# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2021035
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## Effects of take-back legislation on pricing and coordination in a closed-loop supply chain

 College of Economics & Management, Huazhong Agricultural University, Wuhan, Hubei 430070, China

* Corresponding author: Xianpei Hong

Received  April 2020 Revised  November 2020 Early access March 2021

Fund Project: The study is supported in part by the Humanities and Social Science project of Ministry of Education of China (Project No. 19YJC630229), Natural Science Foundation of Hubei Province (Project No. 2019CFB120), National Natural Science Foundation of China (Project No. 71672071), and the Fundamental Research Funds for the Central Universities (Project No. 2662020JGPYG14)

This study investigates the effects of take-back legislation and channel structures on pricing, collection, and coordination in a closed-loop supply chain (CLSC). By establishing the centralized, manufacturer-led, and retailer-led CLSC models, we analyze the equilibrium solutions of channel players and the government. We obtain the following results. (1) The manufacturer can accept a higher collection target and exit the market later in the centralized model than in decentralized decision-making models. Moreover, the manufacturer exists the market earlier in the retailer-led model with regulation compared with the manufacturer-led model. (2) The government's optimal collection target is the same under manufacturer-led and retailer-led models when the regulation comes into force. (3) Revenue-sharing and two-part tariff contracts can effectively coordinate manufacturer-led and retailer-led CLSCs under take-back legislation. Finally, we conduct several numerical examples and obtain relevant managerial insights. Our results indicate that the correlation between take-back legislation and channel structure has a significant impact on the pricing and coordination decisions of the CLSC; furthermore, the government should flexibly set the collection target when facing different supply chain and channel power structures in a CLSC.

Citation: Benrong Zheng, Xianpei Hong. Effects of take-back legislation on pricing and coordination in a closed-loop supply chain. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021035
##### References:
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Chen, What is the role of value-added service in a remanufacturing closed-loop supply chain?, International Journal of Production Research, 59 (2020), 3342-3361.  doi: 10.1080/00207543.2019.1702230.  Google Scholar [29] Z. Hong, H. Wang and Y. Gong, Green product design considering functional-product reference, International Journal of Production Economics, 210 (2019), 155-168.  doi: 10.1016/j.ijpe.2019.01.008.  Google Scholar [30] L. Hsiao, Y. J. Chen and H. Xiong, Supply chain coordination with product line design and a revenue sharing scheme, Naval Research Logistics, 66 (2019), 213-229.  doi: 10.1002/nav.21836.  Google Scholar [31] X. Huang, A. Atasu and L. B. Toktay, Design implications of extended producer responsibility for durable products, Management Science, 65 (2019), 2573-2590.   Google Scholar [32] B. W. Jacobs and R. 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show all references

##### References:
 [1] S. Alizamir, F. Iravani and H. Mamani, An analysis of price vs. revenue protection: Government subsidies in the agriculture industry, Management Science, 65 (2018), 1-18.  doi: 10.1287/mnsc.2017.2927.  Google Scholar [2] A. Arya and B. Mittendorf, Supply chain consequences of subsidies for corporate social responsibility, Production and Operations Management, 24 (2015), 1346-1357.  doi: 10.1111/poms.12326.  Google Scholar [3] A. Atasu, L. N. Van Wassenhove and M. Sarvary, Efficient take-back legislation, Production and Operations Management, 18 (2009), 243-258.  doi: 10.1111/j.1937-5956.2009.01004.x.  Google Scholar [4] A. Atasu and L. N. Van Wassenhove, An operations perspective on product take-back legislation for e-waste: Theory, practice, and research needs, Production and Operations Management, 21 (2012), 407-422.  doi: 10.1111/j.1937-5956.2011.01291.x.  Google Scholar [5] A. Atasu, L. B. Toktay and L. N. Van Wassenhove., How collection cost structure drives a manufacturer's reverse channel choice, Production and Operations Management, 22 (2013), 1089-1102.  doi: 10.1111/j.1937-5956.2012.01426.x.  Google Scholar [6] Q. G. Bai, M. Y. Chen and L. Xu, Revenue and promotional cost-sharing contract versus two-part tariff contract in coordinating sustainable supply chain systems with deteriorating items, International Journal of Production Economics, 187 (2017), 85-101.   Google Scholar [7] I. Biswas, A. Raj and S. K. Srivastava, Supply chain channel coordination with triple bottom line approach, Transportation Research Part E: Logistics and Transportation Review, 115 (2018), 213-226.  doi: 10.1016/j.tre.2018.05.007.  Google Scholar [8] G. S. Cai, Z. G. Zhang and M. Zhang, Game theoretical perspectives on dual-channel supply chain competition with price discounts and pricing schemes, International Journal of Production Economics, 117 (2009), 80-96.  doi: 10.1016/j.ijpe.2008.08.053.  Google Scholar [9] C. K. Chen and M. Akmalul Ulya, Analyses of the reward-penalty mechanism in green closed-loop supply chains with product remanufacturing, International Journal of Production Economics, 210 (2019), 211-223.  doi: 10.1016/j.ijpe.2019.01.006.  Google Scholar [10] X. Chen and X. J. Wang, Free or bundled: Channel selection decisions under different power structures, Omega, 53 (2015), 11-20.  doi: 10.1016/j.omega.2014.11.008.  Google Scholar [11] X. Chen, X. J. Wang and H. K. Chan, Manufacturer and retailer coordination for environmental and economic competitiveness: A power perspective, Transportation Research Part E: Logistics and Transportation Review, 97 (2017), 268-281.  doi: 10.1016/j.tre.2016.11.007.  Google Scholar [12] J. Y. Chen, S. Dimitrov and H. Pun, The impact of government subsidy on supply Chains' sustainability innovation, Omega, 86 (2019), 42-58.  doi: 10.1016/j.omega.2018.06.012.  Google Scholar [13] P. Chintapalli, S. M. Disney and C. S. Tang, Coordinating supply chains via advance-order discounts, minimum order quantities, and delegations, Production and Operations Management, 26 (2017), 2175-2186.  doi: 10.1111/poms.12751.  Google Scholar [14] T. M. Choi, Y. J. Li and L. Xu., Channel leadership, performance and coordination in closed loop supply chains, International Journal of Production Economics, 146 (2013), 371-380.  doi: 10.1016/j.ijpe.2013.08.002.  Google Scholar [15] J. Ding, W. Chen and W. Wang, Production and carbon emission reduction decisions for remanufacturing firms under carbon tax and take-back legislation, Computers & Industrial Engineering, 143 (2020), 106419. doi: 10.1016/j.cie.2020.106419.  Google Scholar [16] G. Esenduran, A. Atasu and L. N. Van Wassenhove, Valuable e-waste: Implications for extended producer responsibility, IISE Transactions, 51 (2019), 382-396.   Google Scholar [17] G. Esenduran, E. Kemahlioglu-Ziya and J. M. Swaminathan, Impact of take-back regulation on the remanufacturing industry, Production and Operations Management, 26 (2017), 924-944.  doi: 10.1111/poms.12673.  Google Scholar [18] G. Esenduran and E. Kemahlioglu-Ziya, A comparison of product take-back compliance schemes, Production and Operations Management, 24 (2015), 71-88.  doi: 10.1111/poms.12213.  Google Scholar [19] L. Feng, K. Govindan and C. Li, Strategic planning: Design and coordination for dual-recycling channel reverse supply chain considering consumer behavior, European Journal of Operational Research, 260 (2017), 601-612.  doi: 10.1016/j.ejor.2016.12.050.  Google Scholar [20] J. H. Gao, H. S. Han, L. T. Hou and H. Y. Wang, Pricing and effort decisions in a closed-loop supply chain under different channel power structures, Journal of Cleaner Production, 112 (2016), 2043-2057.  doi: 10.1016/j.jclepro.2015.01.066.  Google Scholar [21] L. Y. Gui, A. Atasu, O. Ergun and L. Toktay, Design incentives under collective extended producer responsibility: A network perspective, Management Science, 64 (2018), 5083-5104.   Google Scholar [22] L. Y. Gui, A. Atasu, O. Ergun and L. B. Toktay, Efficient implementation of collective extended producer responsibility legislation, Management Science, 62 (2015), 1098-1123.  doi: 10.1287/mnsc.2015.2163.  Google Scholar [23] P. Hasanov, M. Y. Jaber and N. Tahirov, Four-level closed loop supply chain with remanufacturing, Applied Mathematical Modelling, 66 (2019), 141-155.  doi: 10.1016/j.apm.2018.08.036.  Google Scholar [24] P. He, Y. He and H. Xu, Channel structure and pricing in a dual-channel closed-loop supply chain with government subsidy, International Journal of Production Economics, 213 (2019), 108-123.  doi: 10.1016/j.ijpe.2019.03.013.  Google Scholar [25] Q. He, N. Wang, Z. Yang, Z. He, Zh eng and B. Jiang, Competitive collection under channel inconvenience in closed-loop supply chain, European Journal of Operational Research, 275 (2019), 155-166.  doi: 10.1016/j.ejor.2018.11.034.  Google Scholar [26] Y. He, Acquisition pricing and remanufacturing decisions in a closed-loop supply chain, International Journal of Production Economics, 163 (2015), 48-60.  doi: 10.1016/j.ijpe.2015.02.002.  Google Scholar [27] Y. He and X. Zhao, Contracts and coordination: Supply chains with uncertain demand and supply, Naval Research Logistics, 63 (2016), 305-319.  doi: 10.1002/nav.21695.  Google Scholar [28] X. Hong, L. Wang, Y. Gong and W. Chen, What is the role of value-added service in a remanufacturing closed-loop supply chain?, International Journal of Production Research, 59 (2020), 3342-3361.  doi: 10.1080/00207543.2019.1702230.  Google Scholar [29] Z. Hong, H. Wang and Y. Gong, Green product design considering functional-product reference, International Journal of Production Economics, 210 (2019), 155-168.  doi: 10.1016/j.ijpe.2019.01.008.  Google Scholar [30] L. Hsiao, Y. J. Chen and H. Xiong, Supply chain coordination with product line design and a revenue sharing scheme, Naval Research Logistics, 66 (2019), 213-229.  doi: 10.1002/nav.21836.  Google Scholar [31] X. Huang, A. Atasu and L. B. Toktay, Design implications of extended producer responsibility for durable products, Management Science, 65 (2019), 2573-2590.   Google Scholar [32] B. W. Jacobs and R. Subramanian, Sharing responsibility for product recovery across the supply chain, Production and Operations Management, 21 (2012), 85-100.  doi: 10.1111/j.1937-5956.2011.01246.x.  Google Scholar [33] Z. J. Ma, Y. S. Ye, Y. Dai and H. Yan, The price of anarchy in closed–loop supply chains, International Transactions in Operational Research, 2019. doi: 10.1111/itor.12743.  Google Scholar [34] T. Maiti and B. C. Giri, A closed loop supply chain under retail price and product quality dependent demand, Journal of Manufacturing Systems, 37 (2015), 624-637.  doi: 10.1016/j.jmsy.2014.09.009.  Google Scholar [35] S. Mitra and S. Webster, Competition in remanufacturing and the effects of government subsidies, International Journal of Production Economics, 111 (2008), 287-298.  doi: 10.1016/j.ijpe.2007.02.042.  Google Scholar [36] G. Raz and G. C. Souza, Recycling as a strategic supply source, Production and Operations Management, 27 (2018), 902-916.  doi: 10.1111/poms.12851.  Google Scholar [37] S. Sarkar, S. Tiwari, H. M. Wee and B. C. Giri, Channel coordination with price discount mechanism under price–sensitive market demand, International Transactions in Operational Research, 27 (2020), 2509-2533.  doi: 10.1111/itor.12678.  Google Scholar [38] R. C. Savaskan, S. Bhattacharya and L. N. Van Wassenhove, Closed-loop supply chain models with product remanufacturing, Management Science, 50 (2004), 133-279.  doi: 10.1287/mnsc.1030.0186.  Google Scholar [39] R. C. Savaskan and L. N. Van Wassenhove, Reverse channel design: The case of competing retailers, Management Science, 52 (2006), 1-14.  doi: 10.1287/mnsc.1050.0454.  Google Scholar [40] M. A. Sieke, R. W. Seifert and U. W. Thonemann, Designing service level contracts for supply chain coordination, Production and Operations Management, 21 (2012), 698-714.  doi: 10.1111/j.1937-5956.2011.01301.x.  Google Scholar [41] R. Sousa, E. Agante, J. Cerejeira and M. Portela, EEE fees and the WEEE system-A model of efficiency and income in European countries, Waste Management, 79 (2018), 770-780.  doi: 10.1016/j.wasman.2018.08.008.  Google Scholar [42] R. Subramanian, S. Gupta and F. B. Talbot, Product design and supply chain coordination under extended producer responsibility, Production and Operations Management, 18 (2009), 259-277.   Google Scholar [43] F. Toyasaki, T. Boyaci and V. Verter, An analysis of monopolistic and competitive take-back schemes for WEEE recycling, Production and Operations Management, 20 (2011), 805-823.  doi: 10.1111/j.1937-5956.2010.01207.x.  Google Scholar [44] W. B. Wang, S. Q. Yang, L. Xu and X. L. 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Effects of $\tau_g$ on equilibrium prices $w^{*}$ and $p^{*}$
Effect of $\tau_g$ on equilibrium profits
Effects of $\kappa$ and $\chi$ on equilibrium collection target $\tau_g^{*}$
Effects of $\Delta$ on contract parameters $\phi^{*}$ and $F^{*}$
Comparison of our study and related literature
 Research paper Take-back legislation CLSC power structure Supply chain coordination Endogenous government's decision Choi et al. [14] $\surd$ $\surd$ Chen et al. [11] $\surd$ $\surd$ He et al. [25] $\surd$ Zheng et al. [54] $\surd$ Bai et al. [6] $\surd$ Zheng et al. [53] $\surd$ $\surd$ Wang et al. [45] $\surd$ Toyasaki et al. [43] $\surd$ $\surd$ Esenduran and Kemahlioglu-Ziya [18] $\surd$ $\surd$ Subramanian et al. [42] $\surd$ $\surd$ $\surd$ Jacobs and Subramanian [32] $\surd$ $\surd$ Chen and Akmalul Ulya [9] $\surd$ Alizamir et al. [1] $\surd$ $\surd$ Our work $\surd$ $\surd$ $\surd$ $\surd$
 Research paper Take-back legislation CLSC power structure Supply chain coordination Endogenous government's decision Choi et al. [14] $\surd$ $\surd$ Chen et al. [11] $\surd$ $\surd$ He et al. [25] $\surd$ Zheng et al. [54] $\surd$ Bai et al. [6] $\surd$ Zheng et al. [53] $\surd$ $\surd$ Wang et al. [45] $\surd$ Toyasaki et al. [43] $\surd$ $\surd$ Esenduran and Kemahlioglu-Ziya [18] $\surd$ $\surd$ Subramanian et al. [42] $\surd$ $\surd$ $\surd$ Jacobs and Subramanian [32] $\surd$ $\surd$ Chen and Akmalul Ulya [9] $\surd$ Alizamir et al. [1] $\surd$ $\surd$ Our work $\surd$ $\surd$ $\surd$ $\surd$
Basic parameter set
 Parameter $a$ $b$ $c_m$ $\Delta$ $f$ $C_L$ Initial value $200$ $10$ $10$ $8$ $10$ $900$
 Parameter $a$ $b$ $c_m$ $\Delta$ $f$ $C_L$ Initial value $200$ $10$ $10$ $8$ $10$ $900$
Comparison of equilibrium decisions in CLSC under RS contract
 recycling is not constrained recycling is constrained Model $DM$ $DR$ $CM$ $CR$ $I$ Model $DM$ $DR$ $CM$ $CR$ $I$ $w^{*}$ $14.51$ $11.96$ $3.14$ $25.68$ $-$ $w^{*}$ $13.80$ $10.70$ $3.04$ $25.20$ $-$ $p^{*}$ $17.26$ $16.96$ $13.92$ $13.92$ $13.92$ $p^{*}$ $16.90$ $16.90$ $13.80$ $13.80$ $13.80$ $\tau^{*}$ $0.12$ $0.14$ $0.27$ $0.27$ $0.27$ $\tau^{*}$ $0.30$ $0.30$ $0.30$ $0.30$ $0.30$ $\pi_M^{*}$ $127.20$ $66.01$ $146.14$ $72.18$ $-$ $\pi_M^{*}$ $101.20$ $5.10$ $139.64$ $62.76$ $-$ $\pi_R^{*}$ $75.29$ $152.00$ $147.92$ $221.88$ $-$ $\pi_R^{*}$ $96.10$ $192.20$ $153.76$ $230.64$ $-$ $\pi_{T}^{*}$ $202.49$ $218.01$ $294.10$ $294.10$ $294.10$ $\pi_{T}^{*}$ $197.30$ $197.30$ $293.40$ $293.40$ $293.40$
 recycling is not constrained recycling is constrained Model $DM$ $DR$ $CM$ $CR$ $I$ Model $DM$ $DR$ $CM$ $CR$ $I$ $w^{*}$ $14.51$ $11.96$ $3.14$ $25.68$ $-$ $w^{*}$ $13.80$ $10.70$ $3.04$ $25.20$ $-$ $p^{*}$ $17.26$ $16.96$ $13.92$ $13.92$ $13.92$ $p^{*}$ $16.90$ $16.90$ $13.80$ $13.80$ $13.80$ $\tau^{*}$ $0.12$ $0.14$ $0.27$ $0.27$ $0.27$ $\tau^{*}$ $0.30$ $0.30$ $0.30$ $0.30$ $0.30$ $\pi_M^{*}$ $127.20$ $66.01$ $146.14$ $72.18$ $-$ $\pi_M^{*}$ $101.20$ $5.10$ $139.64$ $62.76$ $-$ $\pi_R^{*}$ $75.29$ $152.00$ $147.92$ $221.88$ $-$ $\pi_R^{*}$ $96.10$ $192.20$ $153.76$ $230.64$ $-$ $\pi_{T}^{*}$ $202.49$ $218.01$ $294.10$ $294.10$ $294.10$ $\pi_{T}^{*}$ $197.30$ $197.30$ $293.40$ $293.40$ $293.40$
Comparison of equilibrium decisions under TPT contract
 recycling is not constrained recycling is constrained Model $DM$ $DR$ $CM$ $CR$ $I$ Model $DM$ $DR$ $CM$ $CR$ $I$ $w^{*}$ $14.51$ $11.96$ $7.84$ $13.92$ $-$ $w^{*}$ $13.80$ $10.70$ $7.60$ $13.80$ $-$ $p^{*}$ $17.26$ $16.96$ $13.92$ $13.92$ $13.92$ $p^{*}$ $16.90$ $16.90$ $13.80$ $13.80$ $13.80$ $\tau^{*}$ $0.12$ $0.14$ $0.27$ $0.27$ $0.27$ $\tau^{*}$ $0.30$ $0.30$ $0.30$ $0.30$ $0.30$ $\pi_M^{*}$ $127.20$ $66.01$ $139.30$ $79.05$ $-$ $\pi_M^{*}$ $101.20$ $5.10$ $124.00$ $78.40$ $-$ $\pi_R^{*}$ $75.29$ $152.00$ $154.80$ $215.05$ $-$ $\pi_R^{*}$ $96.10$ $192.20$ $169.40$ $215.00$ $-$ $\pi_{T}^{*}$ $202.49$ $218.01$ $294.10$ $294.10$ $294.10$ $\pi_{T}^{*}$ $197.30$ $197.30$ $293.40$ $293.40$ $293.40$
 recycling is not constrained recycling is constrained Model $DM$ $DR$ $CM$ $CR$ $I$ Model $DM$ $DR$ $CM$ $CR$ $I$ $w^{*}$ $14.51$ $11.96$ $7.84$ $13.92$ $-$ $w^{*}$ $13.80$ $10.70$ $7.60$ $13.80$ $-$ $p^{*}$ $17.26$ $16.96$ $13.92$ $13.92$ $13.92$ $p^{*}$ $16.90$ $16.90$ $13.80$ $13.80$ $13.80$ $\tau^{*}$ $0.12$ $0.14$ $0.27$ $0.27$ $0.27$ $\tau^{*}$ $0.30$ $0.30$ $0.30$ $0.30$ $0.30$ $\pi_M^{*}$ $127.20$ $66.01$ $139.30$ $79.05$ $-$ $\pi_M^{*}$ $101.20$ $5.10$ $124.00$ $78.40$ $-$ $\pi_R^{*}$ $75.29$ $152.00$ $154.80$ $215.05$ $-$ $\pi_R^{*}$ $96.10$ $192.20$ $169.40$ $215.00$ $-$ $\pi_{T}^{*}$ $202.49$ $218.01$ $294.10$ $294.10$ $294.10$ $\pi_{T}^{*}$ $197.30$ $197.30$ $293.40$ $293.40$ $293.40$
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