Fourth-Party Logistics Environmental Compliance Management: Investment and Logistics Audit
Abstract
:1. Introduction
- Strategies for the 3PL to make more efforts. The 4PL can use different strategies to motivate the 3PL to make efforts. Firstly, when the investment cost is lower, the 4PL can incentivize the 3PL to make efforts by investment. Secondly, when the investment cost is higher, the 4PL can incentivize the 3PL to make efforts by offering a high enough wholesale price that it incurs a potential loss if it loses the contract with the 4PL. Thirdly, the 4PL can use low investment and medium wholesale price to deter the 3PL from not making efforts, which should only be used in the commitment case, as the 3PL would like to adopt the medium wholesale price and make efforts only if it knows the 4PL’s investment.
- Factors affecting the 4PL’s strategies. Increasing the goodwill cost can improve the 3PL’s efforts. However, reducing the investment cost does not necessarily increase the 3PL’s efforts, as the 4PL may replace the price premium with an investment strategy. When the investment cost is higher, the 4PL is faced with high goodwill cost, and will offer a high wholesale price to increase the 3PL’s efforts. When the investment is lower, the 4PL may rely solely on the investment to improve the 3PL’s efforts, which could lead to a decrease in the 3PL’s efforts, since the investment strategy only partially increases the 3PL’s efforts. In addition, increasing the audit level can increase the 3PL’s effort level when its rectification costs are sufficiently high.
- The commitment to investment effort. Commitment to investment effort certainly improves the final logistics compliance level. The 4PL’s commitment to investment effort can help the 3PL make efforts by using a high-investment and medium wholesale price strategy. In addition, a commitment to investment effort enables the 4PL to use a high-investment strategy, which can complement the 3PL’s efforts.
2. Literature Review
2.1. Sustainability Supply Chain Management
2.2. Audits in the Supply Chain
2.3. Logistics Service Supply Chain Management
3. The Model
4. Base Model
- The 4PL provided a wholesale price contract to the 3PL;
- The 3PL accepted the contract if its expected profits were higher than the reservation profit;
- The 3PL chose the efforts level, , and delivered, whereas the 4PL chose its investment level, ev, and invested; we assumed that their decisions were simultaneous.
- The 4PL conducted the process audit.
- After the delivery was completed, the 4PL paid to the 3PL, and may have suffered from goodwill cost, .
4.1. Equilibrium in a Subgame
4.2. Subgame-Perfect Equilibrium
- (i)
- is decreasing in;
- (ii)
- If , is increasing in ; if , is decreasing in ;
- (iii)
- If , is increasing in ; If , is decreasing in .
5. Commitment to the 4PL Effort
- The 4PL provided a wholesale price, , and committed the investment level, , to the 3PL;
- The 3PL accepted the contract if its expected profits were higher than the reservation profit;
- The 3PL chose the effort level, , and delivered, whereas the 4PL conducted its investment;
- The 4PL conducted a process audit;
- After the delivery was over, the 4PL paid to the 3PL, and could suffer from the goodwill cost, .
5.1. Subgame-Perfect Equilibrium
- (i)
- When , the subgame-perfect equilibrium in the commitment scenario is:
- ii
- When , the subgame-perfect equilibrium in the commitment scenario is:
- (i)
- When , :
- (a)
- If the rectification cost , then and are increasing in the audit level, while ,, are decreasing in the audit level;
- (b)
- If the rectification cost , then and are decreasing in the audit level, while ,, are increasing in the audit level.
- (ii)
- When :
- (a)
- If the rectification cost , then , and are increasing in the audit level, while and are decreasing in the audit level;
- (b)
- If the rectification cost , then , and are decreasing in the audit level, while and are increasing in the audit level.
5.2. Effects of Commitment
- , low-investment high-investment.
- , low-investment high-investment-and-premium.
- , low-investment-and premium high-investment-and-premium.
- , high-investment high-investment-and-premium.
- (i)
- The 3PL’s profit remains unchanged in A, decreases in C, and increases in B and D.
- (ii)
- The 4PL’s profit increases in all regions.
- (iii)
- The efforts made by the 3PL increase in A, B, and D, and remain the same in C.
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
- (i)
- From , we obtained , and from , we obtained , since , we obtained ;
- (ii)
- .
- (i)
- If , the 4PL chooses when
- (ii)
- If , the 4PL chooses when
Appendix B
Appendix C
- (i)
- , , for ;
- (ii)
- , , for .
- (iii)
- , , for .
- (a)
- If , program [21] can be simplified as follows:
- (i)
- is the equilibrium outcome if, and only if, and
- (ii)
- is the equilibrium outcome if, and only if, , and
- (iii)
- is the equilibrium outcome if, and only if, , and
- (iv)
- is the equilibrium outcome if, and only if, and .
- (b)
- If , we obtained:
- (i)
- is the equilibrium outcome if, and only if, and
- (ii)
- is the equilibrium outcome if, and only if, , and ;
- (iii)
- is the equilibrium outcome if, and only if, , and
- (iv)
- is the equilibrium outcome if, and only if, , and . □
Appendix D
- (i)
- When , from , we obtained ; From , if , i.e., , we obtained ; From , we obtained , then is in the interval . We let .
- (ii)
- When , from , we obtained ; From , we had ; From , if , we obtained ; then is in the interval . We let .
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4PL’s Investment Level | |||
---|---|---|---|
evl | evh | ||
3PL’s effort level | et = 0 | γevl | γevh |
et = 1 | 1 | 1 |
4PL’s Investment Level | |||
---|---|---|---|
evl | evh | ||
3PL’s effort level | et = 0 | B − α − Pl(1 − ea)(1 − p)g (1 − δlPl(1 − ea)(1 − p))(α − Pleaφ) | B − α – Ph(1 − ea)(1 − p)g − kv (1 – δhPh(1 − ea)(1 − p))(α – Pheaφ) |
et = 1 | B − α α − kt | B − α − kv α − kt |
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Wang, H.; Huang, M.; Wang, H. Fourth-Party Logistics Environmental Compliance Management: Investment and Logistics Audit. Sustainability 2022, 14, 10106. https://doi.org/10.3390/su141610106
Wang H, Huang M, Wang H. Fourth-Party Logistics Environmental Compliance Management: Investment and Logistics Audit. Sustainability. 2022; 14(16):10106. https://doi.org/10.3390/su141610106
Chicago/Turabian StyleWang, Hongyan, Min Huang, and Hongfeng Wang. 2022. "Fourth-Party Logistics Environmental Compliance Management: Investment and Logistics Audit" Sustainability 14, no. 16: 10106. https://doi.org/10.3390/su141610106