# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2022122
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## Differential decision of low-carbon supply chain based on market preferences with fairness concerns

 Department of Economics and Management, North China Electric Power University, Baoding 071003, China

*Corresponding author: Jianglin Xia

Received  February 2022 Revised  May 2022 Early access July 2022

Fund Project: This research was supported in part by the National Social Science Foundation of China (No.17BGL252)

Under the dual background of energy economy and environmental protection, expanding the optimal decision-making of the low-carbon supply chain is significant to the energy manufacturing industry. This paper discusses the impact of low-carbon preference, price elasticity, and low-carbon research and development investment (LR & DI) on equilibrium decisions of a three-echelon supply chain system under the scenarios of market segments and fairness concerns. Firstly, it is found that the optimal price and yield are positively correlated with the counterparty's demand elasticity coefficient and sensitivity coefficient, and the supply chain profit is better under the decentralized decision of the retailer's fairness concerns. Secondly, there is a positive correlation between each member's interests and the degree of the manufacturer's fairness concern. While considering the retailer, the manufacturer is responsible for the supply chain income loss. Finally, because the optimal pricing and yield are positively correlated with consumers' low-carbon preference and LR & DI, manufacturers may optimize profits by raising LR & DI within a tolerable range. In addition, it is verified that the Stackelberg game optimizes the traditional model by a numerical example, providing theoretical support for decision-making in different scenarios.

Citation: Qunli Wu, Jianglin Xia. Differential decision of low-carbon supply chain based on market preferences with fairness concerns. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2022122
##### References:
 [1] F. X. Aguilar and R. P. Vlosky, Consumer willingness to pay price premiums for environmentally certified wood products in the U.S, Forest Policy Econ., 9 (2007), 1100-1112.  doi: 10.1016/j.forpol.2006.12.001. [2] M. Alinaghian and A. Goli, Location, allocation and routing of temporary health centers in rural areas in crisis, solved by improved harmony search algorithm, Internat. J. Comput. Intell. Syst., 10 (2017), 894-913.  doi: 10.2991/ijcis.2017.10.1.60. [3] L. Chen, J. Peng, Z. Liu and R. Zhao, Pricing and effort decisions for a supply chain with uncertain information, Internat. J. Comput. Intell. Syst., 55 (2017), 264-284.  doi: 10.1080/00207543.2016.1204475. [4] S. K. Das, M. Pervin, S. K. Roy and G. W. Weber, Multi-objective solid transportation-location problem with variable carbon emission in inventory management: A hybrid approach, Ann. Oper. Res., (2021), 1–27. doi: 10.1007/s10479-020-03809-z. [5] B. Du, Q. Liu and G. Li, Coordinating leader-follower supply chain with sustainable green technology innovation on their fairness concerns, Internat. J. Environ. Res. Public Health, 14 (2017). doi: 10.3390/ijerph14111357. [6] N. Du and Q. Han, Pricing and service quality guarantee decisions in logistics service supply chain with fairness concern, Asia-Pac. J. Oper. Res., 35 (2018), 41 pp. doi: 10.1142/S0217595918500367. [7] D. Ghosh and J. Shah, A comparative analysis of greening policies across supply chain structures, Internat. J. Prod. Econ., 135 (2012), 568-583.  doi: 10.1016/j.ijpe.2011.05.027. [8] S. Ghosh and S. K. Roy, Fuzzy-rough multi-objective product blending fixed-charge transportation problem with truck load constraints through transfer station, RAIRO Oper. Res., 55 (2021), S2923–S2952. doi: 10.1051/ro/2020129. [9] A. Goli and T. Keshavarz, Just-in-time scheduling in identical parallel machine sequence-dependent group scheduling problem, to appear, J. Ind. Manag. Optim. . doi: 10.3934/jimo. 2021124. [10] A. Goli and B. Malmir, A covering tour approach for disaster relief locating and routing with fuzzy demand, Internat. J. Intell. Transport. Syst. Res., 18 (2020), 140-152.  doi: 10.1007/s13177-019-00185-2. [11] A. Goli and H. Mohammadi, Developing a sustainable operational management system using hybrid Shapley value and Multimoora method: Case study petrochemical supply chain, Environ. Develop. Sustainability, (2021). doi: 10.1007/s10668-021-01844-9. [12] A. Goli, H. K. Zare, R. Tavakkoli-Moghaddamb and A. Sadeghieh, Hybrid artificial intelligence and robust optimization for a multi-objective product portfolio problem case study: The dairy products industry, Comput. Indust. Engrg., 137 (2019). doi: 10.1016/j. cie. 2019.106090. [13] R. Hammami, I. Nouira and Y. Frein, Effects of customers' environmental awareness and environmental regulations on the emission intensity and price of a product, Decision Sci., 49 (2018), 1116-1155.  doi: 10.1111/deci.12302. [14] Q. Han and Y. Wang, Decision and coordination in a low-carbon e-supply chain considering the manufacturer's carbon emission reduction behavior, Sustainability, 10 (2018). doi: 10.3390/su10051686. [15] J. Ji, Z. Zhang and L. Yang, Carbon emission reduction decisions in the retail-/dual-channel supply chain with consumers' preference, J. Cleaner Prod., 141 (2017), 852-867.  doi: 10.1016/j.jclepro.2016.09.135. [16] K. Kang, Y. Zhao, J. Zhang and C. Qiang, Evolutionary game theoretic analysis on low-carbon strategy for supply chain enterprises, J. Cleaner Prod., 230 (2019), 981-994.  doi: 10.1016/j.jclepro.2019.05.118. [17] E. Katok, T. Olsen and V. Pavlov, Wholesale pricing under mild and privately known concerns for fairness, Prod. Oper. Mgmt., 23 (2014), 285-302.  doi: 10.1111/j.1937-5956.2012.01388.x. [18] G. Li, H. Zheng, X. Ji and H. Li, Game theoretical analysis of firms' operational low-carbon strategy under various cap-and-trade mechanisms, J. Cleaner Prod., 197 (2018), 124-133.  doi: 10.1016/j.jclepro.2018.06.177. [19] H. Li, C. Wang, L. Xu and W. Ou, Pricing, carbon emission reduction, collection decision, and coordination in a low-carbon closed-loop supply chain, J. Renewable Sustainable Energy, 9 (2017). doi: 10.1063/1.4991668. [20] Q. Li, T. Xiao and Y. Qiu, Price and carbon emission reduction decisions and revenue-sharing contract considering fairness concerns, J. Cleaner Prod., 190 (2018), 303-314.  doi: 10.1016/j.jclepro.2018.04.032. [21] L. Liang and L. Futou, Differential game modelling of joint carbon reduction strategy and contract coordination based on low-carbon reference of consumers, J. Cleaner Prod., 277 (2020). doi: 10.1016/j. jclepro. 2020.123798. [22] L. Zheng, X. Chen and X. Wang, The role of co-opetition in low carbon manufacturing, European J. Oper. Res., 253 (2016), 392-403.  doi: 10.1016/j.ejor.2016.02.030. [23] S. Midya, S. K. Roy and V. F. Yu, Intuitionistic fuzzy multi-stage multi-objective fixed-charge solid transportation problem in a green supply chain, Internat. J. Machine Learning Cybernetics, 12 (2021), 699-717.  doi: 10.1007/s13042-020-01197-1. [24] A. Mondal and S. K. Roy, Application of Choquet integral in interval type-2 Pythagorean fuzzy sustainable supply chain management under risk, Internat. J. Intell. Syst., 37 (2022), 217-263.  doi: 10.1002/int.22623. [25] A. Mondal and S. K. Roy, Multi-objective sustainable opened- and closed-loop supply chain under mixed uncertainty during COVID-19 pandemic situation, Comput. Indust. Engrg., 159 (2021). doi: 10.1016/j. cie. 2021.107453. [26] A. Paul, M. Pervin, S. K. Roy, N. Maculan and G.-W. Weber, A green inventory model with the effect of carbon taxation, Ann. Oper. Res., 309 (2022), 233-248.  doi: 10.1007/s10479-021-04143-8. [27] H. Peng, T. Pang and J. Cong, Coordination contracts for a supply chain with yield uncertainty and low-carbon preference, J. Cleaner Prod., 205 (2018), 291-302.  doi: 10.1016/j.jclepro.2018.09.038. [28] X. Qian, F. T. S. 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, J. Cleaner Prod., 244 (2020). doi: 10.1016/j. jclepro. 2019.118715. [29] S. A. Raza and S. M. Govindaluri, Greening and price differentiation coordination in a supply chain with partial demand information and cannibalization, J. Cleaner Prod., 229 (2019), 706-726.  doi: 10.1016/j.jclepro.2019.04.371. [30] Y. Sun, Z. Liu and H. Yang, How does suppliers' fairness affect the relationship quality of agricultural product supply chains?, J. Food Quality, 2018 (2018), 1-15.  doi: 10.1155/2018/9313068. [31] E. B. Tirkolaee, A. Goli, P. Ghasemi and F. Goodarzian, Designing a sustainable closed-loop supply chain network of face masks during the COVID-19 pandemic: Pareto-based algorithms, J. Cleaner Prod., 333 (2022). doi: 10.1016/j. jclepro. 2021.130056. [32] N. Wang, Z.-P. Fan and X. Chen, Effect of fairness on channel choice of the mobile phone supply chain, Int. Trans. Oper. Res., 28 (2021), 2110-2138.  doi: 10.1111/itor.12660. [33] Q. Wang, D. Zhao and L. He, Contracting emission reduction for supply chains considering market low-carbon preference, J. Cleaner Prod., 120 (2016), 72-84.  doi: 10.1016/j.jclepro.2015.11.049. [34] Y. Wang, M. Sun, X. Yang and X. Yuan, Public awareness and willingness to pay for tackling smog pollution in China: A case study, J. Cleaner Prod., 112 (2016), 1627-1634.  doi: 10.1016/j.jclepro.2015.04.135. [35] Y. Wang, Z. Yu and L. Shen, Study on the decision-making and coordination of an e-commerce supply chain with manufacturer fairness concerns, Internat. J. Prod. Res., 57 (2019), 2788-2808.  doi: 10.1080/00207543.2018.1500043. [36] J. Wei, J. Zhao and Y. Li, Price and warranty period decisions for complementary products with horizontal firms' cooperation/noncooperation strategies, J. Cleaner Prod., 105 (2015), 86-102.  doi: 10.1016/j.jclepro.2014.09.059. [37] X. Xia, J. Ruan, Z. Juan, Y. Shi, X. Wang and F. T. S. Chan, Upstream-downstream joint carbon reduction strategies based on low-carbon promotion, Internat. J. Environ. Res. Public Health, 15 (2018). doi: 10.3390/ijerph15071351. [38] J. Xie, J. Li, L. Liang, X. Fang, G. Yang and L. Wei, Contracting emissions reduction supply chain based on market low-carbon preference and carbon intensity constraint, Asia-Pac. J. Oper. Res., 37 (2020), 34 pp. doi: 10.1142/S0217595920500037. [39] B. Yan, Y.-R. Chen and S.-Y. He, Decision making and coordination of fresh agriculture product supply chain considering fairness concerns, RAIRO Oper. Res., 54 (2020), 1231-1248.  doi: 10.1051/ro/2019031. [40] B. Yan, J. Wu, Z. Jin and S. He, Decision-making of fresh agricultural product supply chain considering the manufacturer's fairness concerns, 4OR, 18 (2020), 91-122.  doi: 10.1007/s10288-019-00409-x. [41] L. Yang, Q. Zhang and J. Ji, Pricing and carbon emission reduction decisions in supply chains with vertical and horizontal cooperation, Internat. J. Prod. Econ., 191 (2017), 286-297.  doi: 10.1016/j.ijpe.2017.06.021. [42] F. Yao, H. Gao, H. Jiang and Y. Zhou, Study on low-carbon supply chain coordination considering reference emission reduction effect, Asia-Pac. J. Oper. Res., 38 (2021), 21 pp. doi: 10.1142/S0217595920400229. [43] H. Yu, S. Bai and D. Chen, An optimal control model of the low-carbon supply chain: Joint emission reduction, pricing strategies, and new coordination contract design, IEEE Access, 8 (2020), 106273-106283.  doi: 10.1109/ACCESS.2020.3000482. [44] A. Z. Zeng and J. Hou, Procurement and coordination under imperfect quality and uncertain demand in reverse mobile phone supply chain, Internat. J. Prod. Econ., 209 (2019), 346-359.  doi: 10.1016/j.ijpe.2018.05.014. [45] L. Zhang, B. Xue and X. Liu, Carbon emission reduction with regard to retailer's fairness concern and subsidies, Sustainability, 10 (2018). doi: 10.3390/su10041209. [46] L. Zhang, H. Zhou, Y. Liu and R. Lu, Optimal environmental quality and price with consumer environmental awareness and retailer's fairness concerns in supply chain, J. Cleaner Prod., 213 (2019), 1063-1079.  doi: 10.1016/j.jclepro.2018.12.187. [47] X.-X. Zheng, D.-F. Li, Z. Liu, F. Jia and J.-B. Sheu, Coordinating a closed-loop supply chain with fairness concerns through variable-weighted Shapley values, Transport. Res. E, 126 (2019), 227-253.  doi: 10.1016/j.tre.2019.04.006. [48] Y. Zhou, M. Bao, X. Chen and X. Xu, Co-op advertising and emission reduction cost sharing contracts and coordination in low-carbon supply chain based on fairness concerns, J. Cleaner Prod., 133 (2016), 402-413.  doi: 10.1016/j.jclepro.2016.05.097. [49] Y. Zu, L. Chen and Y. Fan, Research on low-carbon strategies in supply chain with environmental regulations based on differential game, J. Cleaner Prod., 177 (2018), 527-546.  doi: 10.1016/j.jclepro.2017.12.220.

show all references

##### References:
 [1] F. X. Aguilar and R. P. Vlosky, Consumer willingness to pay price premiums for environmentally certified wood products in the U.S, Forest Policy Econ., 9 (2007), 1100-1112.  doi: 10.1016/j.forpol.2006.12.001. [2] M. Alinaghian and A. Goli, Location, allocation and routing of temporary health centers in rural areas in crisis, solved by improved harmony search algorithm, Internat. J. Comput. Intell. Syst., 10 (2017), 894-913.  doi: 10.2991/ijcis.2017.10.1.60. [3] L. Chen, J. Peng, Z. Liu and R. Zhao, Pricing and effort decisions for a supply chain with uncertain information, Internat. J. Comput. Intell. Syst., 55 (2017), 264-284.  doi: 10.1080/00207543.2016.1204475. [4] S. K. Das, M. Pervin, S. K. Roy and G. W. Weber, Multi-objective solid transportation-location problem with variable carbon emission in inventory management: A hybrid approach, Ann. Oper. Res., (2021), 1–27. doi: 10.1007/s10479-020-03809-z. [5] B. Du, Q. Liu and G. Li, Coordinating leader-follower supply chain with sustainable green technology innovation on their fairness concerns, Internat. J. Environ. Res. Public Health, 14 (2017). doi: 10.3390/ijerph14111357. [6] N. Du and Q. Han, Pricing and service quality guarantee decisions in logistics service supply chain with fairness concern, Asia-Pac. J. Oper. Res., 35 (2018), 41 pp. doi: 10.1142/S0217595918500367. [7] D. Ghosh and J. Shah, A comparative analysis of greening policies across supply chain structures, Internat. J. Prod. Econ., 135 (2012), 568-583.  doi: 10.1016/j.ijpe.2011.05.027. [8] S. Ghosh and S. K. Roy, Fuzzy-rough multi-objective product blending fixed-charge transportation problem with truck load constraints through transfer station, RAIRO Oper. Res., 55 (2021), S2923–S2952. doi: 10.1051/ro/2020129. [9] A. Goli and T. Keshavarz, Just-in-time scheduling in identical parallel machine sequence-dependent group scheduling problem, to appear, J. Ind. Manag. Optim. . doi: 10.3934/jimo. 2021124. [10] A. Goli and B. Malmir, A covering tour approach for disaster relief locating and routing with fuzzy demand, Internat. J. Intell. Transport. Syst. Res., 18 (2020), 140-152.  doi: 10.1007/s13177-019-00185-2. [11] A. Goli and H. Mohammadi, Developing a sustainable operational management system using hybrid Shapley value and Multimoora method: Case study petrochemical supply chain, Environ. Develop. Sustainability, (2021). doi: 10.1007/s10668-021-01844-9. [12] A. Goli, H. K. Zare, R. Tavakkoli-Moghaddamb and A. Sadeghieh, Hybrid artificial intelligence and robust optimization for a multi-objective product portfolio problem case study: The dairy products industry, Comput. Indust. Engrg., 137 (2019). doi: 10.1016/j. cie. 2019.106090. [13] R. Hammami, I. Nouira and Y. Frein, Effects of customers' environmental awareness and environmental regulations on the emission intensity and price of a product, Decision Sci., 49 (2018), 1116-1155.  doi: 10.1111/deci.12302. [14] Q. Han and Y. Wang, Decision and coordination in a low-carbon e-supply chain considering the manufacturer's carbon emission reduction behavior, Sustainability, 10 (2018). doi: 10.3390/su10051686. [15] J. Ji, Z. Zhang and L. Yang, Carbon emission reduction decisions in the retail-/dual-channel supply chain with consumers' preference, J. Cleaner Prod., 141 (2017), 852-867.  doi: 10.1016/j.jclepro.2016.09.135. [16] K. Kang, Y. Zhao, J. Zhang and C. Qiang, Evolutionary game theoretic analysis on low-carbon strategy for supply chain enterprises, J. Cleaner Prod., 230 (2019), 981-994.  doi: 10.1016/j.jclepro.2019.05.118. [17] E. Katok, T. Olsen and V. Pavlov, Wholesale pricing under mild and privately known concerns for fairness, Prod. Oper. Mgmt., 23 (2014), 285-302.  doi: 10.1111/j.1937-5956.2012.01388.x. [18] G. Li, H. Zheng, X. Ji and H. Li, Game theoretical analysis of firms' operational low-carbon strategy under various cap-and-trade mechanisms, J. Cleaner Prod., 197 (2018), 124-133.  doi: 10.1016/j.jclepro.2018.06.177. [19] H. Li, C. Wang, L. Xu and W. Ou, Pricing, carbon emission reduction, collection decision, and coordination in a low-carbon closed-loop supply chain, J. Renewable Sustainable Energy, 9 (2017). doi: 10.1063/1.4991668. [20] Q. Li, T. Xiao and Y. Qiu, Price and carbon emission reduction decisions and revenue-sharing contract considering fairness concerns, J. Cleaner Prod., 190 (2018), 303-314.  doi: 10.1016/j.jclepro.2018.04.032. [21] L. Liang and L. Futou, Differential game modelling of joint carbon reduction strategy and contract coordination based on low-carbon reference of consumers, J. Cleaner Prod., 277 (2020). doi: 10.1016/j. jclepro. 2020.123798. [22] L. Zheng, X. Chen and X. Wang, The role of co-opetition in low carbon manufacturing, European J. Oper. Res., 253 (2016), 392-403.  doi: 10.1016/j.ejor.2016.02.030. [23] S. Midya, S. K. Roy and V. F. Yu, Intuitionistic fuzzy multi-stage multi-objective fixed-charge solid transportation problem in a green supply chain, Internat. J. Machine Learning Cybernetics, 12 (2021), 699-717.  doi: 10.1007/s13042-020-01197-1. [24] A. Mondal and S. K. Roy, Application of Choquet integral in interval type-2 Pythagorean fuzzy sustainable supply chain management under risk, Internat. J. Intell. Syst., 37 (2022), 217-263.  doi: 10.1002/int.22623. [25] A. Mondal and S. K. Roy, Multi-objective sustainable opened- and closed-loop supply chain under mixed uncertainty during COVID-19 pandemic situation, Comput. Indust. Engrg., 159 (2021). doi: 10.1016/j. cie. 2021.107453. [26] A. Paul, M. Pervin, S. K. Roy, N. Maculan and G.-W. Weber, A green inventory model with the effect of carbon taxation, Ann. Oper. Res., 309 (2022), 233-248.  doi: 10.1007/s10479-021-04143-8. [27] H. Peng, T. Pang and J. Cong, Coordination contracts for a supply chain with yield uncertainty and low-carbon preference, J. Cleaner Prod., 205 (2018), 291-302.  doi: 10.1016/j.jclepro.2018.09.038. [28] X. Qian, F. T. S. 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, J. Cleaner Prod., 244 (2020). doi: 10.1016/j. jclepro. 2019.118715. [29] S. A. Raza and S. M. Govindaluri, Greening and price differentiation coordination in a supply chain with partial demand information and cannibalization, J. Cleaner Prod., 229 (2019), 706-726.  doi: 10.1016/j.jclepro.2019.04.371. [30] Y. Sun, Z. Liu and H. Yang, How does suppliers' fairness affect the relationship quality of agricultural product supply chains?, J. Food Quality, 2018 (2018), 1-15.  doi: 10.1155/2018/9313068. [31] E. B. Tirkolaee, A. Goli, P. Ghasemi and F. Goodarzian, Designing a sustainable closed-loop supply chain network of face masks during the COVID-19 pandemic: Pareto-based algorithms, J. Cleaner Prod., 333 (2022). doi: 10.1016/j. jclepro. 2021.130056. [32] N. Wang, Z.-P. Fan and X. Chen, Effect of fairness on channel choice of the mobile phone supply chain, Int. Trans. Oper. Res., 28 (2021), 2110-2138.  doi: 10.1111/itor.12660. [33] Q. Wang, D. Zhao and L. He, Contracting emission reduction for supply chains considering market low-carbon preference, J. Cleaner Prod., 120 (2016), 72-84.  doi: 10.1016/j.jclepro.2015.11.049. [34] Y. Wang, M. Sun, X. Yang and X. Yuan, Public awareness and willingness to pay for tackling smog pollution in China: A case study, J. Cleaner Prod., 112 (2016), 1627-1634.  doi: 10.1016/j.jclepro.2015.04.135. [35] Y. Wang, Z. Yu and L. Shen, Study on the decision-making and coordination of an e-commerce supply chain with manufacturer fairness concerns, Internat. J. Prod. Res., 57 (2019), 2788-2808.  doi: 10.1080/00207543.2018.1500043. [36] J. Wei, J. Zhao and Y. Li, Price and warranty period decisions for complementary products with horizontal firms' cooperation/noncooperation strategies, J. Cleaner Prod., 105 (2015), 86-102.  doi: 10.1016/j.jclepro.2014.09.059. [37] X. Xia, J. Ruan, Z. Juan, Y. Shi, X. Wang and F. T. S. Chan, Upstream-downstream joint carbon reduction strategies based on low-carbon promotion, Internat. J. Environ. Res. Public Health, 15 (2018). doi: 10.3390/ijerph15071351. [38] J. Xie, J. Li, L. Liang, X. Fang, G. Yang and L. Wei, Contracting emissions reduction supply chain based on market low-carbon preference and carbon intensity constraint, Asia-Pac. J. Oper. Res., 37 (2020), 34 pp. doi: 10.1142/S0217595920500037. [39] B. Yan, Y.-R. Chen and S.-Y. He, Decision making and coordination of fresh agriculture product supply chain considering fairness concerns, RAIRO Oper. Res., 54 (2020), 1231-1248.  doi: 10.1051/ro/2019031. [40] B. Yan, J. Wu, Z. Jin and S. He, Decision-making of fresh agricultural product supply chain considering the manufacturer's fairness concerns, 4OR, 18 (2020), 91-122.  doi: 10.1007/s10288-019-00409-x. [41] L. Yang, Q. Zhang and J. Ji, Pricing and carbon emission reduction decisions in supply chains with vertical and horizontal cooperation, Internat. J. Prod. Econ., 191 (2017), 286-297.  doi: 10.1016/j.ijpe.2017.06.021. [42] F. Yao, H. Gao, H. Jiang and Y. Zhou, Study on low-carbon supply chain coordination considering reference emission reduction effect, Asia-Pac. J. Oper. Res., 38 (2021), 21 pp. doi: 10.1142/S0217595920400229. [43] H. Yu, S. Bai and D. Chen, An optimal control model of the low-carbon supply chain: Joint emission reduction, pricing strategies, and new coordination contract design, IEEE Access, 8 (2020), 106273-106283.  doi: 10.1109/ACCESS.2020.3000482. [44] A. Z. Zeng and J. Hou, Procurement and coordination under imperfect quality and uncertain demand in reverse mobile phone supply chain, Internat. J. Prod. Econ., 209 (2019), 346-359.  doi: 10.1016/j.ijpe.2018.05.014. [45] L. Zhang, B. Xue and X. Liu, Carbon emission reduction with regard to retailer's fairness concern and subsidies, Sustainability, 10 (2018). doi: 10.3390/su10041209. [46] L. Zhang, H. Zhou, Y. Liu and R. Lu, Optimal environmental quality and price with consumer environmental awareness and retailer's fairness concerns in supply chain, J. Cleaner Prod., 213 (2019), 1063-1079.  doi: 10.1016/j.jclepro.2018.12.187. [47] X.-X. Zheng, D.-F. Li, Z. Liu, F. Jia and J.-B. Sheu, Coordinating a closed-loop supply chain with fairness concerns through variable-weighted Shapley values, Transport. Res. E, 126 (2019), 227-253.  doi: 10.1016/j.tre.2019.04.006. [48] Y. Zhou, M. Bao, X. Chen and X. Xu, Co-op advertising and emission reduction cost sharing contracts and coordination in low-carbon supply chain based on fairness concerns, J. Cleaner Prod., 133 (2016), 402-413.  doi: 10.1016/j.jclepro.2016.05.097. [49] Y. Zu, L. Chen and Y. Fan, Research on low-carbon strategies in supply chain with environmental regulations based on differential game, J. Cleaner Prod., 177 (2018), 527-546.  doi: 10.1016/j.jclepro.2017.12.220.
Low Carbon Supply Chain Structure of Market Segments
The impact of the ratio of elasticity coefficient to sensitivity coefficient on the optimal price and yield
The impact of the ratio of elasticity coefficient to sensitivity coefficient on the optimal wholesale price and the supply chain profit
The impact of fairness concern coefficient on the optimal price, yield and profit
The impact of low carbon preferences on the optimal price, yield
The impact of low carbon preferences on the optimal wholesale price and the supply chain profit
The impact of FC on the optimal carbon emission
The impact of LS & DI on market demand
Comparisons of related literature
 References LSC FC Obj.F Uncertainty Method Katok et al. (2014) [17] - M D PEC BG Zhou et al. (2016) [48] LR & DI, LS R D MP SG Ji et al. (2017) [15] LR & DI, LS - D PEC SG H. Li et al. (2017) [19] LR & DI M C - SG B. Du et al. (2017) [5] LS M, R D PEC SG Xia et al. (2018) [37] LR & DI, LS - C, D MP DG Han & Wang (2018) [14] LR & DI, LS - C, D PEC SG Yu et al. (2020) [43] LR & DI, LS - C, D PEC DG Ghosh et al. (2021) [8] LS - - - FM Midya et al. (2021) [23] LS - D MP FM Qian et al. (2020) [28] LR & DI M, R C, D PEC SG Paul et al. (2021) [26] LS - D MP EOQ Yao et al. (2021) [42] LR & DI, LS - C, D MP, PEC DG This work LR & DI, LS M, R C, D MP, PEC SG
 References LSC FC Obj.F Uncertainty Method Katok et al. (2014) [17] - M D PEC BG Zhou et al. (2016) [48] LR & DI, LS R D MP SG Ji et al. (2017) [15] LR & DI, LS - D PEC SG H. Li et al. (2017) [19] LR & DI M C - SG B. Du et al. (2017) [5] LS M, R D PEC SG Xia et al. (2018) [37] LR & DI, LS - C, D MP DG Han & Wang (2018) [14] LR & DI, LS - C, D PEC SG Yu et al. (2020) [43] LR & DI, LS - C, D PEC DG Ghosh et al. (2021) [8] LS - - - FM Midya et al. (2021) [23] LS - D MP FM Qian et al. (2020) [28] LR & DI M, R C, D PEC SG Paul et al. (2021) [26] LS - D MP EOQ Yao et al. (2021) [42] LR & DI, LS - C, D MP, PEC DG This work LR & DI, LS M, R C, D MP, PEC SG
Basic notation definition
 Notations Definition Sets i i={h, l}; i=h represents the highly dynamic market; i=l represents the low dynamic market y y={C, R, M}; y=C means the centralized decision-making; y=R means the decentralized decision of the retailer's fairness concern; y=M means the decentralized decision of the manufacturer's fairness concern Parameters $\alpha$ Share of low carbon products in highly dynamic market $\beta$ Price elasticity coefficient of demand in consumer markets $\gamma$ Price sensitivity coefficient of counterparty in supply chains $\varepsilon _i$ Consumers' perception of carbon emissions per unit of low-carbon products in i market, where i=h, l $\lambda$ The retailer fairness concern coefficient $\eta$ The manufacturer fairness concern coefficient $\eta _i$ i=h represents the manufacturer's fairness concern when the retailer sell to highly dynamic market; i=l represents the manufacturer's fairness concern when the retailer sell to lowly dynamic market C The unit production cost of products e Low-carbon level of products produced by the manufacturer k LR & DI coefficient $\theta$ Share of LR & DI in highly dynamic market I LR & DI of low carbon products Q Total demand of consumer markets Decision variables $\omega _y$ In the scenario of y, the wholesale price set by the manufacturer, where y=R, M $P _i$ The retailer's price to the i market, where i=h, l $P _{yi}$ In the scenario of y, the retailer's price to the i market, where i=C, R, M; i=h, l $q _i$ The manufacturer's output to the i market, where i=h, l $q _{yi}$ In the scenario of y, the manufacturer's output to the i market, where i=C, R, M; i=h, l $e _y$ In the scenario of y, the optimal low carbon level of products produced by manufacturers, where y=C, R, M Functions $Pi _i^y$ In the scenario of y, the profit function of the retailer for i market, where i=R, M; i=h, l $Pi _M$ In decentralized decision-making, the manufacturer's profit function $Pi _R$ In decentralized decision-making, the retailer's profit function for the whole consumer market $U _i^y$ In the scenario of y, the utility of the retailer for i market, where i=R, M; i=h, l $U _M$ In decentralized decision-making, the manufacturer's utility function $U _R$ In decentralized decision-making, the retailer's utility function for the whole consumer market
 Notations Definition Sets i i={h, l}; i=h represents the highly dynamic market; i=l represents the low dynamic market y y={C, R, M}; y=C means the centralized decision-making; y=R means the decentralized decision of the retailer's fairness concern; y=M means the decentralized decision of the manufacturer's fairness concern Parameters $\alpha$ Share of low carbon products in highly dynamic market $\beta$ Price elasticity coefficient of demand in consumer markets $\gamma$ Price sensitivity coefficient of counterparty in supply chains $\varepsilon _i$ Consumers' perception of carbon emissions per unit of low-carbon products in i market, where i=h, l $\lambda$ The retailer fairness concern coefficient $\eta$ The manufacturer fairness concern coefficient $\eta _i$ i=h represents the manufacturer's fairness concern when the retailer sell to highly dynamic market; i=l represents the manufacturer's fairness concern when the retailer sell to lowly dynamic market C The unit production cost of products e Low-carbon level of products produced by the manufacturer k LR & DI coefficient $\theta$ Share of LR & DI in highly dynamic market I LR & DI of low carbon products Q Total demand of consumer markets Decision variables $\omega _y$ In the scenario of y, the wholesale price set by the manufacturer, where y=R, M $P _i$ The retailer's price to the i market, where i=h, l $P _{yi}$ In the scenario of y, the retailer's price to the i market, where i=C, R, M; i=h, l $q _i$ The manufacturer's output to the i market, where i=h, l $q _{yi}$ In the scenario of y, the manufacturer's output to the i market, where i=C, R, M; i=h, l $e _y$ In the scenario of y, the optimal low carbon level of products produced by manufacturers, where y=C, R, M Functions $Pi _i^y$ In the scenario of y, the profit function of the retailer for i market, where i=R, M; i=h, l $Pi _M$ In decentralized decision-making, the manufacturer's profit function $Pi _R$ In decentralized decision-making, the retailer's profit function for the whole consumer market $U _i^y$ In the scenario of y, the utility of the retailer for i market, where i=R, M; i=h, l $U _M$ In decentralized decision-making, the manufacturer's utility function $U _R$ In decentralized decision-making, the retailer's utility function for the whole consumer market
Parameter Initial Value
 Parameters Q e $\lambda$ $\lambda '$ $\eta$ C k I $\alpha$ $\beta$ $\gamma$ $\varepsilon _h$ $\varepsilon _l$ Value 5 1 0.5 1/3 0.5 2 5 25 0.6 0.3 0.4 0.8 0.4
 Parameters Q e $\lambda$ $\lambda '$ $\eta$ C k I $\alpha$ $\beta$ $\gamma$ $\varepsilon _h$ $\varepsilon _l$ Value 5 1 0.5 1/3 0.5 2 5 25 0.6 0.3 0.4 0.8 0.4
Results of LINGO and MATLAB optimal values
 Model Method Parameters $P_h$ $P_l$ $q_h$ $q_l$ $\Pi$ Model C L $\beta /\gamma$ 10.333 9.167 2.812 2.059 32.794 $\varepsilon _i$ 19.2 17.8 5.16 4.74 183.444 M $\beta /\gamma$ 11.25 8.274 3.333 2.867 34.93 $\varepsilon _i$ 21.09 20.02 6.774 5.574 248.1 DR L $\beta /\gamma$ 11.541 8.112 2.898 2.532 36.441 $\lambda$ 20.72 19.32 5.31 4.89 204.5 $\varepsilon _i$ 22.69 21.32 5.417 4.983 244.498 M $\beta /\gamma$ 13.34 12.87 3.333 2.917 41.46 $\lambda$ 20.743 19.333 5.315 4.894 204.778 $\varepsilon _i$ 24.82 23.82 6.982 5.782 311 DM L $\beta /\gamma$ 16.2 14.8 3.4 3.067 52.763 $\eta$ 16.49 15.09 4.89 4.47 148.1 $\varepsilon _i$ 18.69 17.29 5.11 4.69 176.596 M $\beta /\gamma$ 16.54 15.48 3.464 3.081 57.28 $\eta$ 18.6 17.4 5.06 4.7 155.9 $\varepsilon _i$ 20.82 19.79 6.686 5.456 243.5
 Model Method Parameters $P_h$ $P_l$ $q_h$ $q_l$ $\Pi$ Model C L $\beta /\gamma$ 10.333 9.167 2.812 2.059 32.794 $\varepsilon _i$ 19.2 17.8 5.16 4.74 183.444 M $\beta /\gamma$ 11.25 8.274 3.333 2.867 34.93 $\varepsilon _i$ 21.09 20.02 6.774 5.574 248.1 DR L $\beta /\gamma$ 11.541 8.112 2.898 2.532 36.441 $\lambda$ 20.72 19.32 5.31 4.89 204.5 $\varepsilon _i$ 22.69 21.32 5.417 4.983 244.498 M $\beta /\gamma$ 13.34 12.87 3.333 2.917 41.46 $\lambda$ 20.743 19.333 5.315 4.894 204.778 $\varepsilon _i$ 24.82 23.82 6.982 5.782 311 DM L $\beta /\gamma$ 16.2 14.8 3.4 3.067 52.763 $\eta$ 16.49 15.09 4.89 4.47 148.1 $\varepsilon _i$ 18.69 17.29 5.11 4.69 176.596 M $\beta /\gamma$ 16.54 15.48 3.464 3.081 57.28 $\eta$ 18.6 17.4 5.06 4.7 155.9 $\varepsilon _i$ 20.82 19.79 6.686 5.456 243.5
Results of LINGO and MATLAB optimal values
 Model Parameters $P_h$ $P_l$ $q_h$ $q_l$ $\Pi$ Model C $\beta /\gamma$ 8.874% 10.793% 18.528% 39.242% 6.513% $\varepsilon _i$ 9.844% 12.472% 31.279% 17.595% 35.246% DR $\beta /\gamma$ 15.588% 58.654% 15.010% 15.205% 13.773% $\lambda$ 0.111% 0.067% 0.094% 0.082% 1.359% $\varepsilon _i$ 9.387% 11.726% 28.891% 16.035% 27.199% DM $\beta /\gamma$ 2.099% 4.595% 1.882% 0.465% 8.561% $\eta$ 12.796% 15.308% 3.476% 5.145% 5.267% $\varepsilon _i$ 11.396% 14.459% 30.841% 16.333% 37.885%
 Model Parameters $P_h$ $P_l$ $q_h$ $q_l$ $\Pi$ Model C $\beta /\gamma$ 8.874% 10.793% 18.528% 39.242% 6.513% $\varepsilon _i$ 9.844% 12.472% 31.279% 17.595% 35.246% DR $\beta /\gamma$ 15.588% 58.654% 15.010% 15.205% 13.773% $\lambda$ 0.111% 0.067% 0.094% 0.082% 1.359% $\varepsilon _i$ 9.387% 11.726% 28.891% 16.035% 27.199% DM $\beta /\gamma$ 2.099% 4.595% 1.882% 0.465% 8.561% $\eta$ 12.796% 15.308% 3.476% 5.145% 5.267% $\varepsilon _i$ 11.396% 14.459% 30.841% 16.333% 37.885%
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