject | (1) Manufacturer (supplier, manufacturer) leading (2) Retailer leading (3) Manufacturers and retailers are evenly matched | Wang et al. [36] Ata Allah et al. [37] Yu et al. [38] |

Author | Consumers’ Low-Carbon Preference | Consumers’ Freshness Preference | Dual Channel | Mixed Dual Channel | Comparative Analysis of Different Dual Channels |
---|---|---|---|---|---|

Guo and Chen [39] | √ | ||||

Yang et al. [8] | √ | √ | √ | ||

Du et al. [14] | √ | ||||

Zhang and Ma [24] | √ | √ | |||

Wang et al. [20] | √ | √ | |||

Zhang and Yu [21] | √ | √ | |||

This paper | √ | √ | √ | √ | √ |

$p$ | Online and offline sales prices $w\text{}\text{}p$ |

$w$ | Wholesale prices of fresh food $0\text{}\text{}w$ |

$e$ | The carbon footprint of fresh food $0\text{}\text{}e$ |

$h$ | Carbon emission reduction investment cost coefficient |

$\theta $ | Final freshness level $0\text{}\text{}\theta $ |

$\gamma $ | Consumers’ low-carbon preference coefficient |

$\phi $ | Consumers’ purchasing preferences for the retailer’s offline channel |

$\varphi $ | Consumers’ purchasing preferences for the retailer’s online channel |

$a$ | Basic market demand |

${C}_{f}$ | Cost of carbon reduction |

$D$ | Market demand |

${\prod}_{r}$ | Retailer’s profit |

${\prod}_{p}$ | Producer’s profit |

${\prod}_{sc}$ | Profit of the supply chain |

**Table 4.**The optimal decision, market demand, and profit under the three dual-channel supply chains.

Retailer Dual Channel | Producer Dual Channel | Mixed Dual Channel | |
---|---|---|---|

$p$ | $\frac{3h\left(a+2\theta \right)}{8h-4{\gamma}^{2}}$ | $\frac{4h\theta +a\left[h\left(1+2\phi \right)+2{\gamma}^{2}\left(1-2\phi \right)\right]}{2\left(3h-2{\gamma}^{2}\right)}$ | $\frac{7h\theta +a\left[h+2{\gamma}^{2}\left(2-3\sigma \right)+2h\sigma \right]}{10h-9{\gamma}^{2}}$ |

$e$ | $\frac{\gamma \left(a+2\theta \right)}{4h-2{\gamma}^{2}}$ | $\frac{2\gamma \left[a\left(1-\phi \right)+\theta \right]}{3h-2{\gamma}^{2}}$ | $\frac{\gamma \left[9\theta +a\left(7-6\sigma \right)\right]}{10h-9{\gamma}^{2}}$ |

$D$ | $\frac{h\left(a+2\theta \right)}{4h-2{\gamma}^{2}}$ | $\frac{2h\left[a\left(1-\phi \right)+\theta \right)}{3h-2{\gamma}^{2}}$ | $\frac{h\left[9\theta +a\left(7-6\sigma \right)\right]}{10h-9{\gamma}^{2}}$ |

${\prod}_{r}$ | $\frac{h{\left(a+2\theta \right)}^{2}}{16h-8{\gamma}^{2}}$ | $\frac{4h{\theta}^{2}-8ah\theta \left(\phi -1\right)+{a}^{2}\left[2{\gamma}^{2}{\left(1-2\phi \right)}^{2}+h\left(1+4\phi -8{\phi}^{2}\right)\right]}{4\left(3h-2{\gamma}^{2}\right)}$ | $\frac{{\left[6h\theta +3a{\gamma}^{2}\left(2-3\sigma \right)+2ah\left(3\sigma -1\right)\right]}^{2}}{2{\left(10h-9{\gamma}^{2}\right)}^{2}}$ |

${\prod}_{p}$ | $\frac{{h}^{2}{\left(a+2\theta \right)}^{2}}{8{\left(-2h+{\gamma}^{2}\right)}^{2}}$ | $\frac{{\left[2h\theta +2a{\gamma}^{2}\left(1-2\phi \right)+ah\left(4\phi -1\right)\right]}^{2}}{4{\left(3h-2{\gamma}^{2}\right)}^{2}}$ | $\frac{9h{\theta}^{2}+2ah\theta \left(7-6\sigma \right)+{a}^{2}\left[{\gamma}^{2}{\left(2-3\sigma \right)}^{2}+h\left(1+4\sigma -6{\sigma}^{2}\right)\right]}{20h-18{\gamma}^{2}}$ |

${\prod}_{sc}$ | $\frac{h\left(3h-{\gamma}^{2}\right){\left(a+2\theta \right)}^{2}}{8{\left(-2h+{\gamma}^{2}\right)}^{2}}$ | $\frac{h\left[a\left(1-\phi \right)+\theta \right]\left[4h\theta -2{\gamma}^{2}\theta +a\left(h+2h\phi -2{\gamma}^{2}\phi \right)\right]}{{\left(3h-2{\gamma}^{2}\right)}^{2}}$ | $\frac{h\left[9\theta +a\left(7-6\sigma \right)\right]\left[\left(14h-9{\gamma}^{2}\right)\theta +a{\gamma}^{2}\left(1-6\sigma \right)+2ah\left(1+2\sigma \right)\right]}{2{\left(10h-9{\gamma}^{2}\right)}^{2}}$ |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Xie, J.; Liu, J.; Huo, X.; Meng, Q.; Chu, M.
Fresh Food Dual-Channel Supply Chain Considering Consumers’ Low-Carbon and Freshness Preferences. *Sustainability* **2021**, *13*, 6445.
https://doi.org/10.3390/su13116445

**AMA Style**

Xie J, Liu J, Huo X, Meng Q, Chu M.
Fresh Food Dual-Channel Supply Chain Considering Consumers’ Low-Carbon and Freshness Preferences. *Sustainability*. 2021; 13(11):6445.
https://doi.org/10.3390/su13116445

**Chicago/Turabian Style**

Xie, Jingci, Jianjian Liu, Xin Huo, Qingchun Meng, and Mengyu Chu.
2021. "Fresh Food Dual-Channel Supply Chain Considering Consumers’ Low-Carbon and Freshness Preferences" *Sustainability* 13, no. 11: 6445.
https://doi.org/10.3390/su13116445