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doi: 10.3934/jimo.2019037

Impact of risk aversion on two-echelon supply chain systems with carbon emission reduction constraints

1. 

Institute of Operations Research, School of Management, Qufu Normal University, Rizhao, Shandong 276826, China

2. 

Department of Health Services and Outcomes Research, National Healthcare Group, 138543, Singapore

* Corresponding author

Received  June 2018 Revised  November 2018 Published  May 2019

Fund Project: The research is partly supported by the National Natural Science Foundation of China under grant 71771138, Humanities and Social Sciences Youth Foundation of Ministry of Education of China under grant 17YJC630004, Natural Science Foundation of Shandong Province, China under Grant ZR2017MG009, and Special Foundation for Taishan Scholars of Shandong Province, China under Grant tsqn201812061

This study examines a two-echelon supply chain consisting of two competing manufacturers and one retailer that has the channel power, in which one manufacturer is engaged in sustainable technology to curb carbon emissions under the cap-and-trade regulation while the other one operates its business as usual in a traditional manner. Two different supply chain configurations concerning risk attributes of the agents are considered, that is, (ⅰ) two risk-neutral manufacturers with one risk-averse retailer; and (ⅱ) two risk-averse manufacturers with one risk-neutral retailer. Under the mean-variance framework, we use a retailer-leader game optimization approach to study operational decisions of these two systems. Specifically, optimal operational decisions of the agents are established in closed-form expressions and the corresponding profits and carbon emissions are assessed. Numerical experiments are conducted to analyze the impact of risk aversion of the underlying supply chains. The results show that each risk-averse agent would benefit from a low scale risk aversion. Further, low carbon emissions could be attainable if risk aversion scale of the underlying manufacturer is small or moderate. In addition, the carbon emissions might increase when risk aversion of the traditional manufacturer or the retailer is of small or moderate scale.

Citation: Qingguo Bai, Fanwen Meng. Impact of risk aversion on two-echelon supply chain systems with carbon emission reduction constraints. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2019037
References:
[1]

T. AvinadavT. Chernonog and Y. Perlman, Consignment contract for mobile apps between a single retailer and compertitive developers with different risk attitudes, Eur. J. Oper. Res., 246 (2015), 949-957. doi: 10.1016/j.ejor.2015.05.016.

[2]

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, Int. J. Prod. Econ., 187 (2017), 85-101. doi: 10.1016/j.ijpe.2017.02.012.

[3]

E. BazanM. Y. Jaber and S. Zanoni, A review of mathematical inventory models for reverse logistics and the future of its modeling: An environmental perspective, Appl. Math. Model., 40 (2016), 4151-4178. doi: 10.1016/j.apm.2015.11.027.

[4]

P. BeskeA. Land and S. Seuring, Sustainable supply chain management practices and dynamic capabilities in the food industry: A critical analysis of the literature, Int. J. Prod. Econ., 152 (2014), 131-143. doi: 10.1016/j.ijpe.2013.12.026.

[5]

M. Bonney and M. Y. Jaber, Environmentally responsible inventory models: Non-classical models for a non-classical era, Int. J. Prod. Econ., 133 (2011), 43-53. doi: 10.1016/j.ijpe.2009.10.033.

[6]

J. Bull, Loads of green washing–can behavioural economics increase willingness-to-pay for efficient washing machines in the UK?, Energ. Policy., 50 (2012), 242-252. doi: 10.1016/j.enpol.2012.07.001.

[7]

B. CaoZ. Xiao and X. Li, Joint decision on pricing and waste emission level in industrial symbiosis chain, J. Ind. Manag. Optim., 14 (2018), 135-164. doi: 10.3934/jimo.2017040.

[8]

X. ChenG. Hao and L. Li, Channel coordination with a loss-averse retailer and option contracts, Int. J. Prod. Econ., 150 (2014), 52-57. doi: 10.1016/j.ijpe.2013.12.004.

[9]

C. H. Chiu and T. M. Choi, Supply chain risk analysis with mean-variance models: A technical review, Ann. Oper. Res., 240 (2016), 489-507. doi: 10.1007/s10479-013-1386-4.

[10]

T. M. ChoiD. LiH. Yan and C. H. Chiu, Channel coordination in supply chains with agents having mean-variance objectives, Omega, 36 (2008), 565-576. doi: 10.1016/j.omega.2006.12.003.

[11]

C. DongB. ShenP. S. ChowL. Yang and C. To Ng, Sustainability investment under cap-and-trade regulation, Ann. Oper. Res., 240 (2016), 509-531. doi: 10.1007/s10479-013-1514-1.

[12]

S. DuL. ZhuL. Liang and F. Ma, Emission-dependent supply chain and environment-policy-making in the 'cap-and-trade' system, Energ. Policy., 57 (2013), 61-67. doi: 10.1016/j.enpol.2012.09.042.

[13]

S. DuL. 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.

[14]

European Commission, Attitudes of Europeans citizens towards the environment, Eurobarometer, 295(2008), Available from: http://www.ec.europa.eu/public_opinion/archives/ebs_295_en.pdf

[15]

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[16]

X. Gan, S. P. Sethi and H. Yan, Coordination of supply chains with risk-averse agents, Supply Chain Coordination under Uncertainty, (2011), 3–31. doi: 10.1007/978-3-642-19257-9_1.

[17]

D. HeX. Chen and Q. Huang, Influences of carbon emission abatement on firms' production policy based on newsboy model, J. Ind. Manag. Optim., 13 (2017), 251-265. doi: 10.3934/jimo.2016015.

[18]

M. Y. JaberC. H. Glock and A. M. A. El Saadany, Supply chain coordination with emissions reduction incentives, Int. J. Prod. Res., 51 (2013), 69-82. doi: 10.1080/00207543.2011.651656.

[19]

J. JiZ. Zhang and L. Yang, Comparisons of initial carbon allowance allocation rules in an O2O retail supply chain with the cap-and-trade regulation, Int. J. Prod. Econ., 187 (2017), 68-84. doi: 10.1016/j.ijpe.2017.02.011.

[20]

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

[21]

J. LiT. M. Choi and T. C. E. Cheng, Mean variance analysis of fast fashion supply chains with returns policy, IEEE. Trans. Syst. Man. Cybern. Syst., 44 (2014), 422-434. doi: 10.1109/TSMC.2013.2264934.

[22]

Q. LiB. LiP. Chen and P. Hou, Dual-channel supply chain decisions under asymmetric information with a risk-averse retailer, Ann. Oper. Res., 257 (2017), 423-447. doi: 10.1007/s10479-015-1852-2.

[23]

W. Liu and Y. Wang, Quality control game model in logistics service supply chain based on different combinations of risk attitude, Int. J. Prod. Econ., 161 (2015), 181-191. doi: 10.1016/j.ijpe.2014.12.026.

[24]

S. Ohmura and H. Matsuo, The effect of risk aversion on distribution channel contracts: Implications for return policies, Int. J. Prod. Econ., 176 (2016), 29-40. doi: 10.1016/j.ijpe.2016.02.019.

[25]

S. K. PaulR. Sarker and D. Essam, Managing risk and disruption in production-inventory and supply chain systems: A review, J. Ind. Manag. Optim., 12 (2016), 1009-1029. doi: 10.3934/jimo.2016.12.1009.

[26]

Q. QiJ. Wang and Q. Bai, Pricing decision of a two-echelon supply chain with one supplier and two retailers under a carbon cap regulation, J. Clean. Prod., 151 (2017), 286-302. doi: 10.1016/j.jclepro.2017.03.011.

[27]

Y. ShenJ. Xie and T. Li, The risk-averse newsvendor game with competition on demand, J. Ind. Manag. Optim., 12 (2016), 931-947. doi: 10.3934/jimo.2016.12.931.

[28]

F. TaoT. Fan and K. K. Lai, Optimal inventory control policy and supplly chain coordination problem with carbon footprint constraints, Int. T. Oper. Res., 25 (2018), 1831-1853. doi: 10.1111/itor.12271.

[29]

C. WangW. Wang and R. Huang, Supply chain enterprise operations and government carbon tax decisions considering carbon emissions, J. Clean. Prod., 152 (2017), 271-280. doi: 10.1016/j.jclepro.2017.03.051.

[30]

X. WangY. Lan and W. Tang, An uncertain wage contract model for risk-averse worker under bilateral moral hazard, J. Ind. Manag. Optim., 13 (2017), 1815-1840. doi: 10.3934/jimo.2017020.

[31]

L. XiaT. GuoJ. QinX. Yue and N. Zhu, Carbon emission redcution and pricing policies of a supply chain considering reciprocal preferences in cap-and-trade system, Ann. Oper. Res., 268 (2018), 149-175. doi: 10.1007/s10479-017-2657-2.

[32]

T. Xiao and T. M. Choi, Purchasing choices and channel structure strategies for a two-echelon system with risk-averse players, Int. J. Prod. Econ., 120 (2009), 54-65. doi: 10.1016/j.ijpe.2008.07.028.

[33]

T. Xiao and T. Xu, Pricing and product line strategy in a supply chain with risk-averse players, Int. J. Prod. Econ., 156 (2014), 305-315. doi: 10.1016/j.ijpe.2014.06.021.

[34]

T. Xiao and D. Yang, Price and service competition of supply chains with riks-averse retailers under demand uncertainty, Int. J. Prod. Econ., 114 (2008), 187-200.

[35]

G. XieW. Yue and S. Wang, Optimal selection of cleaner productions in a green supply chain with risk aversion, J. Ind. Manag. Optim., 11 (2015), 515-528. doi: 10.3934/jimo.2015.11.515.

[36]

J. XuY. Chen and Q. Bai, A two-echelon sustainable supply chain coordination under cap-and-trade regulation, J. Clean. Prod., 135 (2016), 42-56. doi: 10.1016/j.jclepro.2016.06.047.

[37]

X. XuP. HeH. Xu and Q. Zhang, Supply chain coordiantion with green technology under cap-and-trade regulation, Int. J. Prod. Econ., 183 (2017), 433-442.

[38]

X. XuW. ZhangP. He and X. Xu, Production and pricing problems in make-to-order supply chain with cap-and-trade regulation, Omega, 66 (2017), 248-257. doi: 10.1016/j.omega.2015.08.006.

[39]

W. XueT. M. Choi and L. Ma, Diversification strategy with random yield suppliers for a mean-variance risk-sensitive manufacturer, Transpor. Res. E-Log., 90 (2016), 90-107. doi: 10.1016/j.tre.2016.01.013.

[40]

H. Yang and W. Chen, Retailer-driven carbon emission abatement with consumer environmental awareness and carbon tax: Revenue-sharing versus Cost-sharing, Omega, 78 (2018), 179-191. doi: 10.1016/j.omega.2017.06.012.

[41]

L. YangQ. Zhang and J. Ji, Pricing and carbon emission recuction decisions in supply chains with vertical and horizontal cooperation, Int. J. Prod. Econ., 191 (2017), 286-297.

[42]

L. ZhangJ. Wang and J. You, Consumer environmetal awareness and channel coordination with two substitutable products, Eur. J. Oper. Res., 241 (2015), 63-73. doi: 10.1016/j.ejor.2014.07.043.

[43]

J. ZhaoJ. Wei and Y. Li, Pricing and remanufacturing decisions for two substitutable products with a common retailer, J. Ind. Manag. Optim., 13 (2017), 1125-1147. doi: 10.3934/jimo.2016065.

[44]

Y. ZhaoT. M. ChoiT. C. E. Cheng and S. Wang, Mean-risk analysis of wholesale price contracts with stochastic price-dependent demand, Ann. Oper. Res., 257 (2017), 491-518. doi: 10.1007/s10479-014-1689-0.

[45]

Y. ZhouZ. ShenR. Ying and X. Xu, A loss-averse two-product odering model with information updating in two-echelon inventory system, J. Ind. Manag. Optim., 14 (2018), 687-705. doi: 10.3934/jimo.2017069.

[46]

Y. ZuL. Chen and Y. Fan, Research on low-carbon strategies in supply chain with environmental regulations based on differential game, J. Clean. Prod., 177 (2018), 527-546. doi: 10.1016/j.jclepro.2017.12.220.

show all references

References:
[1]

T. AvinadavT. Chernonog and Y. Perlman, Consignment contract for mobile apps between a single retailer and compertitive developers with different risk attitudes, Eur. J. Oper. Res., 246 (2015), 949-957. doi: 10.1016/j.ejor.2015.05.016.

[2]

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, Int. J. Prod. Econ., 187 (2017), 85-101. doi: 10.1016/j.ijpe.2017.02.012.

[3]

E. BazanM. Y. Jaber and S. Zanoni, A review of mathematical inventory models for reverse logistics and the future of its modeling: An environmental perspective, Appl. Math. Model., 40 (2016), 4151-4178. doi: 10.1016/j.apm.2015.11.027.

[4]

P. BeskeA. Land and S. Seuring, Sustainable supply chain management practices and dynamic capabilities in the food industry: A critical analysis of the literature, Int. J. Prod. Econ., 152 (2014), 131-143. doi: 10.1016/j.ijpe.2013.12.026.

[5]

M. Bonney and M. Y. Jaber, Environmentally responsible inventory models: Non-classical models for a non-classical era, Int. J. Prod. Econ., 133 (2011), 43-53. doi: 10.1016/j.ijpe.2009.10.033.

[6]

J. Bull, Loads of green washing–can behavioural economics increase willingness-to-pay for efficient washing machines in the UK?, Energ. Policy., 50 (2012), 242-252. doi: 10.1016/j.enpol.2012.07.001.

[7]

B. CaoZ. Xiao and X. Li, Joint decision on pricing and waste emission level in industrial symbiosis chain, J. Ind. Manag. Optim., 14 (2018), 135-164. doi: 10.3934/jimo.2017040.

[8]

X. ChenG. Hao and L. Li, Channel coordination with a loss-averse retailer and option contracts, Int. J. Prod. Econ., 150 (2014), 52-57. doi: 10.1016/j.ijpe.2013.12.004.

[9]

C. H. Chiu and T. M. Choi, Supply chain risk analysis with mean-variance models: A technical review, Ann. Oper. Res., 240 (2016), 489-507. doi: 10.1007/s10479-013-1386-4.

[10]

T. M. ChoiD. LiH. Yan and C. H. Chiu, Channel coordination in supply chains with agents having mean-variance objectives, Omega, 36 (2008), 565-576. doi: 10.1016/j.omega.2006.12.003.

[11]

C. DongB. ShenP. S. ChowL. Yang and C. To Ng, Sustainability investment under cap-and-trade regulation, Ann. Oper. Res., 240 (2016), 509-531. doi: 10.1007/s10479-013-1514-1.

[12]

S. DuL. ZhuL. Liang and F. Ma, Emission-dependent supply chain and environment-policy-making in the 'cap-and-trade' system, Energ. Policy., 57 (2013), 61-67. doi: 10.1016/j.enpol.2012.09.042.

[13]

S. DuL. 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.

[14]

European Commission, Attitudes of Europeans citizens towards the environment, Eurobarometer, 295(2008), Available from: http://www.ec.europa.eu/public_opinion/archives/ebs_295_en.pdf

[15]

European Commission, 2013. Available from: http://www.ec.europa.eu/clima/policies/ets /index_en.htm.

[16]

X. Gan, S. P. Sethi and H. Yan, Coordination of supply chains with risk-averse agents, Supply Chain Coordination under Uncertainty, (2011), 3–31. doi: 10.1007/978-3-642-19257-9_1.

[17]

D. HeX. Chen and Q. Huang, Influences of carbon emission abatement on firms' production policy based on newsboy model, J. Ind. Manag. Optim., 13 (2017), 251-265. doi: 10.3934/jimo.2016015.

[18]

M. Y. JaberC. H. Glock and A. M. A. El Saadany, Supply chain coordination with emissions reduction incentives, Int. J. Prod. Res., 51 (2013), 69-82. doi: 10.1080/00207543.2011.651656.

[19]

J. JiZ. Zhang and L. Yang, Comparisons of initial carbon allowance allocation rules in an O2O retail supply chain with the cap-and-trade regulation, Int. J. Prod. Econ., 187 (2017), 68-84. doi: 10.1016/j.ijpe.2017.02.011.

[20]

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

[21]

J. LiT. M. Choi and T. C. E. Cheng, Mean variance analysis of fast fashion supply chains with returns policy, IEEE. Trans. Syst. Man. Cybern. Syst., 44 (2014), 422-434. doi: 10.1109/TSMC.2013.2264934.

[22]

Q. LiB. LiP. Chen and P. Hou, Dual-channel supply chain decisions under asymmetric information with a risk-averse retailer, Ann. Oper. Res., 257 (2017), 423-447. doi: 10.1007/s10479-015-1852-2.

[23]

W. Liu and Y. Wang, Quality control game model in logistics service supply chain based on different combinations of risk attitude, Int. J. Prod. Econ., 161 (2015), 181-191. doi: 10.1016/j.ijpe.2014.12.026.

[24]

S. Ohmura and H. Matsuo, The effect of risk aversion on distribution channel contracts: Implications for return policies, Int. J. Prod. Econ., 176 (2016), 29-40. doi: 10.1016/j.ijpe.2016.02.019.

[25]

S. K. PaulR. Sarker and D. Essam, Managing risk and disruption in production-inventory and supply chain systems: A review, J. Ind. Manag. Optim., 12 (2016), 1009-1029. doi: 10.3934/jimo.2016.12.1009.

[26]

Q. QiJ. Wang and Q. Bai, Pricing decision of a two-echelon supply chain with one supplier and two retailers under a carbon cap regulation, J. Clean. Prod., 151 (2017), 286-302. doi: 10.1016/j.jclepro.2017.03.011.

[27]

Y. ShenJ. Xie and T. Li, The risk-averse newsvendor game with competition on demand, J. Ind. Manag. Optim., 12 (2016), 931-947. doi: 10.3934/jimo.2016.12.931.

[28]

F. TaoT. Fan and K. K. Lai, Optimal inventory control policy and supplly chain coordination problem with carbon footprint constraints, Int. T. Oper. Res., 25 (2018), 1831-1853. doi: 10.1111/itor.12271.

[29]

C. WangW. Wang and R. Huang, Supply chain enterprise operations and government carbon tax decisions considering carbon emissions, J. Clean. Prod., 152 (2017), 271-280. doi: 10.1016/j.jclepro.2017.03.051.

[30]

X. WangY. Lan and W. Tang, An uncertain wage contract model for risk-averse worker under bilateral moral hazard, J. Ind. Manag. Optim., 13 (2017), 1815-1840. doi: 10.3934/jimo.2017020.

[31]

L. XiaT. GuoJ. QinX. Yue and N. Zhu, Carbon emission redcution and pricing policies of a supply chain considering reciprocal preferences in cap-and-trade system, Ann. Oper. Res., 268 (2018), 149-175. doi: 10.1007/s10479-017-2657-2.

[32]

T. Xiao and T. M. Choi, Purchasing choices and channel structure strategies for a two-echelon system with risk-averse players, Int. J. Prod. Econ., 120 (2009), 54-65. doi: 10.1016/j.ijpe.2008.07.028.

[33]

T. Xiao and T. Xu, Pricing and product line strategy in a supply chain with risk-averse players, Int. J. Prod. Econ., 156 (2014), 305-315. doi: 10.1016/j.ijpe.2014.06.021.

[34]

T. Xiao and D. Yang, Price and service competition of supply chains with riks-averse retailers under demand uncertainty, Int. J. Prod. Econ., 114 (2008), 187-200.

[35]

G. XieW. Yue and S. Wang, Optimal selection of cleaner productions in a green supply chain with risk aversion, J. Ind. Manag. Optim., 11 (2015), 515-528. doi: 10.3934/jimo.2015.11.515.

[36]

J. XuY. Chen and Q. Bai, A two-echelon sustainable supply chain coordination under cap-and-trade regulation, J. Clean. Prod., 135 (2016), 42-56. doi: 10.1016/j.jclepro.2016.06.047.

[37]

X. XuP. HeH. Xu and Q. Zhang, Supply chain coordiantion with green technology under cap-and-trade regulation, Int. J. Prod. Econ., 183 (2017), 433-442.

[38]

X. XuW. ZhangP. He and X. Xu, Production and pricing problems in make-to-order supply chain with cap-and-trade regulation, Omega, 66 (2017), 248-257. doi: 10.1016/j.omega.2015.08.006.

[39]

W. XueT. M. Choi and L. Ma, Diversification strategy with random yield suppliers for a mean-variance risk-sensitive manufacturer, Transpor. Res. E-Log., 90 (2016), 90-107. doi: 10.1016/j.tre.2016.01.013.

[40]

H. Yang and W. Chen, Retailer-driven carbon emission abatement with consumer environmental awareness and carbon tax: Revenue-sharing versus Cost-sharing, Omega, 78 (2018), 179-191. doi: 10.1016/j.omega.2017.06.012.

[41]

L. YangQ. Zhang and J. Ji, Pricing and carbon emission recuction decisions in supply chains with vertical and horizontal cooperation, Int. J. Prod. Econ., 191 (2017), 286-297.

[42]

L. ZhangJ. Wang and J. You, Consumer environmetal awareness and channel coordination with two substitutable products, Eur. J. Oper. Res., 241 (2015), 63-73. doi: 10.1016/j.ejor.2014.07.043.

[43]

J. ZhaoJ. Wei and Y. Li, Pricing and remanufacturing decisions for two substitutable products with a common retailer, J. Ind. Manag. Optim., 13 (2017), 1125-1147. doi: 10.3934/jimo.2016065.

[44]

Y. ZhaoT. M. ChoiT. C. E. Cheng and S. Wang, Mean-risk analysis of wholesale price contracts with stochastic price-dependent demand, Ann. Oper. Res., 257 (2017), 491-518. doi: 10.1007/s10479-014-1689-0.

[45]

Y. ZhouZ. ShenR. Ying and X. Xu, A loss-averse two-product odering model with information updating in two-echelon inventory system, J. Ind. Manag. Optim., 14 (2018), 687-705. doi: 10.3934/jimo.2017069.

[46]

Y. ZuL. Chen and Y. Fan, Research on low-carbon strategies in supply chain with environmental regulations based on differential game, J. Clean. Prod., 177 (2018), 527-546. doi: 10.1016/j.jclepro.2017.12.220.

Figure 1.  Effects of $ \lambda_{r} $ on DM$ _{1} $
Figure 2.  Effects of $ \lambda_{m_{1}} $ on DM$ _{2} $
Figure 3.  Effects of $ \lambda_{m_{2}} $ on DM$ _{2} $
Table 1.  The optimal solutions for DM$ _{1} $
Decentralized Model 1 $ w^{*}_{1} $ $ w^{*}_{2} $ $ s^{*} $ $ p^{*}_{1} $ $ p^{*}_{2} $
$ C = 9000 $ 422.5471 207.3770 8.0263 483.9910297.6065
$ C = 12569 $ 422.5471 207.3770 8.0263 483.9910 297.6065
$ C = 15000 $ 422.5471 207.3770 8.0263 483.9910 297.6065
Decentralized Model 1 $ w^{*}_{1} $ $ w^{*}_{2} $ $ s^{*} $ $ p^{*}_{1} $ $ p^{*}_{2} $
$ C = 9000 $ 422.5471 207.3770 8.0263 483.9910297.6065
$ C = 12569 $ 422.5471 207.3770 8.0263 483.9910 297.6065
$ C = 15000 $ 422.5471 207.3770 8.0263 483.9910 297.6065
Table 2.  The optimal profits and carbon emissions for DM$ _{1} $
Decentralized Model 1 $ U^{*}(\pi_{r}) $ $ E^{*}(\pi_{m_{1}}) $ $ E^{*}(\pi_{m_{2}}) $ $ J(s^{*}) $
$ C = 9000 $ 17,627 57,17031,16612,569
$ C = 12569 $ 17,627 67,877 31,166 12,569
$ C = 15000 $ 17,627 75,170 31,166 12,569
Decentralized Model 1 $ U^{*}(\pi_{r}) $ $ E^{*}(\pi_{m_{1}}) $ $ E^{*}(\pi_{m_{2}}) $ $ J(s^{*}) $
$ C = 9000 $ 17,627 57,17031,16612,569
$ C = 12569 $ 17,627 67,877 31,166 12,569
$ C = 15000 $ 17,627 75,170 31,166 12,569
Table 3.  The optimal solutions for DM$ _{2} $
Decentralized Model 2 $ w^{**}_{1} $ $ w^{**}_{2} $ $ s^{**} $ $ p^{**}_{1} $ $ p^{**}_{2} $
$ C = 9000 $ 298.4721 67.4862 2.1871506.5056311.8028
$ C = 11416 $ 298.4721 67.4862 2.1871506.5056311.8028
$ C = 15000 $ 298.4721 67.4862 2.1871506.5056311.8028
Decentralized Model 2 $ w^{**}_{1} $ $ w^{**}_{2} $ $ s^{**} $ $ p^{**}_{1} $ $ p^{**}_{2} $
$ C = 9000 $ 298.4721 67.4862 2.1871506.5056311.8028
$ C = 11416 $ 298.4721 67.4862 2.1871506.5056311.8028
$ C = 15000 $ 298.4721 67.4862 2.1871506.5056311.8028
Table 4.  The optimal profits and carbon emissions for DM$ _{2} $
Decentralized Model 2 $ E^{**}(\pi_{r}) $ $ U^{**}(\pi_{m_{1}}) $ $ U^{**}(\pi_{m_{2}}) $ $ J(s^{**}) $
$ C = 9000 $ 66,868 31,809 5617.911,416
$ C = 11416 $ 66,86839,057 5617.911,416
$ C = 15000 $ 66,868 49,8095617.911,416
Decentralized Model 2 $ E^{**}(\pi_{r}) $ $ U^{**}(\pi_{m_{1}}) $ $ U^{**}(\pi_{m_{2}}) $ $ J(s^{**}) $
$ C = 9000 $ 66,868 31,809 5617.911,416
$ C = 11416 $ 66,86839,057 5617.911,416
$ C = 15000 $ 66,868 49,8095617.911,416
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