# Selling Remanufactured Products under One Roof or Two? A Sustainability Analysis on Channel Structures for New and Remanufactured Products

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Model Description and Assumption

_{n}/w

_{r}) and then the retailer(s) responds with the optimal units of q

_{n}/q

_{r}. Note that all decisions being made in a single-period enables the authors to focus on steady-state profits, facilitating analytical tractability in this model and contributing to the solution of the problems [28,29,30,31].

## 4. Model Formulation and Solution

#### 4.1. One-Roof Policy (Model O)

**Lemma**

**1.**

#### 4.2. Two-Roof Policy (Model T)

**Lemma**

**2.**

**Lemma**

**3.**

## 5. Model Analysis

#### 5.1. Analysis on Optimal Outcomes

**Proposition**

**1.**

**Proposition**

**2.**

**Proposition**

**3.**

#### 5.2. Analysis on Economic Sustainability

**Proposition**

**4.**

**Proposition**

**5.**

**Proposition**

**6.**

#### 5.3. Analysis on Environmental Sustainability

**Proposition**

**7.**

## 6. Numerical Example

#### 6.1. Parameters Design and Results

#### 6.1.1. LCD Parameters Design

#### 6.1.2. Mobile Phones Parameters Design

_{r}< 0.4. We conduct the numerical simulation using Matlab 2014 to obtain all figures, which describes how c

_{r}impacts the difference in equilibrium decisions, such as optimal quantities and wholesale prices (see Figure 6), and highlights the results of economic (see Figure 7) and environmental outcomes (see Figure 8).

#### 6.2. Results Analysis of Two Cases

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A. Technical Analysis for Both Models

#### Appendix A.1. Analysis of Model O

#### Appendix A.2. Analysis of Model T

#### Appendix A.3. Analysis of Lemma 3

## Appendix B. All Proofs for Propositions

**Proof of Proposition**

**1.**

**Proof of Proposition**

**2.**

**Proof of Proposition**

**3.**

**Proof of Proposition**

**4.**

**Proof of Proposition**

**5.**

**Proof of Proposition**

**6.**

**Proof of Proposition**

**7.**

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**Figure 3.**Effects of ${c}_{r}$ on related parameters. (

**a**) Effects of ${c}_{r}$ on ${w}_{r}^{i*}$; (

**b**) effects of ${c}_{r}$ on ${q}_{r}^{i*}$; and (

**c**) effects of ${c}_{r}$ on ${q}_{n}^{i*}$.

**Figure 4.**Effects of ${c}_{r}$ on the economic outcomes. (

**a**) Effects of ${c}_{r}$ on ${\mathsf{\Pi}}_{m}^{i*}$; (

**b**) effects of ${c}_{r}$ on ${\mathsf{\Pi}}_{r}^{i*}$; and (

**c**) effects of ${c}_{r}$ on ${\mathsf{\Pi}}_{t}^{i*}$.

**Figure 6.**Effects of ${c}_{r}$ on related parameters. (

**a**) Effects of ${c}_{r}$ on ${w}_{r}^{i*}$; (

**b**) effects of ${c}_{r}$ on ${q}_{r}^{i*}$; and (

**c**) effects of ${c}_{r}$ on ${q}_{n}^{i*}$.

**Figure 7.**Effects of ${c}_{r}$ on the economic outcomes. (

**a**) Effects of ${c}_{r}$ on ${\mathsf{\Pi}}_{m}^{i*}$; (

**b**) effects of ${c}_{r}$ on ${\mathsf{\Pi}}_{r}^{i*}$; and (

**c**) effects of ${c}_{r}$ on ${\mathsf{\Pi}}_{t}^{i*}$.

Related Literature | Ref Source’ No. | Issue Studied | Insights |
---|---|---|---|

Relationship between sustainability and the supply chain | 1 Srivastava [15] | Green Supply Chain | Integrated environmental thinking into supply chain management. |

2 Chaabane [16] | Sustainable Supply Chain | Developed mixed-integer linear programming based framework for a sustainable supply chain. | |

3 Wilhelm [17] | Sustainable Supply Chain | Employed agency and institutional theory arguments to explore the conditions | |

4 Rajeev [18] | Sustainability | Proposed a conceptual framework to classify various factors along the triple bottom line pillars of sustainability issues in the context of supply chains. | |

5 Reefke [19] | Sustainability; Supply Chain | Confirmed, questioned, and extended the knowledge on sustainable supply chain management. | |

Sustainability issues in operations management | 6 Ovchinnikov [20] | Remanufacturing | Revealed that remanufacturing is usually a highly beneficial activity. |

7 Zhang et al. [19] | Channel Distribution | Showed that retail services have a great impact on the manufacturer’s and the retailer’s pricing strategies. | |

8 Golinska [19] | Remanufacturing Process | Provided a new tool for remanufacturing operations and for identifying and prioritizing operations in companies needing improvement. | |

9 Yan [19] | Remanufacturing | Highlighted the question of whether OEMs should also outsource their reverse channels to third-party remanufacturers when outsourcing remanufacturing. | |

The market competition related to roof policy | 10 Desai [24] | Segmentation | Demonstrated that, as the taste preferences of the low-valuation segment become weaker, it is more attractive for high-valuation consumers. |

11 Matsubayashi [19] | Product Differentiation | Studied an instance of price and quality competition between firms. | |

12 Ailawadi [19] | Share of wallet | Developed a model of the relationship between a household’s private-label share and its store loyalty. | |

13 Zhang [13] | Roof Policy | Explored the implications of roof policy for its quality signaling strategies. | |

14 Joshi [27] | Segmentation | Showed that a firm might offer a broader product line to attract a higher demand or charge a higher price. |

Notation | Definition |
---|---|

$\gamma $ | The consumer value discount for remanufactured products |

${c}_{n}/{c}_{r}$ | The unit production cost of the new/remanufactured component |

$k$ | The scaling parameter |

${p}_{n}^{i}/{p}_{r}^{i}$ | The new/remanufactured product price in Model i, $i\in (O,T)$ |

${q}_{n}^{i}/{q}_{r}^{i}$ | The quantity of new/remanufactured products in Model i, $i\in (O,T)$ |

${w}_{n}^{i}/{w}_{r}^{i}$ | The wholesale price of new/remanufactured component in Model i, $i\in (O,T)$ |

${\mathsf{\Pi}}_{x}^{i}$ | The player x’s profit in Model i, $x\in (m,r1,r2,t)$, $i\in (O,T)$ |

${I}_{n}$ | The environmental impact of a new product |

${I}_{r}$ | The environmental impact of a remanufactured product |

${I}_{u}$ | The environmental impact of usage |

${I}_{d}$ | The environmental impact of disposal |

${E}^{i}$ | The environmental impacts in Model i, $i\in (O,T)$ |

Model O | Model T | Propositions | |
---|---|---|---|

${w}_{r}^{O*}$ | < | ${w}_{r}^{T*}$ | 1. The manufacturer upwardly distorts the wholesale price of remanufactured products |

${w}_{n}^{O*}$ | = | ${w}_{n}^{T*}$ | The wholesale price of new products is immune to distortion |

${q}_{r}^{{O}^{*}}$ | < | ${q}_{r}^{{T}^{*}}$ | 2. There is a larger quantity of remanufactured products in Model T |

${q}_{n}^{{O}^{*}}$ | < | ${q}_{n}^{{T}^{*}}$ | 3. There is a larger quantity of new products in Model T |

${\mathsf{\Pi}}_{m}^{O*}$ | < | ${\mathsf{\Pi}}_{m}^{T*}$ | 4. The manufacturer benefits more in Model T |

${\mathsf{\Pi}}_{r}^{O*}$ | > | ${\mathsf{\Pi}}_{r1}^{T*}$/${\mathsf{\Pi}}_{r2}^{T*}$ | 5. The retailer benefits more in Model O |

${\mathsf{\Pi}}_{t}^{O*}$ | < | ${\mathsf{\Pi}}_{t}^{T*}$ | 6. The industry benefits more in Model T |

${E}^{O}$ | < | ${E}^{T}$ | 7. Model O is greener than Model T |

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## Share and Cite

**MDPI and ACS Style**

Liu, Y.; Cheng, Y.; Chen, H.; Guo, S.; Lu, Y.
Selling Remanufactured Products under One Roof or Two? A Sustainability Analysis on Channel Structures for New and Remanufactured Products. *Sustainability* **2018**, *10*, 2427.
https://doi.org/10.3390/su10072427

**AMA Style**

Liu Y, Cheng Y, Chen H, Guo S, Lu Y.
Selling Remanufactured Products under One Roof or Two? A Sustainability Analysis on Channel Structures for New and Remanufactured Products. *Sustainability*. 2018; 10(7):2427.
https://doi.org/10.3390/su10072427

**Chicago/Turabian Style**

Liu, Yan, Yongsheng Cheng, Hong Chen, Sidai Guo, and Yujia Lu.
2018. "Selling Remanufactured Products under One Roof or Two? A Sustainability Analysis on Channel Structures for New and Remanufactured Products" *Sustainability* 10, no. 7: 2427.
https://doi.org/10.3390/su10072427