Decision-Making in a Closed-Loop Supply Chain under Fairness Concerns and Optimal Subsidies
Abstract
:1. Introduction
- (1)
- How does the fairness issue influence pricing decisions and optimal subsidy in CLSC?
- (2)
- What attitude will enterprises choose to treat fairness concerns in the government-led CLSC?
- (3)
- In light of government subsidy and the subordinate retailer’s fairness concerns, how can supply chain companies achieve coordination?
2. Literature Review
2.1. CLSC Management under Government Subsidy
2.2. Fairness Concerns and Coordination in the Supply Chain
2.3. Research Gap
- (1)
- Solving the firms’ pricing decisions and different attitudes towards fairness issues in the government-led CLSC;
- (2)
- A two-part tariff contract is designed to coordinate the three-echelon CLSC with fairness concerns;
- (3)
- Analyzing the impacts of waste pollution and fairness issues on economic benefits and social welfare.
3. Model Description and Assumptions
3.1. Problem Description
3.2. Notations
3.3. Assumptions
- Maximizing social welfare is the purpose of the remanufacturing subsidy, and we denote social welfare as the sum of the revenues of enterprises, consumer surplus , subsidy expenditure , and the environmental impact of products that have not been recycled [38]. The social welfare function is , where is the environmental damage per unit of used unrecycled product. represents the distinction between the price that consumers actually pay in the market and the highest price they are willing to pay for a specific number of products. The function is [20].
4. Model Development and Solution
4.1. Model N
4.2. Model RY
4.3. Model RN
4.4. Model C
4.5. Analysis of Equilibrium Results
- (1) , ; when , and , otherwise, and ; when , , otherwise, ; when , , otherwise, .
- (2) ; when , , otherwise, ; when , , otherwise, ; when , , otherwise, .
- (3) ; when , , otherwise, ; when , , otherwise, ; when , , otherwise, .
- Note: , ,
- , , , , , , .
5. Coordination Mechanism
- Note: , ,
- , .
- (1) The lower bounds of the fixed fees , are related positively with ; is related negatively with , increase with , when , otherwise, it decreases with .
- (2) The upper bounds of the fixed fees , are independent of , and decrease with .
- Note: .
6. Numerical Analysis
6.1. Comparing Models
6.2. The Impacts of Parameters on Firms’ Attitudes toward Fairness Concerns and Coordination
6.3. Analysis of the Coordination Process
6.4. The Impact of Corporate Coordination on Social Welfare
7. Discussion and Managerial Insights
8. Conclusions
- (1)
- The waste product pollution degree impacts government subsidies, while the amount of recycling is not affected by the retailer’s fairness concerns. The government engages in more subsidized expenditure to deal with the fairness concerns ignored by the manufacturer (cf. Conclusion 1).
- (2)
- In the decentralized models, when the unit waste pollution is low while the level of fairness concerns is significant, the manufacturer responds to the fairness concerns to mitigate the profit loss. With the rise in , the manufacturer will choose to ignore concerns, and the increase in the level of fairness concerns would provide more overall benefits to enterprises in this situation (cf. Figure 2 and Figure 3, and Conclusion 2).
- (3)
- As a subordinate enterprise, the retailer is always willing to maintain fairness concerns in response to the manufacturer’s two kinds of attitudes in different scenarios (cf. Figure 2 and Conclusion 2).
- (4)
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
- Solution procedure of model N:
- Solution procedure of model RY:
- Solution procedure of model RN:
- Solution procedure of model C
- (1)
- (2)
- (3)
- , we know that . This means that, when
- when , ;
- when , . □
- (1)
- , ;
- ;
- , when , ,
- otherwise .
- (2)
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Author(s) | Stages of Games | CLSC | Subsidy Set | SW | Treatment of FC | Coordination Contract |
---|---|---|---|---|---|---|
Mitra and Webster [27] | 2 | ✓ | EX | - | - | - |
Long et al. [20] | 3 | ✓ | EX | ✓ | - | - |
Feng et al. [11] | 2 | ✓ | EX | ✓ | - | - |
Liu and Wang [21] | 3 | ✓ | EN | ✓ | - | - |
Shan et al. [22] | 2 | ✓ | EX | ✓ | - | - |
Ma et al. [28] | 2 | ✓ | EX | - | - | - |
He et al. [19] | 2 | ✓ | EX | ✓ | - | - |
Jena et al. [23] | 2 | ✓ | EX | - | - | - |
Wan and Hong [24] | 2 | ✓ | EX | - | - | - |
Zhao et al. [13] | 2 | ✓ | EX | - | - | - |
Zhang et al. [29] | 2 | ✓ | EX | ✓ | - | - |
Ma [1] | 2 | ✓ | EX | - | - | - |
Huang and Liang [30] | 2 | ✓ | EX | - | - | - |
Cui et al. [31] | 2 | - | - | - | R | wholesale price |
Li and Li [32] | 2 | - | - | - | R | wholesale price |
Shu et al. [26] | 2 | ✓ | - | - | R/D | two-part tariff |
Li et al. [25] | 2 | ✓ | - | - | R/D | - |
Liu et al. [17] | 2 | - | - | - | R | - |
Jian et al. [33] | 2 | - | - | - | R | profit-sharing |
Wang et al. [34] | 2 | - | - | - | R | - |
Wang et al. [16] | 2 | - | EX | - | R | sharing of cost and subsidy |
Shi et al. [35] | 2 | - | - | - | R | sharing of cost and profit |
Han et al. [36] | 2 | - | - | - | R | sharing of cost and profit |
This study | 3 | ✓ | EN | ✓ | R/D | two-part tariff |
Notations | Definitions |
---|---|
Indices: | |
, denotes the manufacturer, the retailer, and the supply chain | |
, denotes the models N, RY, RN, and C, and the coordination scenario T | |
Parameters: | |
Initial market scale | |
The price elasticity coefficient of a product | |
Unit production cost of using new materials | |
Unit production cost of using a waste product | |
Unit saving through remanufacturing | |
Consumer’s environmental awareness | |
The consumer sensitivity of the recycling price | |
Environmental burden of an unrecycled product | |
The fairness concern coefficient | |
Decision variables: | |
The retail price | |
The wholesale price | |
Unit recycling price paid to consumers | |
Unit transfer price paid to the retailer | |
Unit remanufacturing subsidy | |
Outcome variables: | |
The market demand | |
The production of products | |
The recycling volume | |
The profit function | |
The fairness-concerned retailer’s utility | |
The social welfare | |
, | The negotiation bottom line and upper bound of enterprises |
Parameters | Value |
---|---|
200 | |
8 | |
19 | |
17 | |
2 | |
0.2 | |
1.4 |
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Deng, Z.; Shaharudin, M.R.; Tseng, M.-L. Decision-Making in a Closed-Loop Supply Chain under Fairness Concerns and Optimal Subsidies. Sustainability 2023, 15, 7380. https://doi.org/10.3390/su15097380
Deng Z, Shaharudin MR, Tseng M-L. Decision-Making in a Closed-Loop Supply Chain under Fairness Concerns and Optimal Subsidies. Sustainability. 2023; 15(9):7380. https://doi.org/10.3390/su15097380
Chicago/Turabian StyleDeng, Zichun, Mohd Rizaimy Shaharudin, and Ming-Lang Tseng. 2023. "Decision-Making in a Closed-Loop Supply Chain under Fairness Concerns and Optimal Subsidies" Sustainability 15, no. 9: 7380. https://doi.org/10.3390/su15097380