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doi: 10.3934/jimo.2021141
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Design of an environmental contract under trade credits and carbon emission reduction

1. 

School of Management, Nanjing University of Posts and Telecommunications, Nanjing, 210003 Jiangsu, China

2. 

School of Economics & Managements, Southeast University, Nanjing, 210089 Jiangsu, China

* Corresponding author: Yaxian Wang

Received  March 2021 Revised  May 2021 Early access August 2021

Fund Project: The paper is supported by the 1311 Programs Foundation of Nanjing University of Posts and Telecommunications, the Scientific Research Foundation of Nanjing University of Posts and Telecommunications (NY220212), the Key Research Base of Philosophy and Social Sciences in Jiangsu–Information Industry Integration Innovation and Emergency Management Research Center

Most of the previous literatures proposed a single coordination contract to increase the total profit of the supply chain, while this paper focuses on how to design environmental contracts to increase economic and environmental performance in the context of sustainable development. This paper designs the environmental contract based on cap-and-trade mechanism and trade credits which has rarely been studied before, especially the impact of trade credit on environmental performance. We consider a green supply chain, assuming that the demand rate is linear with retail prices, joint carbon emission reduction efforts and trade credit. Two models, a decentralized one and a centralized one, are compared; four contracts are proposed. Via numerous examples and sensitivity analysis, we gain some insight into how to select supply chain contracts to better improve environmental performance. The results reveal that the manufacturer sharing the retailer's revenue and cost contract obtains the highest profit. While revenue sharing contract between both parties is the optimal environmental contract, but it is difficult to increase the profit of supply chain. Furthermore, it is found that trade credit works well in protecting the environment and plays a significant role in achieving coordination.

Citation: Chong Zhang, Yaxian Wang, Haiyan Wang. Design of an environmental contract under trade credits and carbon emission reduction. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021141
References:
[1]

S. M. AljazzarA. Gurtu and M. Y. Jaber, Delay-in-payments-A strategy to reduce carbon emissions from supply chains, Journal of Cleaner Production, 170 (2018), 636-644.  doi: 10.1016/j.jclepro.2017.08.177.  Google Scholar

[2]

S. AnB. LiD. Song and X. Chen, Green credit financing versus trade credit financing in a supply chain with carbon emission limits, European Journal of Operational Research, 292 (2021), 125-142.  doi: 10.1016/j.ejor.2020.10.025.  Google Scholar

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Q. BaiM. Chen and L. Xu, Revenue and promotional cost-sharing contract versus two-part tariff contract in coordinating sustainable supply chain systems with deteriorating items, International Journal of Production Economics, 187 (2017), 85-101.  doi: 10.1016/j.ijpe.2017.02.012.  Google Scholar

[4]

Q. Bai, J. Xu and S. S. Chauhan, Effects of sustainability investment and risk aversion on a two-stage supply chain coordination under a carbon tax policy, Computers & Industrial Engineering, 142 (2020), 106324. doi: 10.1016/j.cie.2020.106324.  Google Scholar

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Y. BoucheryA. GhaffariZ. Jemai and Y. Dallery, Including sustainability criteria into inventory models, European Journal of Operational Research, 222 (2012), 229-240.  doi: 10.1016/j.ejor.2012.05.004.  Google Scholar

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E. Cao and M. Yu, Trade credit financing and coordination for an emission-dependent supply chain, Computers & Industrial Engineerin, 119 (2018), 50-62.  doi: 10.1016/j.cie.2018.03.024.  Google Scholar

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X. Cao and T. T. Ke, Cooperative search advertising, Management Science, 38 (2018), 44-67.  doi: 10.1287/mksc.2018.1111.  Google Scholar

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S. EbrahimiS. Hosseinimotlagh and M. Nematollahi, Proposing a delay in payment contract for coordinating a two-echelon periodic review supply chain with stochastic promotional effort dependent demand, International Journal of Machine Learning and Cybernetics, 10 (2019), 1037-1050.  doi: 10.1007/s13042-017-0781-6.  Google Scholar

[9]

M. GiannettiM. Burkart and T. Ellingsen, What you sell is what you lend? explaining trade credit contracts, Review of Financial Studies, 24 (2011), 1261-1298.  doi: 10.2139/ssrn.930390.  Google Scholar

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S. K. Goyal, Economic order quantity under conditions of permissible delay in payments, Journal of the Operational Research Society, 36 (1985), 1069-1069.  doi: 10.1057/jors.1985.56.  Google Scholar

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S. GuoT. M. Choi and B. Shen, Green product development under competition: A study of the fashion apparel industry, European Journal of Operational Research, 280 (2020), 523-538.  doi: 10.1016/j.ejor.2019.07.050.  Google Scholar

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J. Heydari and J. Asl-Najafi, A revised sales rebate contract with effort-dependent demand: A channel coordination approach, International Transactions in Operational Research, 28 (2021), 438-469.  doi: 10.1111/itor.12556.  Google Scholar

[13]

J. HeydariM. Rastegar and C. H. Glock, A two-level delay in payments contract for supply chain coordination: The case of credit-dependent demand, International Journal of Production Economics, 191 (2017), 26-36.  doi: 10.1016/j.ijpe.2017.05.004.  Google Scholar

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Z. Hong and X. Guo, Green product supply chain contracts considering environmental responsibilities, Omega, 83 (2019), 155-166.  doi: 10.1016/j.omega.2018.02.010.  Google Scholar

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S. M. Hosseini–MotlaghM. NematollahiM. Johari and B. R. Sarker, A collaborative model for coordination of monopolistic manufacturer's promotional efforts and competing duopolistic retailers' trade credits, International Journal of Production Economics, 204 (2018), 108-122.  doi: 10.1016/j.ijpe.2018.07.027.  Google Scholar

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X. Hu, Z. Yang, J. Sun and Y. Zhang, Carbon tax or cap-and-trade: Which is more viable for Chinese remanufacturing industry, Journal of Cleaner Production, 243 (2020), 118606. doi: 10.1016/j.jclepro.2019.118606.  Google Scholar

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G. HuaT. C. E. Cheng and S. Wang, Managing carbon footprints in inventory management, International Journal of Production Economics, 132 (2011), 178-185.  doi: 10.1016/j.ijpe.2011.03.024.  Google Scholar

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M. Y. Jaber and I. H. Osman, Coordinating a two-level supply chain with delay in payments and profit sharing, Computers & Industrial Engineering, 50 (2006), 385-400.  doi: 10.1016/j.cie.2005.08.004.  Google Scholar

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J. JiZ. Zhang and L. Yang, Carbon emission reduction decisions in the retail-/dual-channel supply chain with consumers' preference, Journal of Cleaner Production, 141 (2017), 852-867.  doi: 10.1016/j.jclepro.2016.09.135.  Google Scholar

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T. JiX. XuX. Yan and Y. Yu, The production decisions and cap setting with wholesale price and revenue sharing contracts under cap-and-trade regulation, International Journal of Production Research, 58 (2020), 128-147.  doi: 10.1080/00207543.2019.1641239.  Google Scholar

[21]

J. Jian, B. Li, N. Zhang and J. Su, Decision–making and coordination of green closed-loop supply chain with fairness concern, Journal of Cleaner Production, 298 (2021), 126779. doi: 10.1016/j.jclepro.2021.126779.  Google Scholar

[22]

M. KanadaT. FujitaM. Fujii and S. Ohnishi, The long–term impacts of air pollution control policy: Historical links between municipal actions and industrial energy efficiency in kawasaki city, japan, Journal of Cleaner Production, 58 (2013), 92-101.  doi: 10.1016/j.jclepro.2013.04.015.  Google Scholar

[23]

M. KennedyV. N. Dinh and B. Basu, Analysis of consumer choice for low–carbon technologies by using neural networks, Journal of Cleaner Production, 112 (2016), 3402-3412.  doi: 10.1016/j.jclepro.2015.10.035.  Google Scholar

[24]

V. B. Kreng and S. J. Tan, The optimal replenishment decisions under two levels of trade credit policy depending on the order quantity, Expert Systems with Applications, 37 (2010), 5514-5522.  doi: 10.1016/j.eswa.2009.12.014.  Google Scholar

[25]

H. KrishnanR. Kapuscinski and D. A. Butz, Coordinating contracts for decentralized supply chains with retailer promotional effort, Management Science, 50 (2004), 1-131.  doi: 10.1287/mnsc.1030.0154.  Google Scholar

[26]

H. H. LeeJ. Zhou and J. Wang, Trade credit financing under competition and its impact on firm performance in supply chains, Manufacturing & Service Operations Management, 20 (2018), 1-160.  doi: 10.1287/msom.2017.0640.  Google Scholar

[27]

Q. LinY. Xiao and J. Zheng, Selecting the supply chain financing mode under price-sensitive demand: Confirmed warehouse financing vs. trade credit, Journal of Industrial and Management Optimization, 17 (2021), 2031-2049.  doi: 10.3934/jimo.2020057.  Google Scholar

[28]

P. MaH. Wang and J. Shang, Contract design for two-stage supply chain coordination: Integrating manufacturer-quality and retailer-marketing efforts, International Journal of Production Economics, 146 (2013), 745-755.  doi: 10.1016/j.ijpe.2013.09.004.  Google Scholar

[29]

N. PakhiraM. K. Maiti and M. Maiti, Uncertain multi-item supply chain with two level trade credit under promotional cost sharing, Computers & Industrial Engineering, 118 (2018), 451-463.  doi: 10.1016/j.cie.2018.02.030.  Google Scholar

[30]

H. PengT. Pang and J. Cong, Coordination contracts for a supply chain with yield uncertainty and low-carbon preference, Journal of Cleaner Production, 205 (2018), 291-302.  doi: 10.1016/j.jclepro.2018.09.038.  Google Scholar

[31]

H. PeuraS. A. Yang and G. Lai, Trade credit in competition: A horizontal benefit, Manufacturing & Service Operations Management, 19 (2017), 263-289.  doi: 10.1287/msom.2016.0608.  Google Scholar

[32]

D. A. PhanT. L. Vo and A. N. Lai, Supply chain coordination under trade credit and retailer effort, International Journal of Production Research, 57 (2019), 2642-2655.  doi: 10.1080/00207543.2019.1567950.  Google Scholar

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X. Qian, F. T. Chan, J. Zhang, M. Yin and Q. Zhang, Channel coordination of a two-echelon sustainable supply chain with a fair-minded retailer under cap-and-trade regulation, Journal of Cleaner Production, 244 (2020), 118715. doi: 10.1016/j.jclepro.2019.118715.  Google Scholar

[34]

J. QinY. HanG. Wei and L. Xia, The value of advance payment financing to carbon emission reduction and production in a supply chain with game theory analysis, International Journal of Production Research, 58 (2020), 200-219.  doi: 10.1080/00207543.2019.1671626.  Google Scholar

[35]

A. Ranjan and J. K. Jha, Pricing and coordination strategies of a dual-channel supply chain considering green quality and sales effort, Journal of Cleaner Production, 218 (2019), 409-424.  doi: 10.1016/j.jclepro.2019.01.297.  Google Scholar

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S. SaymanS. J. Hoch and J. S. Raju, Positioning of store brands, Marketing Science, 21 (2002), 369-477.  doi: 10.1287/mksc.21.4.378.134.  Google Scholar

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J. T. TengK. R. Lou and L. Wang, Optimal trade credit and lot size policies in economic production quantity models with learning curve production costs, International Journal of Production Economics, 155 (2014), 318-323.  doi: 10.1016/j.ijpe.2013.10.012.  Google Scholar

[40]

W. TongD. MuF. ZhaoG. P. Mendis and J. W. Sutherland, The impact of cap-and-trade mechanism and consumers' environmental preferences on a retailer-led supply Chain. Resources, Conservation and Recycling, 142 (2019), 88-100.  doi: 10.1016/j.resconrec.2018.11.005.  Google Scholar

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Y. C. Tsao, Channel coordination under two-level trade credits and demand uncertainty, Applied Mathematical Modelling, 52 (2017), 160-173.  doi: 10.1016/j.apm.2017.07.046.  Google Scholar

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Y. C. Tsao and G. J. Sheen, Effects of promotion cost sharing policy with the sales learning curve on supply chain coordination, Computers & Operations Research, 39 (2012), 1872-1878.  doi: 10.1016/j.cor.2011.07.009.  Google Scholar

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show all references

References:
[1]

S. M. AljazzarA. Gurtu and M. Y. Jaber, Delay-in-payments-A strategy to reduce carbon emissions from supply chains, Journal of Cleaner Production, 170 (2018), 636-644.  doi: 10.1016/j.jclepro.2017.08.177.  Google Scholar

[2]

S. AnB. LiD. Song and X. Chen, Green credit financing versus trade credit financing in a supply chain with carbon emission limits, European Journal of Operational Research, 292 (2021), 125-142.  doi: 10.1016/j.ejor.2020.10.025.  Google Scholar

[3]

Q. BaiM. Chen and L. Xu, Revenue and promotional cost-sharing contract versus two-part tariff contract in coordinating sustainable supply chain systems with deteriorating items, International Journal of Production Economics, 187 (2017), 85-101.  doi: 10.1016/j.ijpe.2017.02.012.  Google Scholar

[4]

Q. Bai, J. Xu and S. S. Chauhan, Effects of sustainability investment and risk aversion on a two-stage supply chain coordination under a carbon tax policy, Computers & Industrial Engineering, 142 (2020), 106324. doi: 10.1016/j.cie.2020.106324.  Google Scholar

[5]

Y. BoucheryA. GhaffariZ. Jemai and Y. Dallery, Including sustainability criteria into inventory models, European Journal of Operational Research, 222 (2012), 229-240.  doi: 10.1016/j.ejor.2012.05.004.  Google Scholar

[6]

E. Cao and M. Yu, Trade credit financing and coordination for an emission-dependent supply chain, Computers & Industrial Engineerin, 119 (2018), 50-62.  doi: 10.1016/j.cie.2018.03.024.  Google Scholar

[7]

X. Cao and T. T. Ke, Cooperative search advertising, Management Science, 38 (2018), 44-67.  doi: 10.1287/mksc.2018.1111.  Google Scholar

[8]

S. EbrahimiS. Hosseinimotlagh and M. Nematollahi, Proposing a delay in payment contract for coordinating a two-echelon periodic review supply chain with stochastic promotional effort dependent demand, International Journal of Machine Learning and Cybernetics, 10 (2019), 1037-1050.  doi: 10.1007/s13042-017-0781-6.  Google Scholar

[9]

M. GiannettiM. Burkart and T. Ellingsen, What you sell is what you lend? explaining trade credit contracts, Review of Financial Studies, 24 (2011), 1261-1298.  doi: 10.2139/ssrn.930390.  Google Scholar

[10]

S. K. Goyal, Economic order quantity under conditions of permissible delay in payments, Journal of the Operational Research Society, 36 (1985), 1069-1069.  doi: 10.1057/jors.1985.56.  Google Scholar

[11]

S. GuoT. M. Choi and B. Shen, Green product development under competition: A study of the fashion apparel industry, European Journal of Operational Research, 280 (2020), 523-538.  doi: 10.1016/j.ejor.2019.07.050.  Google Scholar

[12]

J. Heydari and J. Asl-Najafi, A revised sales rebate contract with effort-dependent demand: A channel coordination approach, International Transactions in Operational Research, 28 (2021), 438-469.  doi: 10.1111/itor.12556.  Google Scholar

[13]

J. HeydariM. Rastegar and C. H. Glock, A two-level delay in payments contract for supply chain coordination: The case of credit-dependent demand, International Journal of Production Economics, 191 (2017), 26-36.  doi: 10.1016/j.ijpe.2017.05.004.  Google Scholar

[14]

Z. Hong and X. Guo, Green product supply chain contracts considering environmental responsibilities, Omega, 83 (2019), 155-166.  doi: 10.1016/j.omega.2018.02.010.  Google Scholar

[15]

S. M. Hosseini–MotlaghM. NematollahiM. Johari and B. R. Sarker, A collaborative model for coordination of monopolistic manufacturer's promotional efforts and competing duopolistic retailers' trade credits, International Journal of Production Economics, 204 (2018), 108-122.  doi: 10.1016/j.ijpe.2018.07.027.  Google Scholar

[16]

X. Hu, Z. Yang, J. Sun and Y. Zhang, Carbon tax or cap-and-trade: Which is more viable for Chinese remanufacturing industry, Journal of Cleaner Production, 243 (2020), 118606. doi: 10.1016/j.jclepro.2019.118606.  Google Scholar

[17]

G. HuaT. C. E. Cheng and S. Wang, Managing carbon footprints in inventory management, International Journal of Production Economics, 132 (2011), 178-185.  doi: 10.1016/j.ijpe.2011.03.024.  Google Scholar

[18]

M. Y. Jaber and I. H. Osman, Coordinating a two-level supply chain with delay in payments and profit sharing, Computers & Industrial Engineering, 50 (2006), 385-400.  doi: 10.1016/j.cie.2005.08.004.  Google Scholar

[19]

J. JiZ. Zhang and L. Yang, Carbon emission reduction decisions in the retail-/dual-channel supply chain with consumers' preference, Journal of Cleaner Production, 141 (2017), 852-867.  doi: 10.1016/j.jclepro.2016.09.135.  Google Scholar

[20]

T. JiX. XuX. Yan and Y. Yu, The production decisions and cap setting with wholesale price and revenue sharing contracts under cap-and-trade regulation, International Journal of Production Research, 58 (2020), 128-147.  doi: 10.1080/00207543.2019.1641239.  Google Scholar

[21]

J. Jian, B. Li, N. Zhang and J. Su, Decision–making and coordination of green closed-loop supply chain with fairness concern, Journal of Cleaner Production, 298 (2021), 126779. doi: 10.1016/j.jclepro.2021.126779.  Google Scholar

[22]

M. KanadaT. FujitaM. Fujii and S. Ohnishi, The long–term impacts of air pollution control policy: Historical links between municipal actions and industrial energy efficiency in kawasaki city, japan, Journal of Cleaner Production, 58 (2013), 92-101.  doi: 10.1016/j.jclepro.2013.04.015.  Google Scholar

[23]

M. KennedyV. N. Dinh and B. Basu, Analysis of consumer choice for low–carbon technologies by using neural networks, Journal of Cleaner Production, 112 (2016), 3402-3412.  doi: 10.1016/j.jclepro.2015.10.035.  Google Scholar

[24]

V. B. Kreng and S. J. Tan, The optimal replenishment decisions under two levels of trade credit policy depending on the order quantity, Expert Systems with Applications, 37 (2010), 5514-5522.  doi: 10.1016/j.eswa.2009.12.014.  Google Scholar

[25]

H. KrishnanR. Kapuscinski and D. A. Butz, Coordinating contracts for decentralized supply chains with retailer promotional effort, Management Science, 50 (2004), 1-131.  doi: 10.1287/mnsc.1030.0154.  Google Scholar

[26]

H. H. LeeJ. Zhou and J. Wang, Trade credit financing under competition and its impact on firm performance in supply chains, Manufacturing & Service Operations Management, 20 (2018), 1-160.  doi: 10.1287/msom.2017.0640.  Google Scholar

[27]

Q. LinY. Xiao and J. Zheng, Selecting the supply chain financing mode under price-sensitive demand: Confirmed warehouse financing vs. trade credit, Journal of Industrial and Management Optimization, 17 (2021), 2031-2049.  doi: 10.3934/jimo.2020057.  Google Scholar

[28]

P. MaH. Wang and J. Shang, Contract design for two-stage supply chain coordination: Integrating manufacturer-quality and retailer-marketing efforts, International Journal of Production Economics, 146 (2013), 745-755.  doi: 10.1016/j.ijpe.2013.09.004.  Google Scholar

[29]

N. PakhiraM. K. Maiti and M. Maiti, Uncertain multi-item supply chain with two level trade credit under promotional cost sharing, Computers & Industrial Engineering, 118 (2018), 451-463.  doi: 10.1016/j.cie.2018.02.030.  Google Scholar

[30]

H. PengT. Pang and J. Cong, Coordination contracts for a supply chain with yield uncertainty and low-carbon preference, Journal of Cleaner Production, 205 (2018), 291-302.  doi: 10.1016/j.jclepro.2018.09.038.  Google Scholar

[31]

H. PeuraS. A. Yang and G. Lai, Trade credit in competition: A horizontal benefit, Manufacturing & Service Operations Management, 19 (2017), 263-289.  doi: 10.1287/msom.2016.0608.  Google Scholar

[32]

D. A. PhanT. L. Vo and A. N. Lai, Supply chain coordination under trade credit and retailer effort, International Journal of Production Research, 57 (2019), 2642-2655.  doi: 10.1080/00207543.2019.1567950.  Google Scholar

[33]

X. Qian, F. T. Chan, J. Zhang, M. Yin and Q. Zhang, Channel coordination of a two-echelon sustainable supply chain with a fair-minded retailer under cap-and-trade regulation, Journal of Cleaner Production, 244 (2020), 118715. doi: 10.1016/j.jclepro.2019.118715.  Google Scholar

[34]

J. QinY. HanG. Wei and L. Xia, The value of advance payment financing to carbon emission reduction and production in a supply chain with game theory analysis, International Journal of Production Research, 58 (2020), 200-219.  doi: 10.1080/00207543.2019.1671626.  Google Scholar

[35]

A. Ranjan and J. K. Jha, Pricing and coordination strategies of a dual-channel supply chain considering green quality and sales effort, Journal of Cleaner Production, 218 (2019), 409-424.  doi: 10.1016/j.jclepro.2019.01.297.  Google Scholar

[36]

S. SaymanS. J. Hoch and J. S. Raju, Positioning of store brands, Marketing Science, 21 (2002), 369-477.  doi: 10.1287/mksc.21.4.378.134.  Google Scholar

[37]

J. SuC. LiQ. ZengJ. Yang and J. Zhang, A green closed-loop supply chain coordination mechanism based on third-party recycling, Sustainability, 11 (2019), 1-14.   Google Scholar

[38]

T. A. Taylor, Supply chain coordination under channel rebates with sales effort effects, Marketing Science, 48 (2002), 992-1007.  doi: 10.1287/mnsc.48.8.992.168.  Google Scholar

[39]

J. T. TengK. R. Lou and L. Wang, Optimal trade credit and lot size policies in economic production quantity models with learning curve production costs, International Journal of Production Economics, 155 (2014), 318-323.  doi: 10.1016/j.ijpe.2013.10.012.  Google Scholar

[40]

W. TongD. MuF. ZhaoG. P. Mendis and J. W. Sutherland, The impact of cap-and-trade mechanism and consumers' environmental preferences on a retailer-led supply Chain. Resources, Conservation and Recycling, 142 (2019), 88-100.  doi: 10.1016/j.resconrec.2018.11.005.  Google Scholar

[41]

Y. C. Tsao, Channel coordination under two-level trade credits and demand uncertainty, Applied Mathematical Modelling, 52 (2017), 160-173.  doi: 10.1016/j.apm.2017.07.046.  Google Scholar

[42]

Y. C. Tsao, Coordinating contracts under default risk control-based trade credit, International Journal of Production Economics, 212 (2019), 168-175.  doi: 10.1016/j.ijpe.2019.02.018.  Google Scholar

[43]

Y. C. Tsao and G. J. Sheen, Effects of promotion cost sharing policy with the sales learning curve on supply chain coordination, Computers & Operations Research, 39 (2012), 1872-1878.  doi: 10.1016/j.cor.2011.07.009.  Google Scholar

[44]

J. Tu, Z. Sun and M. Huang, Supply chain coordination considering e-tailer's promotion effort and logistics provider's service effort, Journal of Industrial and Management Optimization, (2020). doi: 10.3934/jimo.2021062.  Google Scholar

[45]

Warren, Audrey, Peers and Martin, Video retailers have day in court, Wall Street Journal–Eastern Edition, (2002). Google Scholar

[46]

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Figure 1.  Effects of $ {W_e} $ on optimal solutions
Figure 2.  Effects of $ \varepsilon $ on optimal solutions
Table 1.  Summary of Related Literature
Decision variables Demand dependency Contract
(ⅰ) (ⅱ) (ⅲ) (ⅳ) (ⅰ) (ⅱ) (ⅲ) (ⅳ) (ⅴ) (ⅵ)
[38] $ \times $ $ \times $ $ \surd $ $ \times $ $ \times $ $ \times $ $ \surd $ $ \times $ $ \surd $ $ \times $
Krishnan et al.[25] $ \times $ $ \times $ $ \times $ $ \surd $ $ \times $ $ \times $ $ \times $ $ \surd $ $ \surd $ $ \surd $
Tsao and Sheen [43] $ \times $ $ \times $ $ \surd $ $ \times $ $ \times $ $ \times $ $ \surd $ $ \times $ $ \surd $ $ \times $
Ma et al.[28] $ \times $ $ \times $ $ \surd $ $ \surd $ $ \times $ $ \times $ $ \surd $ $ \surd $ $ \surd $ $ \surd $
Xu et al. [48] $ \times $ $ \surd $ $ \surd $ $ \times $ $ \times $ $ \surd $ $ \surd $ $ \times $ $ \surd $ $ \times $
Ji et al.[19] $ \times $ $ \surd $ $ \surd $ $ \surd $ $ \times $ $ \surd $ $ \surd $ $ \surd $ $ \times $ $ \times $
Bai et al.[3] $ \times $ $ \surd $ $ \surd $ $ \surd $ $ \times $ $ \surd $ $ \surd $ $ \surd $ $ \times $ $ \surd $
Heydari et al.[13] $ \surd $ $ \times $ $ \times $ $ \times $ $ \surd $ $ \times $ $ \times $ $ \times $ $ \surd $ $ \times $
Zhou and Ye [53] $ \times $ $ \surd $ $ \surd $ $ \surd $ $ \times $ $ \surd $ $ \surd $ $ \surd $ $ \surd $ $ \surd $
Yang et al.[50] $ \times $ $ \surd $ $ \surd $ $ \times $ $ \times $ $ \times $ $ \surd $ $ \times $ $ \times $ $ \times $
Hosseini-Motlagh et al.[15] $ \surd $ $ \times $ $ \times $ $ \surd $ $ \surd $ $ \times $ $ \times $ $ \surd $ $ \surd $ $ \times $
Pakhira et al.[29] $ \surd $ $ \times $ $ \times $ $ \surd $ $ \times $ $ \times $ $ \times $ $ \surd $ $ \surd $ $ \times $
Phan et al.[32] $ \times $ $ \times $ $ \times $ $ \surd $ $ \times $ $ \times $ $ \times $ $ \surd $ $ \surd $ $ \surd $
Tsao[42] $ \surd $ $ \times $ $ \times $ $ \times $ $ \surd $ $ \times $ $ \times $ $ \times $ $ \surd $ $ \surd $
Ranjan and Jha[35] $ \times $ $ \times $ $ \surd $ $ \surd $ $ \times $ $ \times $ $ \surd $ $ \surd $ $ \surd $ $ \times $
This paper $ \surd $ $ \surd $ $ \surd $ $ \surd $ $ \surd $ $ \surd $ $ \surd $ $ \surd $ $ \times $ $ \surd $
Decision variables Demand dependency Contract
(ⅰ) (ⅱ) (ⅲ) (ⅳ) (ⅰ) (ⅱ) (ⅲ) (ⅳ) (ⅴ) (ⅵ)
[38] $ \times $ $ \times $ $ \surd $ $ \times $ $ \times $ $ \times $ $ \surd $ $ \times $ $ \surd $ $ \times $
Krishnan et al.[25] $ \times $ $ \times $ $ \times $ $ \surd $ $ \times $ $ \times $ $ \times $ $ \surd $ $ \surd $ $ \surd $
Tsao and Sheen [43] $ \times $ $ \times $ $ \surd $ $ \times $ $ \times $ $ \times $ $ \surd $ $ \times $ $ \surd $ $ \times $
Ma et al.[28] $ \times $ $ \times $ $ \surd $ $ \surd $ $ \times $ $ \times $ $ \surd $ $ \surd $ $ \surd $ $ \surd $
Xu et al. [48] $ \times $ $ \surd $ $ \surd $ $ \times $ $ \times $ $ \surd $ $ \surd $ $ \times $ $ \surd $ $ \times $
Ji et al.[19] $ \times $ $ \surd $ $ \surd $ $ \surd $ $ \times $ $ \surd $ $ \surd $ $ \surd $ $ \times $ $ \times $
Bai et al.[3] $ \times $ $ \surd $ $ \surd $ $ \surd $ $ \times $ $ \surd $ $ \surd $ $ \surd $ $ \times $ $ \surd $
Heydari et al.[13] $ \surd $ $ \times $ $ \times $ $ \times $ $ \surd $ $ \times $ $ \times $ $ \times $ $ \surd $ $ \times $
Zhou and Ye [53] $ \times $ $ \surd $ $ \surd $ $ \surd $ $ \times $ $ \surd $ $ \surd $ $ \surd $ $ \surd $ $ \surd $
Yang et al.[50] $ \times $ $ \surd $ $ \surd $ $ \times $ $ \times $ $ \times $ $ \surd $ $ \times $ $ \times $ $ \times $
Hosseini-Motlagh et al.[15] $ \surd $ $ \times $ $ \times $ $ \surd $ $ \surd $ $ \times $ $ \times $ $ \surd $ $ \surd $ $ \times $
Pakhira et al.[29] $ \surd $ $ \times $ $ \times $ $ \surd $ $ \times $ $ \times $ $ \times $ $ \surd $ $ \surd $ $ \times $
Phan et al.[32] $ \times $ $ \times $ $ \times $ $ \surd $ $ \times $ $ \times $ $ \times $ $ \surd $ $ \surd $ $ \surd $
Tsao[42] $ \surd $ $ \times $ $ \times $ $ \times $ $ \surd $ $ \times $ $ \times $ $ \times $ $ \surd $ $ \surd $
Ranjan and Jha[35] $ \times $ $ \times $ $ \surd $ $ \surd $ $ \times $ $ \times $ $ \surd $ $ \surd $ $ \surd $ $ \times $
This paper $ \surd $ $ \surd $ $ \surd $ $ \surd $ $ \surd $ $ \surd $ $ \surd $ $ \surd $ $ \times $ $ \surd $
Table 2.  Symbols in this paper
Parameters
$ C $ The production cost per unit
$ W $ The wholesale price per unit
$ I $ The market interest rate
$ v $ The effectiveness of carbon reduction efforts on carbon emissions for making a unit, $v > 0$
$ \varepsilon $ The manufacturer's carbon emissions for making a product without efforts on carbon reduction
$ {C_M} $ The manufacturer's carbon pollution limit or cap
$ {W_e} $ The trading price of carbon emissions
$ {\eta _1} $ The investment cost coefficient on carbon reduction efforts, $ {\eta _1} > 0 $
$ {\eta _2} $ The investment cost coefficient on promotional efforts, $ {\eta _2} > 0 $
$ a $ Market scale parameter, $ a > 0 $
$ b $ Price influence on the demand rate, $ b > 0 $
$ {\gamma _1} $ Effect of carbon reduction effort on demand, $ {\gamma _1} > 0 $
$ {\gamma _2} $ Effect of promotional effort on demand, $ {\gamma _2} > 0 $
Decision variables
$ s $ The retailer's promotional efforts
$ P $ The retail price per unit
$ M $ The length of the trade credit period offered by the manufacturer in years. $ M > 0$ represents a credit payment, $M = 0$ represents an advance payment, and $ M < 0$ represents a cash payment
$ {\theta} $ The manufacturer's carbon reduction efforts
Functions
$ {\pi _i} $ The supply chain member i's profit per year; $i = s, r, sc$ refer to the manufacturer, the retailer and the supply chain, respectively
$ * $ Represents the optimal value of a decision variable
Parameters
$ C $ The production cost per unit
$ W $ The wholesale price per unit
$ I $ The market interest rate
$ v $ The effectiveness of carbon reduction efforts on carbon emissions for making a unit, $v > 0$
$ \varepsilon $ The manufacturer's carbon emissions for making a product without efforts on carbon reduction
$ {C_M} $ The manufacturer's carbon pollution limit or cap
$ {W_e} $ The trading price of carbon emissions
$ {\eta _1} $ The investment cost coefficient on carbon reduction efforts, $ {\eta _1} > 0 $
$ {\eta _2} $ The investment cost coefficient on promotional efforts, $ {\eta _2} > 0 $
$ a $ Market scale parameter, $ a > 0 $
$ b $ Price influence on the demand rate, $ b > 0 $
$ {\gamma _1} $ Effect of carbon reduction effort on demand, $ {\gamma _1} > 0 $
$ {\gamma _2} $ Effect of promotional effort on demand, $ {\gamma _2} > 0 $
Decision variables
$ s $ The retailer's promotional efforts
$ P $ The retail price per unit
$ M $ The length of the trade credit period offered by the manufacturer in years. $ M > 0$ represents a credit payment, $M = 0$ represents an advance payment, and $ M < 0$ represents a cash payment
$ {\theta} $ The manufacturer's carbon reduction efforts
Functions
$ {\pi _i} $ The supply chain member i's profit per year; $i = s, r, sc$ refer to the manufacturer, the retailer and the supply chain, respectively
$ * $ Represents the optimal value of a decision variable
Table 3.  Optimal solutions for the example
Model $ M $ $ P $ $ \theta $ $ s $ $ \pi_r $ $ \pi_m $ $ \pi_{sc} $ $ E(D) $
$ Centralized $ 0.74 33.694 7.916 3.401 - - 4094.153 171.326
$ Decentralized $ -0.39 37.683 3.402 1.389 228.357 762.078 990.434 94.911
$ Contract A\left[\rho_{1}, \lambda_{1}\right] $
$ [0.1,0.7] $ -0.14 37.961 3.821 5.469 407.49 796.88 1204.37 131.86
$ [0.1,0.6] $ -0.02 37.207 3.773 4.573 550.99 816.57 1367.55 156.29
$ [0.1,0.5] $ 0.04 36.773 3.735 3.870 650.65 829.39 1480.03 172.24
$ [0.1,0.4] $ 0.08 36.501 3.707 3.325 715.62 837.43 1553.04 182.32
$ [0.2,0.5] $ 0.49 36.049 3.938 5.004 1724.03 967.01 2691.04 314.26
$ [0.3,0.5] $ 0.92 35.660 4.104 6.088 4116.45 1227.64 5344.10 554.05
$ Contract B\left[\rho_{2}, \tau_{1}\right] $
$ [0.1,0.6] $ -0.73 35.846 3.611 0.804 86.24 740.29 826.54 63.78
$ [0.2,0.6] $ -0.25 34.136 3.864 1.387 327.23 788.97 1116.20 122.98
$ [0.3,0.6] $ 0.21 33.440 3.985 1.953 953.53 884.78 1838.31 228.22
$ [0.4,0.6] $ 0.68 33.087 4.060 2.519 2500.88 1077.13 3578.01 419.39
$ [0.2,0.5] $ -0.10 34.401 3.841 1.608 470.48 810.54 1281.02 148.85
$ [0.2,0.4] $ 0.05 34.613 3.825 1.827 663.39 837.37 1500.75 180.05
$ Contract C\left[\varphi_{1}, \lambda_{2}\right] $
$ [0.5,0.5] $ -0.40 43.264 6.599 3.367 198.32 808.30 1006.62 42.36
$ [0.5,0.4] $ -0.35 42.287 6.753 2.925 236.66 819.58 1056.24 45.20
$ [0.5,0.3] $ -0.32 41.707 6.833 2.562 261.25 826.59 1087.83 46.95
$ [0.4,0.2] $ -0.35 41.603 5.377 2.148 247.94 842.09 1090.03 63.22
$ [0.5,0.2] $ -0.30 41.341 6.876 2.269 277.01 831.03 1108.03 48.07
$ [0.6,0.2] $ -0.22 40.962 9.507 2.473 315.25 795.62 1110.88 9.18
$ Contract D\left[\varphi_{2}, \tau_{2}\right] $
$ [0.6,0.05] $ -0.28 41.512 9.147 1.899 263.38 772.25 1035.63 13.98
$ [0.61,0.05] $ -0.27 41.459 9.511 1.921 266.65 774.34 1040.99 8.23
$ [0.62,0.05] $ -0.26 41.404 9.904 1.945 269.71 776.63 1046.34 1.66
$ [0.6,0.05] $ -0.28 41.512 9.147 1.899 263.38 772.25 1035.63 13.98
$ [0.6,0.04] $ -0.27 41.307 9.232 1.920 277.15 775.09 1052.24 13.03
$ [0.6,0.003] $ -0.25 41.105 9.316 1.941 291.41 778.01 1069.42 12.02
Model $ M $ $ P $ $ \theta $ $ s $ $ \pi_r $ $ \pi_m $ $ \pi_{sc} $ $ E(D) $
$ Centralized $ 0.74 33.694 7.916 3.401 - - 4094.153 171.326
$ Decentralized $ -0.39 37.683 3.402 1.389 228.357 762.078 990.434 94.911
$ Contract A\left[\rho_{1}, \lambda_{1}\right] $
$ [0.1,0.7] $ -0.14 37.961 3.821 5.469 407.49 796.88 1204.37 131.86
$ [0.1,0.6] $ -0.02 37.207 3.773 4.573 550.99 816.57 1367.55 156.29
$ [0.1,0.5] $ 0.04 36.773 3.735 3.870 650.65 829.39 1480.03 172.24
$ [0.1,0.4] $ 0.08 36.501 3.707 3.325 715.62 837.43 1553.04 182.32
$ [0.2,0.5] $ 0.49 36.049 3.938 5.004 1724.03 967.01 2691.04 314.26
$ [0.3,0.5] $ 0.92 35.660 4.104 6.088 4116.45 1227.64 5344.10 554.05
$ Contract B\left[\rho_{2}, \tau_{1}\right] $
$ [0.1,0.6] $ -0.73 35.846 3.611 0.804 86.24 740.29 826.54 63.78
$ [0.2,0.6] $ -0.25 34.136 3.864 1.387 327.23 788.97 1116.20 122.98
$ [0.3,0.6] $ 0.21 33.440 3.985 1.953 953.53 884.78 1838.31 228.22
$ [0.4,0.6] $ 0.68 33.087 4.060 2.519 2500.88 1077.13 3578.01 419.39
$ [0.2,0.5] $ -0.10 34.401 3.841 1.608 470.48 810.54 1281.02 148.85
$ [0.2,0.4] $ 0.05 34.613 3.825 1.827 663.39 837.37 1500.75 180.05
$ Contract C\left[\varphi_{1}, \lambda_{2}\right] $
$ [0.5,0.5] $ -0.40 43.264 6.599 3.367 198.32 808.30 1006.62 42.36
$ [0.5,0.4] $ -0.35 42.287 6.753 2.925 236.66 819.58 1056.24 45.20
$ [0.5,0.3] $ -0.32 41.707 6.833 2.562 261.25 826.59 1087.83 46.95
$ [0.4,0.2] $ -0.35 41.603 5.377 2.148 247.94 842.09 1090.03 63.22
$ [0.5,0.2] $ -0.30 41.341 6.876 2.269 277.01 831.03 1108.03 48.07
$ [0.6,0.2] $ -0.22 40.962 9.507 2.473 315.25 795.62 1110.88 9.18
$ Contract D\left[\varphi_{2}, \tau_{2}\right] $
$ [0.6,0.05] $ -0.28 41.512 9.147 1.899 263.38 772.25 1035.63 13.98
$ [0.61,0.05] $ -0.27 41.459 9.511 1.921 266.65 774.34 1040.99 8.23
$ [0.62,0.05] $ -0.26 41.404 9.904 1.945 269.71 776.63 1046.34 1.66
$ [0.6,0.05] $ -0.28 41.512 9.147 1.899 263.38 772.25 1035.63 13.98
$ [0.6,0.04] $ -0.27 41.307 9.232 1.920 277.15 775.09 1052.24 13.03
$ [0.6,0.003] $ -0.25 41.105 9.316 1.941 291.41 778.01 1069.42 12.02
Table 4.  The increase rates with different contract coefficients
Parameter $ \pi_r $ $ \pi_m $ $ \pi_{sc} $ $ E(D) $
$ Contract A\left[\rho_{1}, \lambda_{1}\right] $
$ [0.1,0.7] $ 78.45% 4.57% 21.60% 38.93%
$ [0.1,0.6] $ 141.28% 7.15% 38.08% 64.67%
$ [0.1,0.5] $ 184.93% 8.83% 49.43% 81.48%
$ [0.1,0.4] $ 213.38% 9.89% 56.81% 92.10%
$ [0.1,0.5] $ 184.93% 8.83% 49.43% 81.48%
$ [0.2,0.5] $ 654.97% 26.89% 171.70% 231.11%
$ [0.3,0.5] $ 1702.6% 61.09% 439.57% 483.76%
$ Contract B\left[\rho_{2}, \tau_{1}\right] $
$ [0.2,0.5] $ 106.02% 6.36% 29.34% 56.83%
$ [0.2,0.4] $ 190.50% 9.88% 51.53% 89.71%
$ [0.2,0.3] $ 303.66% 14.26% 80.99% 129.38%
$ [0.2,0.6] $ 43.30% 3.53% 12.70% 29.57%
$ [0.3,0.6] $ 317.56% 16.10% 85.61% 140.46%
$ [0.4,0.6] $ 995.15% 41.34% 261.26% 341.89%
$ Contract C\left[\varphi_{1}, \lambda_{2}\right] $
$ [0.5,0.4] $ 3.63% 7.55% 6.64% -52.38%
$ [0.5,0.3] $ 14.40% 8.46% 9.83% -50.53%
$ [0.5,0.2] $ 38.05% 4.40% 12.16% -90.32%
$ [0.6,0.2] $ 38.05% 4.40% 12.16% -90.32%
$ [0.5,0.2] $ 21.30% 9.05% 11.87% -49.35%
$ [0.4,0.2] $ 8.58% 10.50% 10.06% -33.39%
$ Contract D\left[\varphi_{2}, \tau_{2}\right] $
$ [0.6,0.05] $ 15.33% 1.34% 4.56% -85.27%
$ [0.61,0.05] $ 16.77% 1.61% 5.10% -91.33%
$ [0.62,0.05] $ 18.11% 1.91% 5.64% -98.25%
$ [0.6,0.05] $ 15.33% 1.34% 4.56% -85.27%
$ [0.6,0.04] $ 21.37% 1.71% 6.24% -86.27%
$ [0.6,0.03] $ 27.61% 2.09% 7.98% -87.34%
Parameter $ \pi_r $ $ \pi_m $ $ \pi_{sc} $ $ E(D) $
$ Contract A\left[\rho_{1}, \lambda_{1}\right] $
$ [0.1,0.7] $ 78.45% 4.57% 21.60% 38.93%
$ [0.1,0.6] $ 141.28% 7.15% 38.08% 64.67%
$ [0.1,0.5] $ 184.93% 8.83% 49.43% 81.48%
$ [0.1,0.4] $ 213.38% 9.89% 56.81% 92.10%
$ [0.1,0.5] $ 184.93% 8.83% 49.43% 81.48%
$ [0.2,0.5] $ 654.97% 26.89% 171.70% 231.11%
$ [0.3,0.5] $ 1702.6% 61.09% 439.57% 483.76%
$ Contract B\left[\rho_{2}, \tau_{1}\right] $
$ [0.2,0.5] $ 106.02% 6.36% 29.34% 56.83%
$ [0.2,0.4] $ 190.50% 9.88% 51.53% 89.71%
$ [0.2,0.3] $ 303.66% 14.26% 80.99% 129.38%
$ [0.2,0.6] $ 43.30% 3.53% 12.70% 29.57%
$ [0.3,0.6] $ 317.56% 16.10% 85.61% 140.46%
$ [0.4,0.6] $ 995.15% 41.34% 261.26% 341.89%
$ Contract C\left[\varphi_{1}, \lambda_{2}\right] $
$ [0.5,0.4] $ 3.63% 7.55% 6.64% -52.38%
$ [0.5,0.3] $ 14.40% 8.46% 9.83% -50.53%
$ [0.5,0.2] $ 38.05% 4.40% 12.16% -90.32%
$ [0.6,0.2] $ 38.05% 4.40% 12.16% -90.32%
$ [0.5,0.2] $ 21.30% 9.05% 11.87% -49.35%
$ [0.4,0.2] $ 8.58% 10.50% 10.06% -33.39%
$ Contract D\left[\varphi_{2}, \tau_{2}\right] $
$ [0.6,0.05] $ 15.33% 1.34% 4.56% -85.27%
$ [0.61,0.05] $ 16.77% 1.61% 5.10% -91.33%
$ [0.62,0.05] $ 18.11% 1.91% 5.64% -98.25%
$ [0.6,0.05] $ 15.33% 1.34% 4.56% -85.27%
$ [0.6,0.04] $ 21.37% 1.71% 6.24% -86.27%
$ [0.6,0.03] $ 27.61% 2.09% 7.98% -87.34%
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