# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2021229
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## Low carbon joint strategy and coordination for a dyadic supply chain with Nash bargaining fairness

 1 School of Management, Guangdong University of Technology, 510520, Guangzhou, China 2 Faculty of Applied Mathematics, Guangdong University of Technology, 510520, Guangzhou, China 3 Department of Mathematics, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia

*Corresponding author: Rui Hou

Received  December 2020 Revised  October 2021 Early access January 2022

Fund Project: The first author is supported by the Chinese National Funding of Social Science grant 19BGL094

In the paper, fairness concern criterion is utilized to explore the coordination of a dyadic supply chain with a fairness-concerned retailer (acting as a newsvendor), who is committed to low carbon efforts. Two models are developed for stochastic demand disturbances in the forms of multiplicative case and additive case, respectively. Firstly, the optimal joint decision of the retailer and the supply chain are proposed in two scenarios, i.e., decentralized decision and the centralized decision. Secondly, in order to realize channel coordination, the contract of revenue sharing combined with the mechanism of low-carbon cost sharing is designed. Moreover, the influences of the retailer's fairness concern and bargaining power on the joint decision and the contract parameters are also investigated. Finally, numerical examples are given to illustrate the theoretical results and some suggestions to supply chain management are also provided. The results show that the revenue sharing contract can make the supply chain achieved coordination with the cost sharing mechanism of low-carbon efforts. Furthermore, the optimal low-carbon effort level and ordering quantity decrease in terms of fairness-concerned parameter and Nash bargaining power parameter, which increases in unit cost. However, the optimal pricing makes the opposite change.

Citation: Jianxin Chen, Lin Sun, Tonghua Zhang, Rui Hou. Low carbon joint strategy and coordination for a dyadic supply chain with Nash bargaining fairness. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2021229
##### References:
 [1] P. Abad, Optimal policy for a reseller when the supplier offers a temporary reduction in price, Decision Sciences, 28 (1997), 637-653.  doi: 10.1111/j.1540-5915.1997.tb01325.x. [2] V. Agrawal and S. Seshadri, Impact of uncertainty and risk aversion on price and order quantity in the newsvendor problem, Manufacturing and Service Operations Management, 2 (2000), 410-423.  doi: 10.1287/msom.2.4.410.12339. [3] D. Brécard, B. Hlaimi, S. Lucas, Y. Perraudeau and F. Salladarré, Determinants of demand for green products: An application to eco-label demand for fish in europe, Ecological Economics, 69 (2009), 115-125.  doi: 10.1016/j.ecolecon.2009.07.017. [4] G. Cachon, Supply chain coordination with contracts, Handbooks in Operations Research and Management Science, 11 (2003), 227-339.  doi: 10.1016/S0927-0507(03)11006-7. [5] O. Caliskan-Demirag, Y. Chen and J. Li, Channel coordination under fairness concerns and nonlinear demand, European J. Oper. Res., 207 (2010), 1321-1326.  doi: 10.1016/j.ejor.2010.07.017. [6] C. Camerer and R. Thaler, Anomalies: Ultimatums, dictators and manners, The Journal of Economic Perspectives, 9 (1995), 209-219.  doi: 10.1257/jep.9.2.209. [7] E. Cao, L. Du and J. Ruan, Financing preferences and performance for an emission-dependent supply chain: Supplier vs. bank, International Journal of Production Economics, 208 (2019), 383-399.  doi: 10.1016/j.ijpe.2018.08.001. [8] E. Cao and M. Yu, The bright side of carbon emission permits on supply chain financing and performance, Omega, 88 (2019), 24-39.  doi: 10.1016/j.omega.2018.11.020. [9] C. Chen, Design for the environment: A quality-based model for green product development, Management Science, 47 (2001), 250-263.  doi: 10.1287/mnsc.47.2.250.9841. [10] J. Chen, T. Zhang, Y. Zhou and Y. Zhong, Joint decision of pricing and ordering in stochastic demand with nash bargaining fairness, Comput. Oper. Res., 123 (2020), 105037.  doi: 10.1016/j.cor.2020.105037. [11] J. Chen, Y. Zhou and Y. Zhong, A pricing/ordering model for a dyadic supply chain with buyback guarantee financing and fairness concerns, International Journal of Production Research, 55 (2017), 5287-5304.  doi: 10.1080/00207543.2017.1308571. [12] Y. Chen, M. Xu and Z. Zhang, Technical note-a risk-averse newsvendor model under the cvar criterion, Operations Research, 57 (2009), 1040-1044.  doi: 10.1287/opre.1080.0603. [13] C. Chung, Y. Chang and C. Wu, Competitive pricing and ordering decisions in a multiple-channel supply chain, International Journal of Production Economics, 154 (2014), 156-165. [14] T. Cui, J. Raju and Z. Zhang, Fairness and channel coordination, Management Science, 53 (2007), 1303-1314. [15] J. Dai, Revenue sharing contract for a supply chain with demand depending on promotion and pricing (in chinese), Chinese Journal of Management, 15 (2018), 395-408. [16] J. Dai and W. Meng, A risk-averse newsvendor model under marketing-dependency and price-dependency, International Journal of Production Economics, 160 (2015), 220-229.  doi: 10.1016/j.ijpe.2014.11.006. [17] C. Dong, B. Shen, P. Chow, L. Yang and C. Ng, Sustainability investment under cap-and-trade regulation, Ann. Oper. Res., 240 (2016), 509-531.  doi: 10.1007/s10479-013-1514-1. [18] S. Du, L. Hu and L. Wang, Low-carbon supply policies and supply chain performance with carbon concerned demand, Ann. Oper. Res., 255 (2017), 569-590.  doi: 10.1007/s10479-015-1988-0. [19] S. Du, T. Nie and C. Chu, Newsvendor model for a dyadic supply chain with nash bargaining fairness concerns, International Journal of Production Research, 52 (2014), 5070-5085. [20] E. Fehr and K. Schmidt, A theory of fairness, competition, and cooperation, Advances in Behavioral Economics, 114 (1999), 817-868.  doi: 10.2307/j.ctvcm4j8j.14. [21] B. Giri, S. Bardhan and T. Maiti, Coordinating a two-echelon supply chain through different contracts under price and promotional effort-dependent demand, Int. J. Oper. Res., 23 (2015), 181-199.  doi: 10.1504/IJOR.2015.069179. [22] W. Guth, On ultimatum bargaining experiments-a personal review, Journal of Economic Behavior and Organization, 27 (1995), 329-344.  doi: 10.1016/0167-2681(94)00071-L. [23] T. Ho, X. Su and Y. Wu, Distributional and peer-induced fairness in supply chain contract design, Production and Operations Management, 23 (2014), 161-175. [24] 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. [25] X. Hu and P. Su, The newsvendor's joint procurement and pricing problem under price-sensitive stochastic demand and purchase price uncertainty, Omega, 79 (2018), 81-90.  doi: 10.1016/j.omega.2017.08.002. [26] Y. Jiang and D. Klabjan, Optimal Emissions Reduction Investment Under Green House Gas Emissions Regulations, Ph.D thesis, Northwestern University in Evanston, 2012. [27] D. Kahneman and A. Tversky, Prospect theory: An analysis of decision under risk, Econometrica, 47 (1979), 263-291.  doi: 10.2307/1914185. [28] E. Katok, T. Olsen and V. Pavlov, Wholesale pricing under mild and privately known concerns for fairness, Production and Operations Management, 23 (2014), 285-302.  doi: 10.1111/j.1937-5956.2012.01388.x. [29] E. Katok and V. Pavlov, Fairness in supply chain contracts: A laboratory study, Journal of Operations Management, 31 (2013), 129-137.  doi: 10.1016/j.jom.2013.01.001. [30] M. Khouja, The single-period (news-vendor) problem: Literature review and suggestions for future research, Omega, 27 (1999), 537-553.  doi: 10.1016/S0305-0483(99)00017-1. [31] H. Krishnan, R. Kapuscinski and D. Butz, Coordinating contracts for decentralized supply chains with retailer promotional effort, Management Science, 50 (2004), 48-63.  doi: 10.1287/mnsc.1030.0154. [32] N. Kumar, The power of trust in manufacturer-retailer relationships, Harvard Business Review, 74 (1996), 92-106. [33] M. Laroche, J. Bergeron and G. Forleo, Targeting consumers who are willing to pay more for environmentally friendly products, Journal of Consumer marketing, 18 (2001), 503-520.  doi: 10.1108/EUM0000000006155. [34] J. Li, J. Lu, Q. Wang and C. Li, Quality and pricing decisions in a two-echelon supply chain with Nash bargaining fairness concerns, Discrete Dyn. Nat. Soc., 2018 (2018), 4267305.  doi: 10.1155/2018/4267305. [35] Z. Liu, T. Anderson and J. Cruz, Consumer environmental awareness and competition in two-stage supply chains, European J. Oper. Res., 218 (2012), 602-613.  doi: 10.1016/j.ejor.2011.11.027. [36] C. Loch and Y. Wu, Social preferences and supply chain performance: An experimental study, Management Science, 54 (2008), 1835-1849.  doi: 10.1287/mnsc.1080.0910. [37] C. Luo and X. Tian, Operational strategy of supply chain with price-dependent stochastic demand under the cvar criterion(in chinese), Management Review, 27 (2015), 167-176. [38] J. Ma and L. Xie, The impact of loss sensitivity on a mobile phone supply chain system stability based on the chaos theory, Commun. Nonlinear Sci. Numer. Simul., 55 (2018), 194-205.  doi: 10.1016/j.cnsns.2017.06.030. [39] S. Madani and M. Barzoki, Sustainable supply chain management with pricing, greening and governmental tariffs determining strategies: A game-theoretic approach, Computers and Industrial Engineering, 105 (2017), 287-298.  doi: 10.1016/j.cie.2017.01.017. [40] G. Mark and M. Sharafali, Price-dependent inventory models with discount offers at random times, Production and Operations Management, 11 (2002), 139-156. [41] J. Nash, The bargaining problem, Econometrica, 18 (1950), 155-162.  doi: 10.2307/1907266. [42] J. Nash, Two-person cooperative games, Econometrica, 21 (1953), 128-140.  doi: 10.2307/1906951. [43] W. Nordhaus, To slow or not to slow: The economics of the greenhouse effect, The Economic Journal, 101 (1991), 920-937.  doi: 10.2307/2233864. [44] A. Olmstead and P. Rhode, Rationing without government: The west coast gas famine of 1920, The American economic review, 75 (1985), 1044-1055. [45] V. Pavlov and E. Katok, Fairness and coordination failures in supply chain contracts, 2011. doi: 10.2139/ssrn.2623821. [46] N. Petruzzi and M. Dada, Pricing and the news vendor problem: A review with extensions, Operations Research, 47 (1999), 183-194. [47] X. Qian, F. 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. [48] M. Rabin, Incorporating fairness into game theory and economics, American Economic Review, 83 (1993), 1281-1302.  doi: 10.2307/j.ctvcm4j8j.15. [49] C. Roheim, F. Asche and J. Santos, The elusive price premium for ecolabelled products: Evidence from seafood in the uk market, Journal of Agricultural Economics, 62 (2011), 655-668.  doi: 10.1111/j.1477-9552.2011.00299.x. [50] B. Ruffle, More is better, but fair is fair: Tipping in dictator and ultimatum games, Games and Economic Behavior, 23 (1998), 247-265.  doi: 10.1006/game.1997.0630. [51] L. Scheer, N. Kumar and J. Steenkamp, Reactions to perceived inequity in us and dutch inter organizational relationships, Academy of Management Journal, 46 (2003), 303-316. [52] M. Schweitzer and G. Cachon, Decision bias in the newsvendor problem with a known demand distribution: Experimental evidence, Management Science, 46 (2000), 404-420.  doi: 10.1287/mnsc.46.3.404.12070. [53] H. Shan, C. Zhang and G. Wei, Bundling or unbundling? pricing strategy for complementary products in a green supply chain, Sustainability, 12 (2020), 1331.  doi: 10.3390/su12041331. [54] G. Singer and E. Khmelnitsky, A production-inventory problem with price-sensitive demand, Appl. Math. Model., 89 (2021), 688-699.  doi: 10.1016/j.apm.2020.06.072. [55] J. Spengler, Vertical integration and antitrust policy, Journal of Political Economy, 58 (1950), 347-352.  doi: 10.1086/256964. [56] A. Taylor, Sale timing in a supply chain: When to sell to the retailer, Manufacturing and Service Operations Management, 8 (2006), 23-42.  doi: 10.1287/msom.1050.0089. [57] R. Thaler, The ultimatum game, The Journal of Economic Perspectives, 2 (1988), 195-206. [58] A. Tversky and D. Kahneman, A Rational choice and the framing of decisions, NATO Adv. Sci. Inst. Ser. F: Comput. Systems Sci., 56 (1989), 81-126. [59] C. Wang and X. Chen, Joint order and pricing decisions for fresh produce with put option contracts, Journal of the Operational Research Society, 69 (2018), 474-484. [60] C. Wang, S. Webster and N. Suresh, Would a risk-averse newsvendor order less at a higher selling price?, European J. Oper. Res., 196 (2009), 544-553.  doi: 10.1016/j.ejor.2008.04.002. [61] D. Wu, Li. Yang and D. Olson, Green supply chain management under capital constraint, International Journal of Production Economics, 215 (2019), 3-10. [62] J. Xu, Y. Chen and Q. Bai, A two-echelon sustainable supply chain coordination under cap-and-trade regulation, Journal of Cleaner Production, 135 (2016), 42-56.  doi: 10.1016/j.jclepro.2016.06.047. [63] M. Xu, Y. Chen and X. Xu, The effect of demand uncertainty in a price setting newsvendor model, European J. Oper. Res., 207 (2010), 946-957.  doi: 10.1016/j.ejor.2010.06.024. [64] X. Xu, P. He, H. Xu and Q. Zhang, Supply chain coordination with green technology under cap-and-trade regulation, International Journal of Production Economics, 183 (2017), 433-442.  doi: 10.1016/j.ijpe.2016.08.029. [65] H. Yang, L. Miao and C. Zhao, The credit strategy of a green supply chain based on capital constraints, Journal of Cleaner Production, 224 (2019), 930-939.  doi: 10.1016/j.jclepro.2019.03.214. [66] J. Yang, J. Xie, X. Deng and H. Xiong, Cooperative advertising in a distribution channel with fairness concerns, European J. Oper. Res., 227 (2013), 401-407.  doi: 10.1016/j.ejor.2012.12.011. [67] L. Yao, Y. Chen and H. Han, Analysis of a supply contract for coordinating the newsvendor with price dependent demand, 2005. Available from: http://www.se.cuhk.edu.hk/yhchen/contractl20502. [68] Y. Zhao, 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, Journal of Cleaner Production, 133 (2016), 402-413.  doi: 10.1016/j.jclepro.2016.05.097. [69] Y. Zhou and X. Ye, Differential game model of joint emission reduction strategies and contract design in a dual-channel supply chain, Journal of Cleaner Production, 190 (2018), 592-607.  doi: 10.1016/j.jclepro.2018.04.133.

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##### References:
 [1] P. Abad, Optimal policy for a reseller when the supplier offers a temporary reduction in price, Decision Sciences, 28 (1997), 637-653.  doi: 10.1111/j.1540-5915.1997.tb01325.x. [2] V. Agrawal and S. Seshadri, Impact of uncertainty and risk aversion on price and order quantity in the newsvendor problem, Manufacturing and Service Operations Management, 2 (2000), 410-423.  doi: 10.1287/msom.2.4.410.12339. [3] D. Brécard, B. Hlaimi, S. Lucas, Y. Perraudeau and F. Salladarré, Determinants of demand for green products: An application to eco-label demand for fish in europe, Ecological Economics, 69 (2009), 115-125.  doi: 10.1016/j.ecolecon.2009.07.017. [4] G. Cachon, Supply chain coordination with contracts, Handbooks in Operations Research and Management Science, 11 (2003), 227-339.  doi: 10.1016/S0927-0507(03)11006-7. [5] O. Caliskan-Demirag, Y. Chen and J. Li, Channel coordination under fairness concerns and nonlinear demand, European J. Oper. Res., 207 (2010), 1321-1326.  doi: 10.1016/j.ejor.2010.07.017. [6] C. Camerer and R. Thaler, Anomalies: Ultimatums, dictators and manners, The Journal of Economic Perspectives, 9 (1995), 209-219.  doi: 10.1257/jep.9.2.209. [7] E. Cao, L. Du and J. Ruan, Financing preferences and performance for an emission-dependent supply chain: Supplier vs. bank, International Journal of Production Economics, 208 (2019), 383-399.  doi: 10.1016/j.ijpe.2018.08.001. [8] E. Cao and M. Yu, The bright side of carbon emission permits on supply chain financing and performance, Omega, 88 (2019), 24-39.  doi: 10.1016/j.omega.2018.11.020. [9] C. Chen, Design for the environment: A quality-based model for green product development, Management Science, 47 (2001), 250-263.  doi: 10.1287/mnsc.47.2.250.9841. [10] J. Chen, T. Zhang, Y. Zhou and Y. Zhong, Joint decision of pricing and ordering in stochastic demand with nash bargaining fairness, Comput. Oper. Res., 123 (2020), 105037.  doi: 10.1016/j.cor.2020.105037. [11] J. Chen, Y. Zhou and Y. Zhong, A pricing/ordering model for a dyadic supply chain with buyback guarantee financing and fairness concerns, International Journal of Production Research, 55 (2017), 5287-5304.  doi: 10.1080/00207543.2017.1308571. [12] Y. Chen, M. Xu and Z. Zhang, Technical note-a risk-averse newsvendor model under the cvar criterion, Operations Research, 57 (2009), 1040-1044.  doi: 10.1287/opre.1080.0603. [13] C. Chung, Y. Chang and C. Wu, Competitive pricing and ordering decisions in a multiple-channel supply chain, International Journal of Production Economics, 154 (2014), 156-165. [14] T. Cui, J. Raju and Z. Zhang, Fairness and channel coordination, Management Science, 53 (2007), 1303-1314. [15] J. Dai, Revenue sharing contract for a supply chain with demand depending on promotion and pricing (in chinese), Chinese Journal of Management, 15 (2018), 395-408. [16] J. Dai and W. Meng, A risk-averse newsvendor model under marketing-dependency and price-dependency, International Journal of Production Economics, 160 (2015), 220-229.  doi: 10.1016/j.ijpe.2014.11.006. [17] C. Dong, B. Shen, P. Chow, L. Yang and C. Ng, Sustainability investment under cap-and-trade regulation, Ann. Oper. Res., 240 (2016), 509-531.  doi: 10.1007/s10479-013-1514-1. [18] S. Du, L. Hu and L. Wang, Low-carbon supply policies and supply chain performance with carbon concerned demand, Ann. Oper. Res., 255 (2017), 569-590.  doi: 10.1007/s10479-015-1988-0. [19] S. Du, T. Nie and C. Chu, Newsvendor model for a dyadic supply chain with nash bargaining fairness concerns, International Journal of Production Research, 52 (2014), 5070-5085. [20] E. Fehr and K. Schmidt, A theory of fairness, competition, and cooperation, Advances in Behavioral Economics, 114 (1999), 817-868.  doi: 10.2307/j.ctvcm4j8j.14. [21] B. Giri, S. Bardhan and T. Maiti, Coordinating a two-echelon supply chain through different contracts under price and promotional effort-dependent demand, Int. J. Oper. Res., 23 (2015), 181-199.  doi: 10.1504/IJOR.2015.069179. [22] W. Guth, On ultimatum bargaining experiments-a personal review, Journal of Economic Behavior and Organization, 27 (1995), 329-344.  doi: 10.1016/0167-2681(94)00071-L. [23] T. Ho, X. Su and Y. Wu, Distributional and peer-induced fairness in supply chain contract design, Production and Operations Management, 23 (2014), 161-175. [24] 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. [25] X. Hu and P. Su, The newsvendor's joint procurement and pricing problem under price-sensitive stochastic demand and purchase price uncertainty, Omega, 79 (2018), 81-90.  doi: 10.1016/j.omega.2017.08.002. [26] Y. Jiang and D. Klabjan, Optimal Emissions Reduction Investment Under Green House Gas Emissions Regulations, Ph.D thesis, Northwestern University in Evanston, 2012. [27] D. Kahneman and A. Tversky, Prospect theory: An analysis of decision under risk, Econometrica, 47 (1979), 263-291.  doi: 10.2307/1914185. [28] E. Katok, T. Olsen and V. Pavlov, Wholesale pricing under mild and privately known concerns for fairness, Production and Operations Management, 23 (2014), 285-302.  doi: 10.1111/j.1937-5956.2012.01388.x. [29] E. Katok and V. Pavlov, Fairness in supply chain contracts: A laboratory study, Journal of Operations Management, 31 (2013), 129-137.  doi: 10.1016/j.jom.2013.01.001. [30] M. Khouja, The single-period (news-vendor) problem: Literature review and suggestions for future research, Omega, 27 (1999), 537-553.  doi: 10.1016/S0305-0483(99)00017-1. [31] H. Krishnan, R. Kapuscinski and D. Butz, Coordinating contracts for decentralized supply chains with retailer promotional effort, Management Science, 50 (2004), 48-63.  doi: 10.1287/mnsc.1030.0154. [32] N. Kumar, The power of trust in manufacturer-retailer relationships, Harvard Business Review, 74 (1996), 92-106. [33] M. Laroche, J. Bergeron and G. Forleo, Targeting consumers who are willing to pay more for environmentally friendly products, Journal of Consumer marketing, 18 (2001), 503-520.  doi: 10.1108/EUM0000000006155. [34] J. Li, J. Lu, Q. Wang and C. Li, Quality and pricing decisions in a two-echelon supply chain with Nash bargaining fairness concerns, Discrete Dyn. Nat. Soc., 2018 (2018), 4267305.  doi: 10.1155/2018/4267305. [35] Z. Liu, T. Anderson and J. Cruz, Consumer environmental awareness and competition in two-stage supply chains, European J. Oper. Res., 218 (2012), 602-613.  doi: 10.1016/j.ejor.2011.11.027. [36] C. Loch and Y. Wu, Social preferences and supply chain performance: An experimental study, Management Science, 54 (2008), 1835-1849.  doi: 10.1287/mnsc.1080.0910. [37] C. Luo and X. Tian, Operational strategy of supply chain with price-dependent stochastic demand under the cvar criterion(in chinese), Management Review, 27 (2015), 167-176. [38] J. Ma and L. Xie, The impact of loss sensitivity on a mobile phone supply chain system stability based on the chaos theory, Commun. Nonlinear Sci. Numer. Simul., 55 (2018), 194-205.  doi: 10.1016/j.cnsns.2017.06.030. [39] S. Madani and M. Barzoki, Sustainable supply chain management with pricing, greening and governmental tariffs determining strategies: A game-theoretic approach, Computers and Industrial Engineering, 105 (2017), 287-298.  doi: 10.1016/j.cie.2017.01.017. [40] G. Mark and M. Sharafali, Price-dependent inventory models with discount offers at random times, Production and Operations Management, 11 (2002), 139-156. [41] J. Nash, The bargaining problem, Econometrica, 18 (1950), 155-162.  doi: 10.2307/1907266. [42] J. Nash, Two-person cooperative games, Econometrica, 21 (1953), 128-140.  doi: 10.2307/1906951. [43] W. Nordhaus, To slow or not to slow: The economics of the greenhouse effect, The Economic Journal, 101 (1991), 920-937.  doi: 10.2307/2233864. [44] A. Olmstead and P. Rhode, Rationing without government: The west coast gas famine of 1920, The American economic review, 75 (1985), 1044-1055. [45] V. Pavlov and E. Katok, Fairness and coordination failures in supply chain contracts, 2011. doi: 10.2139/ssrn.2623821. [46] N. Petruzzi and M. Dada, Pricing and the news vendor problem: A review with extensions, Operations Research, 47 (1999), 183-194. [47] X. Qian, F. 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. [48] M. Rabin, Incorporating fairness into game theory and economics, American Economic Review, 83 (1993), 1281-1302.  doi: 10.2307/j.ctvcm4j8j.15. [49] C. Roheim, F. Asche and J. Santos, The elusive price premium for ecolabelled products: Evidence from seafood in the uk market, Journal of Agricultural Economics, 62 (2011), 655-668.  doi: 10.1111/j.1477-9552.2011.00299.x. [50] B. Ruffle, More is better, but fair is fair: Tipping in dictator and ultimatum games, Games and Economic Behavior, 23 (1998), 247-265.  doi: 10.1006/game.1997.0630. [51] L. Scheer, N. Kumar and J. Steenkamp, Reactions to perceived inequity in us and dutch inter organizational relationships, Academy of Management Journal, 46 (2003), 303-316. [52] M. Schweitzer and G. Cachon, Decision bias in the newsvendor problem with a known demand distribution: Experimental evidence, Management Science, 46 (2000), 404-420.  doi: 10.1287/mnsc.46.3.404.12070. [53] H. Shan, C. Zhang and G. Wei, Bundling or unbundling? pricing strategy for complementary products in a green supply chain, Sustainability, 12 (2020), 1331.  doi: 10.3390/su12041331. [54] G. Singer and E. Khmelnitsky, A production-inventory problem with price-sensitive demand, Appl. Math. Model., 89 (2021), 688-699.  doi: 10.1016/j.apm.2020.06.072. [55] J. Spengler, Vertical integration and antitrust policy, Journal of Political Economy, 58 (1950), 347-352.  doi: 10.1086/256964. [56] A. Taylor, Sale timing in a supply chain: When to sell to the retailer, Manufacturing and Service Operations Management, 8 (2006), 23-42.  doi: 10.1287/msom.1050.0089. [57] R. Thaler, The ultimatum game, The Journal of Economic Perspectives, 2 (1988), 195-206. [58] A. Tversky and D. Kahneman, A Rational choice and the framing of decisions, NATO Adv. Sci. Inst. Ser. F: Comput. Systems Sci., 56 (1989), 81-126. [59] C. Wang and X. Chen, Joint order and pricing decisions for fresh produce with put option contracts, Journal of the Operational Research Society, 69 (2018), 474-484. [60] C. Wang, S. Webster and N. Suresh, Would a risk-averse newsvendor order less at a higher selling price?, European J. Oper. Res., 196 (2009), 544-553.  doi: 10.1016/j.ejor.2008.04.002. [61] D. Wu, Li. Yang and D. Olson, Green supply chain management under capital constraint, International Journal of Production Economics, 215 (2019), 3-10. [62] J. Xu, Y. Chen and Q. Bai, A two-echelon sustainable supply chain coordination under cap-and-trade regulation, Journal of Cleaner Production, 135 (2016), 42-56.  doi: 10.1016/j.jclepro.2016.06.047. [63] M. Xu, Y. Chen and X. Xu, The effect of demand uncertainty in a price setting newsvendor model, European J. Oper. Res., 207 (2010), 946-957.  doi: 10.1016/j.ejor.2010.06.024. [64] X. Xu, P. He, H. Xu and Q. Zhang, Supply chain coordination with green technology under cap-and-trade regulation, International Journal of Production Economics, 183 (2017), 433-442.  doi: 10.1016/j.ijpe.2016.08.029. [65] H. Yang, L. Miao and C. Zhao, The credit strategy of a green supply chain based on capital constraints, Journal of Cleaner Production, 224 (2019), 930-939.  doi: 10.1016/j.jclepro.2019.03.214. [66] J. Yang, J. Xie, X. Deng and H. Xiong, Cooperative advertising in a distribution channel with fairness concerns, European J. Oper. Res., 227 (2013), 401-407.  doi: 10.1016/j.ejor.2012.12.011. [67] L. Yao, Y. Chen and H. Han, Analysis of a supply contract for coordinating the newsvendor with price dependent demand, 2005. Available from: http://www.se.cuhk.edu.hk/yhchen/contractl20502. [68] Y. Zhao, 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, Journal of Cleaner Production, 133 (2016), 402-413.  doi: 10.1016/j.jclepro.2016.05.097. [69] Y. Zhou and X. Ye, Differential game model of joint emission reduction strategies and contract design in a dual-channel supply chain, Journal of Cleaner Production, 190 (2018), 592-607.  doi: 10.1016/j.jclepro.2018.04.133.
Relations between the retailer's expected utility and $\lambda, \gamma, w$ and $c$ in LCAD model
Relations between the retailer's expected utility and $\lambda, \gamma, w$ and $c$ in LCMD model
Relationship between objective and key parameters
Relations between $U(\pi^{r}_{\phi\varphi})$, $\pi^c$ and the retail price $p$, respectively
Notations
 $d(e, p, \xi)$ Stochastic demand $\xi$ Stochastic price-independent component $y(p)$ Deterministic demand $q_i$ Optimal ordering quantity $p_{i}$ Retail price $e_i$ Low-carbon effort level $w$ Wholesale price $c$ Unit cost $s$ Salvage value $\lambda$ Fairness-concerned parameter of the retailer $\gamma$ Retailer's bargaining power $\pi_i^r$ Retailer's profit $\pi_i^s$ Supplier's profit $E(\pi_i^r)$ Expected profit of retailer $E(\pi_i^s)$ Supplier's expected profit $U(\pi_i^r)$ Utility function of retailer $p_i^*$ Optimal ordering $i=M,A$ Multiplicative or additive demand
 $d(e, p, \xi)$ Stochastic demand $\xi$ Stochastic price-independent component $y(p)$ Deterministic demand $q_i$ Optimal ordering quantity $p_{i}$ Retail price $e_i$ Low-carbon effort level $w$ Wholesale price $c$ Unit cost $s$ Salvage value $\lambda$ Fairness-concerned parameter of the retailer $\gamma$ Retailer's bargaining power $\pi_i^r$ Retailer's profit $\pi_i^s$ Supplier's profit $E(\pi_i^r)$ Expected profit of retailer $E(\pi_i^s)$ Supplier's expected profit $U(\pi_i^r)$ Utility function of retailer $p_i^*$ Optimal ordering $i=M,A$ Multiplicative or additive demand
Influence of the important parameter on joint decision ($\nearrow$ and $\searrow$ denote the result is increasing and decreasing in corresponding parameters, respectively). * means that the impact needs certain conditions. Specifically, $p_M^*$ is decreasing in $s$ whereas $Q_M^*$ is increasing in $s$ if $p_M^*>(2w-s)+2\gamma\lambda(w-c)$
 $i=A, M$ $\lambda$ $\gamma$ $w$ $c$ $s$ $i=A$ $i=M$ $p_{i}^*$ $\nearrow$ $\nearrow$ $\nearrow$ $\searrow$ $\searrow$ $\ast$ $e_{i}^*$ $\searrow$ $\searrow$ $\searrow$ $\nearrow$ $\nearrow$ $\nearrow$ $Q_{i}^*$ $\searrow$ $\searrow$ $\searrow$ $\nearrow$ $\nearrow$ $\ast$
 $i=A, M$ $\lambda$ $\gamma$ $w$ $c$ $s$ $i=A$ $i=M$ $p_{i}^*$ $\nearrow$ $\nearrow$ $\nearrow$ $\searrow$ $\searrow$ $\ast$ $e_{i}^*$ $\searrow$ $\searrow$ $\searrow$ $\nearrow$ $\nearrow$ $\nearrow$ $Q_{i}^*$ $\searrow$ $\searrow$ $\searrow$ $\nearrow$ $\nearrow$ $\ast$
Influence of $\lambda$ under LCAD when $\xi \sim U(-50; 50)$
 $\lambda$ $w^*_M$ $p^*_M$ $e^*_M$ $Q^*_M$ $U(\pi_M^r)$ $\pi_M^s$ $U(\pi_M^r)+\pi_M^s$ 0 3.021 5.6186 0.6179 66.3602 99.9620 67.7538 167.7157 0.5 2.817 5.6185 0.6179 66.3683 119.9643 54.2030 174.1673 1.0 2.681 5.6184 0.6178 66.3716 133.2981 45.1692 178.4673 1.5 2.584 5.6182 0.6177 66.3748 142.8241 38.7164 181.5406
 $\lambda$ $w^*_M$ $p^*_M$ $e^*_M$ $Q^*_M$ $U(\pi_M^r)$ $\pi_M^s$ $U(\pi_M^r)+\pi_M^s$ 0 3.021 5.6186 0.6179 66.3602 99.9620 67.7538 167.7157 0.5 2.817 5.6185 0.6179 66.3683 119.9643 54.2030 174.1673 1.0 2.681 5.6184 0.6178 66.3716 133.2981 45.1692 178.4673 1.5 2.584 5.6182 0.6177 66.3748 142.8241 38.7164 181.5406
Influence of $\lambda$ under LCMD when $\xi\sim U(0.1; 1.9)$
 $\lambda$ $w^*_M$ $p^*_M$ $e^*_M$ $Q^*_M$ $U(\pi_M^r)$ $\pi_M^s$ $U(\pi_M^r)+\pi_M^s$ 0 2.675 5.7809 0.4652 53.5966 68.1482 36.1884 104.3366 0.5 2.540 5.7806 0.4652 53.6026 81.7826 28.9507 110.7334 1.0 2.450 5.7803 0.4652 53.6125 90.8785 24.1256 115.0041 1.5 2.386 5.7802 0.4651 53.6145 97.3717 20.6791 118.0508
 $\lambda$ $w^*_M$ $p^*_M$ $e^*_M$ $Q^*_M$ $U(\pi_M^r)$ $\pi_M^s$ $U(\pi_M^r)+\pi_M^s$ 0 2.675 5.7809 0.4652 53.5966 68.1482 36.1884 104.3366 0.5 2.540 5.7806 0.4652 53.6026 81.7826 28.9507 110.7334 1.0 2.450 5.7803 0.4652 53.6125 90.8785 24.1256 115.0041 1.5 2.386 5.7802 0.4651 53.6145 97.3717 20.6791 118.0508
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