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July  2022, 18(4): 2749-2782. doi: 10.3934/jimo.2021090

## The combined impacts of consumer green preference and fairness concern on the decision of three-party supply chain

 School of Information Management, Jiangxi University of Finance and Economics, Nanchang 330032, China

* Corresponding author: Xin Wu

Received  January 2021 Revised  March 2021 Published  July 2022 Early access  April 2021

Fund Project: The first author is supported by the National Natural Science Foundation of China grant 71761015 and the Science and Technology Research Project of Jiangxi Education Department of China grant GJJ150475

Consumer green preference (CGP) and fairness concern have posed significant impact on supply chain, respectively. This paper study the combined impacts of CGP and fairness concern on the supply chain that consists of a manufacturer, a green retailer, and a traditional retailer. Specifically, the optimal decision-makings are solved in seven cases, fairness neutrality (FN), the green retailer and the traditional retailer has vertical fairness concern (VFC) respectively, the two retailers has horizontal fairness concern (HFC) respectively, both retailers have vertical fairness concern (BVFC), both retailers have horizontal fairness concern (BHFC). Our main results via numerical simulation follow. (1) The improvement of CGP benefits the supply chain members except the traditional retailer. (2) The green retailer's VFC benefits itself and the whole supply chain, whereas bad for the manufacturer and the traditional retailer. However, the green retailer's HFC bad for itself, while benefits the manufacturer and the traditional retailer. (3) The traditional retailer's profits are affected by both CGP and fairness concern. (4) The high level of BVFC benefits the two retailers, but bad for the manufacturer. Conversely, the high level of BHFC will intensify competition between retailers and thus bad for them, while the manufacturer can benefit from it.

Citation: Jian Liu, Xin Wu, Jiang-Ling Lei. The combined impacts of consumer green preference and fairness concern on the decision of three-party supply chain. Journal of Industrial and Management Optimization, 2022, 18 (4) : 2749-2782. doi: 10.3934/jimo.2021090
##### References:
 [1] A. Am, B. Dk, A. Reh et al, Evaluation of green and sustainable supply chain management using structural equation modelling: A systematic review of the state of the art literature and recommendations for future research, Journal of Cleaner Production, 249 (2020), 119383. [2] T. H. Cui, J. S. Raju and Z. J. Zhang, Fairness and channel coordination, Management Science, 53 (2007), 1303-1314. [3] B. Dorothée, Environmental quality competition and taxation in the presence of green network effect among consumers, Environmental and Resource Economics, 54 (2013), 1-19. [4] S. F. Du, C. Du and L. Ling, Supply chain coordination considering fairness concerns, Journal of Management Sciences in China, 13 (2010), 41-48. [5] S. F. Du, J. Zhu and D. Gao, Optimal decision- making for Nash bargaining fairness concerned newsvendor in two- level supply chain, Journal of Management Sciences in China, 16 (2013), 68-72. [6] S. Du, J. Zhu and H. Jiao, Game-theoretical analysis for supply chain with consumer preference to low carbon, International Journal of Production Research, 53 (2015), 3753-3768.  doi: 10.1080/00207543.2014.988888. [7] E. Fehr and K. M. Schmidt, A theory of fairness, competition and cooperation, Quarterly Journal of Economics, 114 (1999), 817-868. [8] G. Ferrer and J. M. Swaminathan, Managing new and remanufactured products, Management Science, 52 (2006), 15-26.  doi: 10.1287/mnsc.1050.0465. [9] G. Ferrer and J. M. Swaminathan, Managing new and differentiated remanufactured products, European Journal of Operational Research, 203 (2010), 370-379.  doi: 10.1016/j.ejor.2009.08.007. [10] Frances, Wesetley and Harrie, Strategic bridging: The collaboration between environmentalists and business in the marketing of green products, The Journal of Applied Behavioral Science, 27 (1991), 65-90. [11] P. Gautam and A. Khanna, An imperfect production inventory model with setup cost reduction and carbon emission for an integrated supply chain, Uncertain Supply Chain Management, (2018), 271–286. doi: 10.5267/j.uscm.2017.11.003. [12] P. Gautam, K. M. Kamna and C. K. Jaggi, Sustainable production policies under the effect of volume agility, preservation technology, and price-reliant demand, Yugosl. J. Oper. Res., 30 (2020), 305-322.  doi: 10.2298/yjor190315018g. [13] P. Gautam, A. Kishore, A. Khanna and C. K. Jaggi, Strategic defect management for a sustainable green supply chain, Journal of Cleaner Production, 233 (2019), 226-241.  doi: 10.1016/j.jclepro.2019.06.005. [14] D. Ghosh and J. Shan, A comparative analysis of greening policies across supply chain structures, International Journal of Production Economics, 135 (2012), 568-583.  doi: 10.1016/j.ijpe.2011.05.027. [15] D. Ghosh and J. Shan, Supply chain analysis under green sensitive consumer demand and cost sharing contract, International Journal of Production Economics, 164 (2015), 319-329.  doi: 10.1016/j.ijpe.2014.11.005. [16] Y. Huang, A closed-loop supply chain with trade-in strategy under retail competition, Math. Probl. Eng., 2018 (2018), Art. ID 1510959, 16 pp. doi: 10.1155/2018/1510959. [17] T. Ho, X. Su and Y. Z. Wu, Distributional and peer-induced fairness in supply chain contract design, Production and Operations Management, 23 (2014), 161-175. [18] D. Kahneman, J. L. Knetsch and R. H. Thaler, Fairness and the assumptions of economics, The Journal of Business, 59 (1986), 285-300.  doi: 10.1086/296367. [19] L. J. Li and X. X. Wang, Research of supply chain cooperation strategy based on consumer green preference, Journal of Industrial Technological Economics, 38 (2019), 13-22. [20] Q. Li, T. Xiao and Y. Qiu, Price and carbon emission reduction decisions and revenue-sharing contract considering fairness concerns, Journal of Cleaner Production, 190 (2018), 303-314.  doi: 10.1016/j.jclepro.2018.04.032. [21] Q. Li, Y. Zhang and Y. Huang, The impacts of fairness concern and different business objectives on the complexity of dual-channel value chains, Mathematical Problems in Engineering, 2020 (2020), 1-15.  doi: 10.1155/2020/1716084. [22] Y. Li and D. Z. Zhao, Low-carbonization supply chain two-part tariff coordination based on fairness preference, Management Review, 26 (2014), 159-167. [23] Y. Y. Lu, Cooperative advertising strategy and order policy under retailers' competition, J. Shandong Univ. Nat. Sci., 46 (2011), 71–78+96. [24] N. M. Modak, S. Panda and S. S. Sana, Pricing policy and coordination for a two-layer supply chain of duopolistic retailers and socially responsible manufacturer, International Journal of Logistics Research and Applications, 19 (2016), 487-508.  doi: 10.1080/13675567.2015.1085499. [25] W. Moon, W. J. Florkowski and B. Brückner, Willingness to pay for environmental practices: Implications for Eco-Labeling, Land Economics, 78 (2002), 88-102.  doi: 10.2307/3146925. [26] T. Nie and S. Du, Dual-fairness supply chain with quantity discount contracts, European J. Oper. Res., 258 (2017), 491-500.  doi: 10.1016/j.ejor.2016.08.051. [27] A. Roy, S. S. Sana and K. Chaudhuri, Optimal Pricing of competing retailers under uncertain demand-a two layer supply chain model, Ann. Oper. Res., 260 (2018), 481-500.  doi: 10.1007/s10479-015-1996-0. [28] R. C. Savaskan and L. Wassenhove, Reverse channel design: The case of competing retailers, Management Science, 52 (2006), 1-14.  doi: 10.1287/mnsc.1050.0454. [29] E. B. Tirkolaee, S. Hadian and G.-W. Weber, A robust green traffic-based routing problem for perishable products distribution, Computational Intelligence, 36 (2020), 80-101.  doi: 10.1111/coin.12240. [30] E. B. Tirkolaee, I. Mahdavi, M. M. S. Esfahanib and G.-W. Weber, A robust green location-allocation-inventory problem to design an urban waste management system under uncertainty, Waste Management, 102 (2020), 340-350.  doi: 10.1016/j.wasman.2019.10.038. [31] J. K. Vanclay, J. Shortiss and S. Aulsebrook, Customer response to carbon labelling of groceries, Journal of Consumer Policy, 34 (2011), 153-160. [32] S. J. Yao and J. H. Chen, After-sales service capacity of operation strategy considering retailers competition, Journal of Industrial Engineering and Engineering Management, 30 (2016), 88-95. [33] F. M. Yao and C. X. Teng, Decision models for closed-loop supply chain with two competing retailers considering fairness concerns, Computer Integrated Manufacturing Systems, 23 (2017), 1731-1738. [34] W. Zeng, B. L. Ma, J. Wang et al, Research on decision of the closed-loop supply chain based on consumer's green preferences, Soft Science, 32 (2018), 108–113+118. [35] L. Zhang, J. Wang and J. You, Consumer environmental awareness and channel coordination with two substitutable products, European Journal of Operational Research, 241 (2015), 63-73.  doi: 10.1016/j.ejor.2014.07.043. [36] K. Y. Zhang, Y. Wu and S. W. Hou, Differential pricing strategy of considering retailer's fairness concerns in the closed-loop supply chain, Chinese Journal of Management Science, 22 (2014), 51-58. [37] L. H. Zhang, H. Zhou and Y. Y. Li, Optimal environmental quality and price with consumer environmental awareness and retailer's fairness concerns in supply chain, Journal of Cleaner Production, 213 (2019), 1063-1079. [38] 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, Journal of Cleaner Production, 213 (2019), 1063-1079. [39] D. Zhao and S. F. Ji, Research on emission-reduction investment strategy of supply chain with fairness concerns and low-carbon preference, Management Science, 39 (2020), 94-104. [40] X. Zhen, D. Shi, S.-B. Tsai et al, Pricing decisions of a supply chain with multichannel retailer under fairness concerns, Math. Probl. Eng., 2019 (2019), Art. ID 9547302, 22 pp. doi: 10.1155/2019/9547302. [41] Y. J. Zhou, F. Y. Hu and Z. L. Zhou, Study on optimal decisions of retailer-dominated low-carbon supply chain based on fairness concern, Science and Technology Management Research, 38 (2018), 207-214. [42] Y. H. Zhou and L. F. Wu, Research on the willingness of urban consumers to pay for low-carbon agricultural products - take low-carbon pork as an example, Journal of Agrotechnical Economics, 8 (2012), 4-12.

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##### References:
 [1] A. Am, B. Dk, A. Reh et al, Evaluation of green and sustainable supply chain management using structural equation modelling: A systematic review of the state of the art literature and recommendations for future research, Journal of Cleaner Production, 249 (2020), 119383. [2] T. H. Cui, J. S. Raju and Z. J. Zhang, Fairness and channel coordination, Management Science, 53 (2007), 1303-1314. [3] B. Dorothée, Environmental quality competition and taxation in the presence of green network effect among consumers, Environmental and Resource Economics, 54 (2013), 1-19. [4] S. F. Du, C. Du and L. Ling, Supply chain coordination considering fairness concerns, Journal of Management Sciences in China, 13 (2010), 41-48. [5] S. F. Du, J. Zhu and D. Gao, Optimal decision- making for Nash bargaining fairness concerned newsvendor in two- level supply chain, Journal of Management Sciences in China, 16 (2013), 68-72. [6] S. Du, J. Zhu and H. Jiao, Game-theoretical analysis for supply chain with consumer preference to low carbon, International Journal of Production Research, 53 (2015), 3753-3768.  doi: 10.1080/00207543.2014.988888. [7] E. Fehr and K. M. Schmidt, A theory of fairness, competition and cooperation, Quarterly Journal of Economics, 114 (1999), 817-868. [8] G. Ferrer and J. M. Swaminathan, Managing new and remanufactured products, Management Science, 52 (2006), 15-26.  doi: 10.1287/mnsc.1050.0465. [9] G. Ferrer and J. M. Swaminathan, Managing new and differentiated remanufactured products, European Journal of Operational Research, 203 (2010), 370-379.  doi: 10.1016/j.ejor.2009.08.007. [10] Frances, Wesetley and Harrie, Strategic bridging: The collaboration between environmentalists and business in the marketing of green products, The Journal of Applied Behavioral Science, 27 (1991), 65-90. [11] P. Gautam and A. Khanna, An imperfect production inventory model with setup cost reduction and carbon emission for an integrated supply chain, Uncertain Supply Chain Management, (2018), 271–286. doi: 10.5267/j.uscm.2017.11.003. [12] P. Gautam, K. M. Kamna and C. K. Jaggi, Sustainable production policies under the effect of volume agility, preservation technology, and price-reliant demand, Yugosl. J. Oper. Res., 30 (2020), 305-322.  doi: 10.2298/yjor190315018g. [13] P. Gautam, A. Kishore, A. Khanna and C. K. Jaggi, Strategic defect management for a sustainable green supply chain, Journal of Cleaner Production, 233 (2019), 226-241.  doi: 10.1016/j.jclepro.2019.06.005. [14] D. Ghosh and J. Shan, A comparative analysis of greening policies across supply chain structures, International Journal of Production Economics, 135 (2012), 568-583.  doi: 10.1016/j.ijpe.2011.05.027. [15] D. Ghosh and J. Shan, Supply chain analysis under green sensitive consumer demand and cost sharing contract, International Journal of Production Economics, 164 (2015), 319-329.  doi: 10.1016/j.ijpe.2014.11.005. [16] Y. Huang, A closed-loop supply chain with trade-in strategy under retail competition, Math. Probl. Eng., 2018 (2018), Art. ID 1510959, 16 pp. doi: 10.1155/2018/1510959. [17] T. Ho, X. Su and Y. Z. Wu, Distributional and peer-induced fairness in supply chain contract design, Production and Operations Management, 23 (2014), 161-175. [18] D. Kahneman, J. L. Knetsch and R. H. Thaler, Fairness and the assumptions of economics, The Journal of Business, 59 (1986), 285-300.  doi: 10.1086/296367. [19] L. J. Li and X. X. Wang, Research of supply chain cooperation strategy based on consumer green preference, Journal of Industrial Technological Economics, 38 (2019), 13-22. [20] Q. Li, T. Xiao and Y. Qiu, Price and carbon emission reduction decisions and revenue-sharing contract considering fairness concerns, Journal of Cleaner Production, 190 (2018), 303-314.  doi: 10.1016/j.jclepro.2018.04.032. [21] Q. Li, Y. Zhang and Y. Huang, The impacts of fairness concern and different business objectives on the complexity of dual-channel value chains, Mathematical Problems in Engineering, 2020 (2020), 1-15.  doi: 10.1155/2020/1716084. [22] Y. Li and D. Z. Zhao, Low-carbonization supply chain two-part tariff coordination based on fairness preference, Management Review, 26 (2014), 159-167. [23] Y. Y. Lu, Cooperative advertising strategy and order policy under retailers' competition, J. Shandong Univ. Nat. Sci., 46 (2011), 71–78+96. [24] N. M. Modak, S. Panda and S. S. Sana, Pricing policy and coordination for a two-layer supply chain of duopolistic retailers and socially responsible manufacturer, International Journal of Logistics Research and Applications, 19 (2016), 487-508.  doi: 10.1080/13675567.2015.1085499. [25] W. Moon, W. J. Florkowski and B. Brückner, Willingness to pay for environmental practices: Implications for Eco-Labeling, Land Economics, 78 (2002), 88-102.  doi: 10.2307/3146925. [26] T. Nie and S. Du, Dual-fairness supply chain with quantity discount contracts, European J. Oper. Res., 258 (2017), 491-500.  doi: 10.1016/j.ejor.2016.08.051. [27] A. Roy, S. S. Sana and K. Chaudhuri, Optimal Pricing of competing retailers under uncertain demand-a two layer supply chain model, Ann. Oper. Res., 260 (2018), 481-500.  doi: 10.1007/s10479-015-1996-0. [28] R. C. Savaskan and L. Wassenhove, Reverse channel design: The case of competing retailers, Management Science, 52 (2006), 1-14.  doi: 10.1287/mnsc.1050.0454. [29] E. B. Tirkolaee, S. Hadian and G.-W. Weber, A robust green traffic-based routing problem for perishable products distribution, Computational Intelligence, 36 (2020), 80-101.  doi: 10.1111/coin.12240. [30] E. B. Tirkolaee, I. Mahdavi, M. M. S. Esfahanib and G.-W. Weber, A robust green location-allocation-inventory problem to design an urban waste management system under uncertainty, Waste Management, 102 (2020), 340-350.  doi: 10.1016/j.wasman.2019.10.038. [31] J. K. Vanclay, J. Shortiss and S. Aulsebrook, Customer response to carbon labelling of groceries, Journal of Consumer Policy, 34 (2011), 153-160. [32] S. J. Yao and J. H. Chen, After-sales service capacity of operation strategy considering retailers competition, Journal of Industrial Engineering and Engineering Management, 30 (2016), 88-95. [33] F. M. Yao and C. X. Teng, Decision models for closed-loop supply chain with two competing retailers considering fairness concerns, Computer Integrated Manufacturing Systems, 23 (2017), 1731-1738. [34] W. Zeng, B. L. Ma, J. Wang et al, Research on decision of the closed-loop supply chain based on consumer's green preferences, Soft Science, 32 (2018), 108–113+118. [35] L. Zhang, J. Wang and J. You, Consumer environmental awareness and channel coordination with two substitutable products, European Journal of Operational Research, 241 (2015), 63-73.  doi: 10.1016/j.ejor.2014.07.043. [36] K. Y. Zhang, Y. Wu and S. W. Hou, Differential pricing strategy of considering retailer's fairness concerns in the closed-loop supply chain, Chinese Journal of Management Science, 22 (2014), 51-58. [37] L. H. Zhang, H. Zhou and Y. Y. Li, Optimal environmental quality and price with consumer environmental awareness and retailer's fairness concerns in supply chain, Journal of Cleaner Production, 213 (2019), 1063-1079. [38] 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, Journal of Cleaner Production, 213 (2019), 1063-1079. [39] D. Zhao and S. F. Ji, Research on emission-reduction investment strategy of supply chain with fairness concerns and low-carbon preference, Management Science, 39 (2020), 94-104. [40] X. Zhen, D. Shi, S.-B. Tsai et al, Pricing decisions of a supply chain with multichannel retailer under fairness concerns, Math. Probl. Eng., 2019 (2019), Art. ID 9547302, 22 pp. doi: 10.1155/2019/9547302. [41] Y. J. Zhou, F. Y. Hu and Z. L. Zhou, Study on optimal decisions of retailer-dominated low-carbon supply chain based on fairness concern, Science and Technology Management Research, 38 (2018), 207-214. [42] Y. H. Zhou and L. F. Wu, Research on the willingness of urban consumers to pay for low-carbon agricultural products - take low-carbon pork as an example, Journal of Agrotechnical Economics, 8 (2012), 4-12.
Proposed supply chain structure
The potential demand distribution of consumers in the market
Combined impacts of CGP and R1VFC on profits
Combined impacts of CGP and R2VFC on profits
Combined impacts of CGP and R1HFC on profits
Combined impacts of CGP and R2HFC on profits
Combined impacts of CGP and BVFC on profits (σ = 1.3)
Combined impacts of CGP and BVFC on profits (σ = 1.9)
Combined impacts of CGP and BHFC on profits (σ = 1.3)
Combined impacts of CGP and BHFC on profits (σ = 1.9)
The literature positioning of this paper
 Literature Consumer green preference Vertical fairness concern Horizontal fairness concern Both fairness concern Three-party supply chain Vanclay et al. [31] √ Ghosh et al. [14] √ Moon et al. [25] √ Du et al. [6] √ Cui et al. [2] √ Du et al. [4] √ Zhang et al. [38] √ Savaskan et al. [28] √ Yao et al. [32] √ Modak et al. [24] √ Nie et al. [26] √ √ √ Ho et al. [17] √ √ √ Yao et al. [33] √ √ This paper √ √ √ √ √
 Literature Consumer green preference Vertical fairness concern Horizontal fairness concern Both fairness concern Three-party supply chain Vanclay et al. [31] √ Ghosh et al. [14] √ Moon et al. [25] √ Du et al. [6] √ Cui et al. [2] √ Du et al. [4] √ Zhang et al. [38] √ Savaskan et al. [28] √ Yao et al. [32] √ Modak et al. [24] √ Nie et al. [26] √ √ √ Ho et al. [17] √ √ √ Yao et al. [33] √ √ This paper √ √ √ √ √
Symbol and notations
 Notations Definition ${{c}_{1}},{{c}_{2}}$ Unit cost for the manufacturer to produce green products and traditional products, respectively ${{w}_{1}},{{w}_{2}}$ Wholesale price of green products and traditional products, respectively ${{p}_{1}},{{p}_{2}}$ Retail price of green products and traditional products, respectively $Q$ Potential consumers in the market $\sigma$ Consumer green preference ${{q}_{1}},{{q}_{2}}$ Sales of green products and traditional products, respectively ${{\pi }_{m}}$ Profit function of the manufacturer ${{\pi }_{r1}}$ Profit function of the green retailer ${{\pi }_{r2}}$ Profit function of the traditional retailer ${{\pi }_{s}}$ Profit function of the whole supply chain ${{u}_{r1}}(m)$ Utility of the green retailer vertical fairness concern ${{u}_{r2}}(m)$ Utility of the traditional retailer vertical fairness concern ${{u}_{r1}}({{r}_{2}})$ Utility of the green retailer horizontal fairness concern ${{u}_{r2}}({{r}_{1}})$ Utility of the traditional retailer horizontal fairness concern ${{\lambda }_{1}},{{\lambda }_{2}},{{\lambda }_{3}},{{\lambda }_{4}}$ Coefficients of fairness concern under different scenarios
 Notations Definition ${{c}_{1}},{{c}_{2}}$ Unit cost for the manufacturer to produce green products and traditional products, respectively ${{w}_{1}},{{w}_{2}}$ Wholesale price of green products and traditional products, respectively ${{p}_{1}},{{p}_{2}}$ Retail price of green products and traditional products, respectively $Q$ Potential consumers in the market $\sigma$ Consumer green preference ${{q}_{1}},{{q}_{2}}$ Sales of green products and traditional products, respectively ${{\pi }_{m}}$ Profit function of the manufacturer ${{\pi }_{r1}}$ Profit function of the green retailer ${{\pi }_{r2}}$ Profit function of the traditional retailer ${{\pi }_{s}}$ Profit function of the whole supply chain ${{u}_{r1}}(m)$ Utility of the green retailer vertical fairness concern ${{u}_{r2}}(m)$ Utility of the traditional retailer vertical fairness concern ${{u}_{r1}}({{r}_{2}})$ Utility of the green retailer horizontal fairness concern ${{u}_{r2}}({{r}_{1}})$ Utility of the traditional retailer horizontal fairness concern ${{\lambda }_{1}},{{\lambda }_{2}},{{\lambda }_{3}},{{\lambda }_{4}}$ Coefficients of fairness concern under different scenarios
Simulation results in R1VFC scenario $(\sigma \rm{ = }1.3)$
 $\lambda$ 0 0.2 0.4 0.6 0.8 1 ${{\pi}_{m}}$ 87460.3 86524.9 86036.2 85740.9 85545.3 85407.2 ${{\pi}_{r1}}$ 5461.07 6860.16 7658.16 8173.59 8533.38 8798.38 ${{u}_{r1}}(m)$ 5461.07 -9072.79 -23693.1 -38366.8 -53076.2 -67810.4 ${{\pi}_{r2}}$ 4151.55 3743.56 3474.7 3283.23 3139.67 3027.98 ${{\pi}_{s}}$ 97072.9 97128.6 97169.1 97197.8 97218.4 97233.5 ${{w}_{1}}$ 950 940.76 935.74 932.61 930.47 928.93 ${{w}_{2}}$ 700 702.32 703.72 704.67 705.36 705.89 ${{p}_{1}}$ 990.48 989.44 988.47 987.64 986.96 986.39 ${{p}_{2}}$ 730.95 731.71 732.04 732.2 732.28 732.32 ${{q}_{1}}$ 134.92 140.92 145.25 148.52 151.08 153.13 ${{q}_{2}}$ 134.13 127.37 122.71 119.28 119.28 114.55
 $\lambda$ 0 0.2 0.4 0.6 0.8 1 ${{\pi}_{m}}$ 87460.3 86524.9 86036.2 85740.9 85545.3 85407.2 ${{\pi}_{r1}}$ 5461.07 6860.16 7658.16 8173.59 8533.38 8798.38 ${{u}_{r1}}(m)$ 5461.07 -9072.79 -23693.1 -38366.8 -53076.2 -67810.4 ${{\pi}_{r2}}$ 4151.55 3743.56 3474.7 3283.23 3139.67 3027.98 ${{\pi}_{s}}$ 97072.9 97128.6 97169.1 97197.8 97218.4 97233.5 ${{w}_{1}}$ 950 940.76 935.74 932.61 930.47 928.93 ${{w}_{2}}$ 700 702.32 703.72 704.67 705.36 705.89 ${{p}_{1}}$ 990.48 989.44 988.47 987.64 986.96 986.39 ${{p}_{2}}$ 730.95 731.71 732.04 732.2 732.28 732.32 ${{q}_{1}}$ 134.92 140.92 145.25 148.52 151.08 153.13 ${{q}_{2}}$ 134.13 127.37 122.71 119.28 119.28 114.55
Simulation results in R1VFC scenario $(\sigma \rm{ = }1.9)$
 $\lambda$ 0 0.2 0.4 0.6 0.8 1 ${{\pi }_{m}}$ 155017 144557 138808 135178 132680 130857 ${{\pi }_{r1}}$ 39855.6 51731.2 58474.1 62842.1 65909.7 68185.7 ${{u}_{r1}}(m)$ 39855.6 33166.1 26340.7 19440.7 12493.6 5514.37 ${{\pi }_{r2}}$ 1749.57 1341.72 1111.64 963.61 860.41 784.43 ${{\pi }_{s}}$ 196622 197630 198393 198983 199450 199827 ${{w}_{1}}$ 1250 1198.2 1169.67 1151.63 1139.2 1130.12 ${{w}_{2}}$ 700 707.25 711.43 714.17 716.11 717.56 ${{p}_{1}}$ 1439.39 1439.58 1438.92 1438.11 1437.33 1436.62 ${{p}_{2}}$ 728.79 732.46 734.38 735.53 736.3 736.84 ${{q}_{1}}$ 210.44 214.32 217.18 219.36 221.08 222.47 ${{q}_{2}}$ 60.77 53.22 48.44 45.1 42.62 40.69
 $\lambda$ 0 0.2 0.4 0.6 0.8 1 ${{\pi }_{m}}$ 155017 144557 138808 135178 132680 130857 ${{\pi }_{r1}}$ 39855.6 51731.2 58474.1 62842.1 65909.7 68185.7 ${{u}_{r1}}(m)$ 39855.6 33166.1 26340.7 19440.7 12493.6 5514.37 ${{\pi }_{r2}}$ 1749.57 1341.72 1111.64 963.61 860.41 784.43 ${{\pi }_{s}}$ 196622 197630 198393 198983 199450 199827 ${{w}_{1}}$ 1250 1198.2 1169.67 1151.63 1139.2 1130.12 ${{w}_{2}}$ 700 707.25 711.43 714.17 716.11 717.56 ${{p}_{1}}$ 1439.39 1439.58 1438.92 1438.11 1437.33 1436.62 ${{p}_{2}}$ 728.79 732.46 734.38 735.53 736.3 736.84 ${{q}_{1}}$ 210.44 214.32 217.18 219.36 221.08 222.47 ${{q}_{2}}$ 60.77 53.22 48.44 45.1 42.62 40.69
Simulation results in R2VFC scenario $(\sigma \rm{ = }1.3)$
 $\lambda$ 0 0.2 0.4 0.6 0.8 1 ${{\pi}_{m}}$ 87460.3 86899.2 86618.8 86456.2 86352.7 86282.2 ${{\pi}_{r1}}$ 5461.07 4999.86 4691.87 4470.61 4303.71 4173.24 ${{\pi}_{r2}}$ 4151.55 5123.74 5674.9 6027.98 6272.3 6450.71 ${{u}_{r2}}(m)$ 4151.55 -11231.3 -26702.7 -42229 -57792 -73380.8 ${{\pi}_{s}}$ 97072.9 97022.8 96985.5 96954.8 96928.7 96906.1 ${{w}_{1}}$ 950 952.33 953.75 954.72 955.43 955.97 ${{w}_{2}}$ 700 693.48 689.96 687.77 686.28 685.21 ${{p}_{1}}$ 990.48 991.06 991.27 991.34 991.36 991.36 ${{p}_{2}}$ 730.95 729.78 728.78 727.96 727.29 726.74 ${{q}_{1}}$ 134.92 129.1 125.06 122.07 119.77 117.94 ${{q}_{2}}$ 134.13 141.12 146.16 149.96 152.93 155.32
 $\lambda$ 0 0.2 0.4 0.6 0.8 1 ${{\pi}_{m}}$ 87460.3 86899.2 86618.8 86456.2 86352.7 86282.2 ${{\pi}_{r1}}$ 5461.07 4999.86 4691.87 4470.61 4303.71 4173.24 ${{\pi}_{r2}}$ 4151.55 5123.74 5674.9 6027.98 6272.3 6450.71 ${{u}_{r2}}(m)$ 4151.55 -11231.3 -26702.7 -42229 -57792 -73380.8 ${{\pi}_{s}}$ 97072.9 97022.8 96985.5 96954.8 96928.7 96906.1 ${{w}_{1}}$ 950 952.33 953.75 954.72 955.43 955.97 ${{w}_{2}}$ 700 693.48 689.96 687.77 686.28 685.21 ${{p}_{1}}$ 990.48 991.06 991.27 991.34 991.36 991.36 ${{p}_{2}}$ 730.95 729.78 728.78 727.96 727.29 726.74 ${{q}_{1}}$ 134.92 129.1 125.06 122.07 119.77 117.94 ${{q}_{2}}$ 134.13 141.12 146.16 149.96 152.93 155.32
Simulation results in R2VFC scenario $(\sigma \rm{ = }1.9)$
 $\lambda$ 0 0.2 0.4 0.6 0.8 1 ${{\pi}_{m}}$ 155017 155449 155763 156001 156187 156337 ${{\pi}_{r1}}$ 39855.6 38438.3 37444.8 36708.8 36141.3 35690.3 ${{\pi}_{r2}}$ 1749.5 1746.2 1684 1604.9 1524 1447.2 ${{u}_{r2}}(m)$ 1749.5 -28994.2 -59947.4 -91032.7 -122207 -153443 ${{\pi}_{s}}$ 196622 195633 194892 194315 193853 193475 ${{w}_{1}}$ 1250 1252.3 1253.9 1255.1 1256 1256.7 ${{w}_{2}}$ 700 699 698.6 698.4 698.3 698.3 ${{p}_{1}}$ 1439.3 1438.3 1437.5 1436.8 1436.3 1435.9 ${{p}_{2}}$ 728.7 724.3 721.1 718.6 716.7 715.2 ${{q}_{1}}$ 210.4 206.6 203.9 201.9 200.3 199.1 ${{q}_{2}}$ 60.7 69.01 74.9 79.3 82.8 85.6
 $\lambda$ 0 0.2 0.4 0.6 0.8 1 ${{\pi}_{m}}$ 155017 155449 155763 156001 156187 156337 ${{\pi}_{r1}}$ 39855.6 38438.3 37444.8 36708.8 36141.3 35690.3 ${{\pi}_{r2}}$ 1749.5 1746.2 1684 1604.9 1524 1447.2 ${{u}_{r2}}(m)$ 1749.5 -28994.2 -59947.4 -91032.7 -122207 -153443 ${{\pi}_{s}}$ 196622 195633 194892 194315 193853 193475 ${{w}_{1}}$ 1250 1252.3 1253.9 1255.1 1256 1256.7 ${{w}_{2}}$ 700 699 698.6 698.4 698.3 698.3 ${{p}_{1}}$ 1439.3 1438.3 1437.5 1436.8 1436.3 1435.9 ${{p}_{2}}$ 728.7 724.3 721.1 718.6 716.7 715.2 ${{q}_{1}}$ 210.4 206.6 203.9 201.9 200.3 199.1 ${{q}_{2}}$ 60.7 69.01 74.9 79.3 82.8 85.6
Simulation results in R1HFC scenario $(\sigma \rm{ = }1.3)$
 $\lambda$ 0 0.2 0.4 0.6 0.8 1 ${{\pi }_{m}}$ 87460.3 88162.1 88670.6 89055.9 89358 89601.2 ${{\pi }_{r1}}$ 5461.07 4804.17 4323.18 3955.74 3665.87 3431.35 ${{u}_{r1}}({{r}_{2}})$ 5461.07 4914.64 4323.11 3702.96 3063.48 2410.34 ${{\pi }_{r2}}$ 4151.55 4251.8 4323.35 4377.05 4418.87 4452.37 ${{\pi }_{s}}$ 97072.9 97218.1 97317.1 97388.7 97442.8 97484.9 ${{w}_{1}}$ 950 952.61 954.51 955.96 957.1 958.01 ${{w}_{2}}$ 700 697.39 695.52 694.1 692.99 692.1 ${{p}_{1}}$ 990.48 988.05 986.29 984.96 983.91 983.07 ${{p}_{2}}$ 730.95 728.72 727.1 725.88 724.92 724.15 ${{q}_{1}}$ 134.92 135.55 136.02 136.4 136.7 136.94 ${{q}_{2}}$ 134.13 135.74 136.87 137.72 138.38 138.9
 $\lambda$ 0 0.2 0.4 0.6 0.8 1 ${{\pi }_{m}}$ 87460.3 88162.1 88670.6 89055.9 89358 89601.2 ${{\pi }_{r1}}$ 5461.07 4804.17 4323.18 3955.74 3665.87 3431.35 ${{u}_{r1}}({{r}_{2}})$ 5461.07 4914.64 4323.11 3702.96 3063.48 2410.34 ${{\pi }_{r2}}$ 4151.55 4251.8 4323.35 4377.05 4418.87 4452.37 ${{\pi }_{s}}$ 97072.9 97218.1 97317.1 97388.7 97442.8 97484.9 ${{w}_{1}}$ 950 952.61 954.51 955.96 957.1 958.01 ${{w}_{2}}$ 700 697.39 695.52 694.1 692.99 692.1 ${{p}_{1}}$ 990.48 988.05 986.29 984.96 983.91 983.07 ${{p}_{2}}$ 730.95 728.72 727.1 725.88 724.92 724.15 ${{q}_{1}}$ 134.92 135.55 136.02 136.4 136.7 136.94 ${{q}_{2}}$ 134.13 135.74 136.87 137.72 138.38 138.9
Simulation results in R1HFC scenario $(\sigma \rm{ = }1.9)$
 $\lambda$ 0 0.2 0.4 0.6 0.8 1 ${{\pi }_{m}}$ 155017 156078 156896 157543 158064 158493 ${{\pi }_{r1}}$ 39855.6 38221 36996.4 36046.7 35289.5 34671.9 ${{u}_{r1}}({{r}_{2}})$ 39855.6 45435.9 50817.1 56069.3 61233.1 66333.8 ${{\pi }_{r2}}$ 1749.57 2146.42 2444.61 2675.82 2859.98 3009.96 ${{\pi }_{s}}$ 196622 196445 196337 196265 196214 196175 ${{w}_{1}}$ 1250 1252.66 1254.86 1256.67 1258.18 1259.44 ${{w}_{2}}$ 700 691.75 685.91 681.55 678.18 675.48 ${{p}_{1}}$ 1439.39 1435.49 1432.54 1430.24 1428.4 1426.9 ${{p}_{2}}$ 728.79 723.63 719.94 717.16 714.98 713.24 ${{q}_{1}}$ 210.44 209.05 208.22 207.68 207.31 207.04 ${{q}_{2}}$ 134.13 127.37 122.71 119.28 119.28 114.55
 $\lambda$ 0 0.2 0.4 0.6 0.8 1 ${{\pi }_{m}}$ 155017 156078 156896 157543 158064 158493 ${{\pi }_{r1}}$ 39855.6 38221 36996.4 36046.7 35289.5 34671.9 ${{u}_{r1}}({{r}_{2}})$ 39855.6 45435.9 50817.1 56069.3 61233.1 66333.8 ${{\pi }_{r2}}$ 1749.57 2146.42 2444.61 2675.82 2859.98 3009.96 ${{\pi }_{s}}$ 196622 196445 196337 196265 196214 196175 ${{w}_{1}}$ 1250 1252.66 1254.86 1256.67 1258.18 1259.44 ${{w}_{2}}$ 700 691.75 685.91 681.55 678.18 675.48 ${{p}_{1}}$ 1439.39 1435.49 1432.54 1430.24 1428.4 1426.9 ${{p}_{2}}$ 728.79 723.63 719.94 717.16 714.98 713.24 ${{q}_{1}}$ 210.44 209.05 208.22 207.68 207.31 207.04 ${{q}_{2}}$ 134.13 127.37 122.71 119.28 119.28 114.55
Simulation results in R2HFC scenario $(\sigma \rm{ = }1.3)$
 $\lambda$ 0 0.2 0.4 0.6 0.8 1 ${{\pi }_{m}}$ 87460.3 88162.1 88670.6 89055.9 89358 89601.2 ${{\pi }_{r1}}$ 5461.07 5511.81 5550.75 5581.37 5605.99 5626.19 ${{u}_{r2}}({{r}_{1}})$ 4151.55 3544.17 3095.78 2751.42 2478.75 2257.54 ${{\pi }_{r2}}$ 4151.55 3150.64 2113.79 1053.45 -23.04 -1111.1 ${{\pi }_{s}}$ 97072.9 97218.1 97317.1 97388.7 97442.8 97484.9 ${{w}_{1}}$ 950 947.39 945.49 944.04 942.9 941.99 ${{w}_{2}}$ 700 702.61 704.48 705.9 707.01 707.9 ${{p}_{1}}$ 990.48 988.05 986.29 984.96 983.91 983.07 ${{p}_{2}}$ 730.95 728.72 727.1 725.88 724.92 724.15 ${{q}_{1}}$ 134.92 135.55 136.02 136.4 136.7 136.94 ${{q}_{2}}$ 134.13 135.74 136.87 137.72 138.38 138.9
 $\lambda$ 0 0.2 0.4 0.6 0.8 1 ${{\pi }_{m}}$ 87460.3 88162.1 88670.6 89055.9 89358 89601.2 ${{\pi }_{r1}}$ 5461.07 5511.81 5550.75 5581.37 5605.99 5626.19 ${{u}_{r2}}({{r}_{1}})$ 4151.55 3544.17 3095.78 2751.42 2478.75 2257.54 ${{\pi }_{r2}}$ 4151.55 3150.64 2113.79 1053.45 -23.04 -1111.1 ${{\pi }_{s}}$ 97072.9 97218.1 97317.1 97388.7 97442.8 97484.9 ${{w}_{1}}$ 950 947.39 945.49 944.04 942.9 941.99 ${{w}_{2}}$ 700 702.61 704.48 705.9 707.01 707.9 ${{p}_{1}}$ 990.48 988.05 986.29 984.96 983.91 983.07 ${{p}_{2}}$ 730.95 728.72 727.1 725.88 724.92 724.15 ${{q}_{1}}$ 134.92 135.55 136.02 136.4 136.7 136.94 ${{q}_{2}}$ 134.13 135.74 136.87 137.72 138.38 138.9
Simulation results in R2HFC scenario $(\sigma \rm{ = }1.9)$
 $\lambda$ 0 0.2 0.4 0.6 0.8 1 ${{\pi }_{m}}$ 155017 156078 156896 157543 158064 158493 ${{\pi }_{r1}}$ 39855.6 39332 39020.8 38819.5 38680.8 38580.8 ${{u}_{r2}}({{r}_{1}})$ 1749.57 1035.45 420.15 -96.91 -531.35 -898.98 ${{\pi }_{r2}}$ 1749.57 -6623.86 -15020.1 -23446.7 -31901.1 -40378.8 ${{\pi }_{s}}$ 196622 196445 196337 196265 196214 196175 ${{w}_{1}}$ 1250 1247.34 1245.14 1243.32 1241.82 1240.56 ${{w}_{2}}$ 700 708.25 714.09 718.45 721.82 724.52 ${{p}_{1}}$ 1439.39 1435.49 1432.54 1430.24 1428.4 1426.9 ${{p}_{2}}$ 728.79 723.63 719.94 717.16 714.98 713.24 ${{q}_{1}}$ 210.44 209.05 208.22 207.68 207.31 207.04 ${{q}_{2}}$ 134.13 135.74 136.87 137.72 138.38 138.9
 $\lambda$ 0 0.2 0.4 0.6 0.8 1 ${{\pi }_{m}}$ 155017 156078 156896 157543 158064 158493 ${{\pi }_{r1}}$ 39855.6 39332 39020.8 38819.5 38680.8 38580.8 ${{u}_{r2}}({{r}_{1}})$ 1749.57 1035.45 420.15 -96.91 -531.35 -898.98 ${{\pi }_{r2}}$ 1749.57 -6623.86 -15020.1 -23446.7 -31901.1 -40378.8 ${{\pi }_{s}}$ 196622 196445 196337 196265 196214 196175 ${{w}_{1}}$ 1250 1247.34 1245.14 1243.32 1241.82 1240.56 ${{w}_{2}}$ 700 708.25 714.09 718.45 721.82 724.52 ${{p}_{1}}$ 1439.39 1435.49 1432.54 1430.24 1428.4 1426.9 ${{p}_{2}}$ 728.79 723.63 719.94 717.16 714.98 713.24 ${{q}_{1}}$ 210.44 209.05 208.22 207.68 207.31 207.04 ${{q}_{2}}$ 134.13 135.74 136.87 137.72 138.38 138.9
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