# A Two-Stage Closed-Loop Supply Chain Pricing Decision: Cross-Channel Recycling and Channel Preference

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## Abstract

**:**

## 1. Introduction

- (1).
- What is the impact of cross-channel recycling rate on pricing and profitability in a two-stage CLSC system?
- (2).
- What is the impact of channel preference on pricing and profitability in a two-stage CLSC system?

## 2. Literature Review

## 3. Model Description and Basic Assumptions

## 4. Model Analysis

#### 4.1. Centralized Decision Model

#### 4.1.1. Differential Pricing Strategies

**Proposition**

**1.**

**Proof.**

**Corollary**

**1.**

#### 4.1.2. Uniform Pricing Strategy

**Proposition**

**2.**

**Proof.**

**Corollary**

**2.**

#### 4.2. Decentralised Decision Model

#### 4.2.1. Manufacturer-Led Stackelberg Game (MLSG)

**Proposition**

**3.**

**Proof.**

**Corollary**

**3.**

#### 4.2.2. Retailer-Led Stackelberg Game (RLSG)

**Proposition**

**4.**

**Proof.**

**Corollary**

**4.**

#### 4.2.3. Nash Equilibrium Game Pricing (NG)

**Proposition**

**5.**

**Proof.**

**Corollary**

**5.**

## 5. Numerical Analysis

#### 5.1. Comparison of Total Supply Chain Profits under Different Decision Models

#### 5.2. Comparison of Pricing under Different Decision-Making Models

#### 5.3. Comparison of Profits under Different Decision-Making Models

## 6. Conclusions and Future Work

- (1).
- Under centralised decision-making, the total profit of the CLSC under differential pricing is higher than that under uniform pricing. Channel preference and cross-channel recovery rates have a greater impact on the pricing decisions of manufacturers and retailers. Under the differential pricing strategy, regardless of the channel preference, the manufacturer’s pricing decreases if the cross-channel recovery rate increases. However, when the retailer’s pricing is less affected by the cross-channel recovery rate then pricing remains at a stable level. The product pricing and the influence of consumer channel preference are weaker in uniform pricing. Moreover, product pricing decreases if the cross-channel recovery rate is low. As a result, price elasticity and cross-price sensitivity do not exist under a uniform pricing strategy.
- (2).
- Under decentralised decision-making, the trend of the total profit of the supply chain varies under different decision-making models. Here, cross-channel recovery rate and channel preference have a significant impact on the total profit. When the channel consumption preference is constant, the retailer’s pricing increases if the cross-channel recovery rate increase. The manufacturer’s pricing decreases if the cross-channel recovery rate increase. Firstly, retailer and manufacturer pricing are highest in Nash equilibrium. Secondly, retailer and manufacturer pricing are mid-level under retailer dominance. However, retailer and manufacturer pricing are lowest under manufacturer dominance. In addition, under low channel preference, manufacturers and retailers prefer to have the manufacturer dominate the decision. Similarly, under high channel preference, both manufacturers and retailers prefer to have others dominate model to achieve greater profitability for themselves.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

CLSC | Closed-Loop Supply Chain |

MLSG | Manufacturer-Led Stackelberg Game |

RLSG | Retailer-Led Stackelberg Game |

NG | Nash Equilibrium Game Pricing |

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**Figure 4.**Comparison of pricing in a centralised decision-making model: (

**a**) low consumption channel preference θ and (

**b**) high consumption channel preference θ.

**Figure 5.**Comparison of pricing under decentralised decision-making models: (

**a**) low consumption channel preference θ and (

**b**) high consumption channel preference θ.

**Figure 6.**A decentralised decision model for the manufacturer pricing decision options: (

**a**) Low consumption channel preference $\theta $ and (

**b**) high consumption channel preference $\theta $.

**Figure 7.**A decentralised decision model for retailer pricing decision options: (

**a**) low consumption channel preference θ and (

**b**) high consumption channel preference θ.

References | Variables | Theory | Intervention Policy |
---|---|---|---|

Liu et al. [67] | Manufacturing cost; demand | Stackelberg | Price |

Alamdar et al. [68] | Sales dependent demand | Nash | Price |

Hafezalkotob [69] | Policies; investment; financial benefits | Stackelberg | Social welfare |

Fallah et al. [70] | Self-price and cross-price elasticity coefficients; demand; profits | Stackelberg | Price |

Wang [71] | Consumer demand; manufacturing cost | Stackelberg | Warranty service |

Moradinasab et al. [72] | Profits; environmental pollution | Stackelberg; Nash | Price |

Hafezalkotob [73] | manufacturer cost; demand | Stackelberg | Price |

Yang et al. [74] | Market scale; manufacturer profit; retailer profit; price elasticity; sensitivity coefficient of the product | Stackelberg | Price |

Sheu et al. [75] | Wholesale-price; taxation | Nash | Price |

Reza-Gharehbagh et al. [76] | lending-investment; debt financing; equity financing | Stackelberg | Price |

Zhao et al. [77] | Customer demands; manufacturing cost; service cost coefficients | Stackelberg; Nash | Price |

Mahmoudi et al. [78] | Profit; product targets | Stackelberg | Price |

Symbols | Description |
---|---|

${k}_{r}$ | The recovery rate of intact products in the retailer recovery channel. |

${k}_{m}$ | The recycling rate of used products in manufacturers recycling channels. |

$\mathsf{\epsilon}$ | Manufacturer cross-channel recovery rates for intact product recovery. |

${D}_{r}\text{}\mathrm{and}\text{}{D}_{m}$ | Demand for products from retailer and manufacturer channels, respectively. |

$\alpha ,\text{}{\alpha}_{r},\text{}\mathrm{and}\text{}{\alpha}_{m}$ | Total market demand, potential market demand from retailers, and potential market demand from manufacturers, respectively. |

$\theta $ | Consumer preference for visiting a retailer’s physical shop. |

$\beta \text{}\mathrm{and}\text{}\gamma $ | Channel ownership prices and cross-price sensitivity, respectively. |

$\omega $$\text{}\mathrm{and}\text{}\overline{\omega}$ | Manufacturer’s wholesale price and retailer’s transfer price for the recycled product, respectively. |

${p}_{r}$$\text{}\mathrm{and}\text{}{p}_{m}$ | Retailer’s retail prices and manufacturer’s direct sales prices, respectively. |

${c}_{m},\text{}t,\text{}\mathrm{and}\text{}s$ | Manufacturing costs, the value of intact products sold on the secondary market, and profit from the recycling of discarded products, respectively. |

${h}_{j}\left(j=r,\text{}m,\text{}rm\right)$ | The cost of recycling disposal is ${h}_{j}.$ Here, $j=r$ denoting the retailer-recycling channel, $\text{}j=m$ denoting the manufacturer-recycling channel, and $j=rm$ denoting the manufacturer cross-channel recycling channel for intact products. |

$\pi ,\text{}{\pi}_{r},\text{}\mathrm{and}\text{}{\pi}_{m}$ | Total CLSC profit, retailer brick-and-mortar profit, and manufacturer online shop profit, respectively. |

${P}_{r}^{c*}$ | The convex function of consumer channel preference based on retailer’s pricing |

${P}_{m}^{c*}$ | The concave function of consumer channel preferences based on manufacturer’s pricing |

${\omega}^{{M}^{*}}$ | Manufacturer’s wholesale price under Manufacturer-led Stackelberg game |

${P}_{m}^{{M}^{*}}$ | Manufacturer’s direct selling price under Manufacturer-led Stackelberg game |

${P}_{r}^{{M}^{*}}$ | Manufacturer’s retail price under Manufacturer-led Stackelberg game |

${\omega}^{{R}^{*}}$ | Manufacturer’s wholesale price under Retailer-led Stackelberg game |

${P}_{m}^{{R}^{*}}$ | Manufacturer’s the direct selling price under Retailer-led Stackelberg game |

${P}_{r}^{{R}^{*}}$ | Manufacturer’s the retail price under Retailer-led Stackelberg game |

${\omega}^{{N}^{*}}$ | Manufacturer’s wholesale price under Nash equilibrium game |

${P}_{m}^{{N}^{*}}$ | Manufacturer’s direct selling price under Nash equilibrium game |

${P}_{r}^{{N}^{*}}$ | Manufacturer’s retail price under Nash equilibrium game |

${P}_{m}^{C}$ | Manufacturer pricing under differential pricing |

${P}_{r}^{C}$ | Retailer pricing under differential pricing |

${P}_{r}^{MLSG}$ | Retailer pricing under manufacturer-led |

${P}_{r}^{RLSG}$ | Retailer pricing under retailer-led |

${P}_{r}^{NG}$ | Retailer pricing under Nash equilibrium |

${P}_{m}^{MLSG}$ | Manufacturer pricing under manufacturer-led |

${P}_{m}^{RLSG}$ | Manufacturer pricing under retailer-led |

${P}_{m}^{NG}$ | Manufacturer pricing under Nash equilibrium |

${\pi}_{m}^{MLSG}$ | Manufacturer’s profit size under the manufacturer-led model |

${\pi}_{m}^{RLSG}$ | Manufacturer’s profit size under the retailer-led model |

${\pi}_{m}^{NG}$ | Manufacturer’s profit size under Nash equilibrium model |

Parameter | $\mathit{\alpha}$ | ${\mathit{k}}_{\mathit{r}}$ | ${\mathit{k}}_{\mathit{m}}$ | $\mathit{\theta}$ | $\mathit{\beta}$ | $\mathit{\gamma}$ | $\overline{\mathit{\omega}}$ | ${\mathit{c}}_{\mathit{m}}$ | $\mathit{t}$ | s | ${\mathit{h}}_{\mathit{r}}$ | ${\mathit{h}}_{\mathit{m}}$ | ${\mathit{h}}_{\mathit{r}\mathit{m}}$ |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Values | 1000 | 0.2 | 0.1 | (0.4, 0.6) | 10 | 5 | 8 | 20 | 15 | 10 | 2 | 4 | 2 |

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## Share and Cite

**MDPI and ACS Style**

Pan, W.; Lin, M.
A Two-Stage Closed-Loop Supply Chain Pricing Decision: Cross-Channel Recycling and Channel Preference. *Axioms* **2021**, *10*, 120.
https://doi.org/10.3390/axioms10020120

**AMA Style**

Pan W, Lin M.
A Two-Stage Closed-Loop Supply Chain Pricing Decision: Cross-Channel Recycling and Channel Preference. *Axioms*. 2021; 10(2):120.
https://doi.org/10.3390/axioms10020120

**Chicago/Turabian Style**

Pan, Wenjun, and Miao Lin.
2021. "A Two-Stage Closed-Loop Supply Chain Pricing Decision: Cross-Channel Recycling and Channel Preference" *Axioms* 10, no. 2: 120.
https://doi.org/10.3390/axioms10020120