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January  2022, 18(1): 487-510. doi: 10.3934/jimo.2020165

## Coordination of a sustainable reverse supply chain with revenue sharing contract

 Department of Mathematics, Jadavpur University, Kolkata-700032, India

* Corresponding author: Bibhas C. Giri

Received  February 2020 Revised  August 2020 Published  January 2022 Early access  November 2020

In this article, a three-echelon closed-loop supply chain is considered under sustainability consideration through remanufacturing of waste materials. Depending upon quality, the collector collects the used products and forwards to the manufacturer for remanufacturing. The collector offers a reward or incentive to consumers to influence them to return the used items. The shortfall amount of collected used items, if any, is meet up by the supplier by supplying fresh raw materials. In three separate cases viz centralized, decentralized and revenue-sharing contract, optimal incentives for end-customers and optimal profits of supply chain members are determined. The revenue-sharing contract is implemented in two different settings - one including the supplier and the other one excluding the supplier. The win-win outcome for the supply chain members is investigated and a specific range of the sharing parameter for win-win outcome is obtained. Optimal results are supported by numerical analysis, and sensitivity of the optimal results with respect to key parameters is analyzed.

Citation: Sushil Kumar Dey, Bibhas C. Giri. Coordination of a sustainable reverse supply chain with revenue sharing contract. Journal of Industrial and Management Optimization, 2022, 18 (1) : 487-510. doi: 10.3934/jimo.2020165
##### References:
 [1] B. Ageron, A. Gunasekaran and A. Spalanzani, Sustainable supply management: An empirical study, International Journal of Production Economics, 140 (2012), 168-182.  doi: 10.1016/j.ijpe.2011.04.007. [2] L. Aramyan, R. Hoste, W. Van Den Broek, J. Groot, H. Soethoudt, T. L. Nguyen, J. Hermansen and J. van der Vorst, Towards sustainable food production: A scenario study of the European pork sector, Journal on Chain and Network Science, 11 (2011), 177-189.  doi: 10.3920/JCNS2011.Qpork8. [3] A. N. Arnette, B. L. Brewer and T. Choal, Design for sustainability (DFS): The intersection of supply chain and environment, Journal of Cleaner Production, 83 (2004), 374-390.  doi: 10.1016/j.jclepro.2014.07.021. [4] Q. Bai, M. 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. [5] Z. Basiri and J. Heydari, A mathematical model for green supply chain coordination with sustainable products, Journal of Cleaner Production, 145 (2017), 232-249. [6] Y. Bouchery, A. Ghaffari, Z. Jemai and J. Fransoo, Sustainable transportation and order quantity: Insights from multi-objective optimization, Flexible Services and Manufacturing Journal, 28 (2016), 367-396. [7] G. P. 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. [8] O. Capraz, O. Polat and A. Gungor, Planning of waste electrical and electronic equipment(WEEE) recycling facilities: MILP modelling and case study investigation, Flexible Services and Manufacturing Journal, 27 (2015), 479-508.  doi: 10.1007/s10696-015-9217-3. [9] X. Chen, H. Zhang, M. Zhang and J. Chen, Optimal decisions in a retailer Stackelberg supply chain, International Journal of Production Economics, 187 (2017), 260-270.  doi: 10.1016/j.ijpe.2017.03.002. [10] B. Chen, W. Xie, F. Huang and J. He, Quality competition and coordination in a VMI supply chain with two risk-averse manufacturers, Journal of Industrial and Management Optimization, http://dx.doi.org/10.3934/jimo.2020100. [11] D. Chen, J. Ignatis, D. Sun, S. Zhan, C. Zhou, M. Marra and M. Demirbag, Reverse logistics pricing strategy for a green supply chain: A view of customer's environmental awareness, International Journal of Production Economics, 217 (2019), 197-210.  doi: 10.1016/j.ijpe.2018.08.031. [12] K. Das and AH. Chowdhury, Designing a reverse logistics network for optimal collection, recovery and quality-based product-mix planning, International Journal of Production Economics, 135 (2012), 209-221.  doi: 10.1016/j.ijpe.2011.07.010. [13] M. Eskandarpour, P. Dejax, J. Miemczyk and O. Péton, Sustainable supply chain network design: An optimization-oriented review, Omega, 54 (2015), 11-32. [14] B. C. Giri and B. R. Sarker, Coordinating a multi-echelon supply chain under production disruption and price-sensitive stochastic demand, Journal of Industrial and Management Optimization, 15 (2019), 1631-1651.  doi: 10.3934/jimo.2018115. [15] B. C. Giri and S. K. Dey, Game theoretic analysis of a closed-loop supply chain with backup supplier under dual channel recycling, Computers and Industrial Engineering, 129 (2019), 179-191.  doi: 10.1016/j.cie.2019.01.035. [16] K. Govindan, S. G. Azevedo, H. Carvalho and V. Cruz-Machado, Impact of Supply chain Management practices on sustainability, Journal of Cleaner Production, 85 (2014), 212-225.  doi: 10.1016/j.jclepro.2014.05.068. [17] K. Govindan and M. N. Popiuc, Reverse supply chain coordination by revenue sharing contract: A case for the personal computers industry, European Journal of Operational Research, 233 (2014), 326-336.  doi: 10.1016/j.ejor.2013.03.023. [18] K. W. Green, P. J. Zelbst, J. Meacham and V. S. Bhadauria, Green supply chain management practices: Impact on performance, Supply Chain Management: An International Journal, 17 (2012), 290-305.  doi: 10.1108/13598541211227126. [19] J. Heydari, K. Govindan and A. Jafari, Reverse and closed loop supply chain coordination by considering government role, Transportation Research Part D: Transport and Environment, 52 (2017), 379-398.  doi: 10.1016/j.trd.2017.03.008. [20] J. Heydari and M. Ghasemi, A revenue sharing contract for reverse supply chain coordination under stochastic quality of returned products and uncertain remanufacturing capacity, Journal of Cleaner Production, 197 (2018), 607-615.  doi: 10.1016/j.jclepro.2018.06.206. [21] J. Heydari, K. Govindan and R. Sadeghi, Reverse supply chain coordination under stochastic remanufacturing capacity, International Journal of Production Economics, 202 (2018), 1-11.  doi: 10.1016/j.ijpe.2018.04.024. [22] S. Hu, Y. Dai, Z. J. Ma and Y. S. Ye, Designing contracts for a reverse supply chainwith strategic recycling behavior of consumers, International Journal of Production Economics, 180 (2016), 16-24. [23] B. Hu and Y. Feng, Optimization and coordination of supply chain with revenue sharing contracts and service requirement under supply and demand uncertainty, International Journal of Production Economics, 183 (2017), 185-193. [24] G. Hua, S. Wang and T. C. E. Cheng, Price and lead time decisions in dual-channel supply chains, European Journal of Operational Research, 205 (2010), 113-126.  doi: 10.1016/j.ejor.2009.12.012. [25] F. Huang, J. He and J. Wang, Coordination of VMI supply chain with a loss-averse manufacturer under quality-dependency and marketing-dependency, Journal of Industrial and Management Optimization, 15 (2019), 1753-1772.  doi: 10.3934/jimo.2018121. [26] F. Huang, J. He and Q. Lai, Coordination in a retailer-dominated supply chain with a risk-averse manufacturer under marketing dependency, International Transactions in Operational Research, 27 (2020), 3056-3078.  doi: 10.1111/itor.12520. [27] H. Jafari, S. R. Hejazi and R. B. Morteza, Sustainable development by waste recycling under a three-echelon supply chain: A game-theoretic approach, Journal of Cleaner Production, 142 (2017), 2252-2261. [28] H. S. Kilic, U. Cebeci and M. B. Ayhan, Reverse logistics system design for the waste of electrical and electronic equipment (WEEE) in Turkey, Resource Conservation and Recycling, 95 (2015), 120-132.  doi: 10.1016/j.resconrec.2014.12.010. [29] K. Kim, B. Jeong and H. Jung, Supply chain surplus: Comparing conventional and sustainable supply chains, Flexible Services and Manufacturing Journal, 26 (2014), 5-23.  doi: 10.1007/s10696-012-9163-2. [30] S. Kushwaha, A. Ghosh and A. K. Rao, Collection activity channels selection in a reverse supply chain a carbon cap-and-trade regulation, Journal of Cleaner Production, 260 (2020), 121034. doi: 10.1016/j.jclepro.2020.121034. [31] Y. Li, F. Xu and X. Zhao, Governance mechanisms of dual-channel reverse supply chains with informal collection channel, Journal of Cleaner Production, 155 (2017), 125-140.  doi: 10.1016/j.jclepro.2016.09.084. [32] T. Li, R. Zhang, S. Zhao and B. Liu, Low carbon strategy analysis under revenue-sharing and cost-sharing contracts, Journal of Cleaner Production, 212 (2019), 1462-1477.  doi: 10.1016/j.jclepro.2018.11.282. [33] L. Liu, Z. Wang, L. Xu, X. Hong and K. Govindan, Collection effort and reverse channel choices in a closed-loop supply chain, Journal of Cleaner Production, 144 (2017), 492-500.  doi: 10.1016/j.jclepro.2016.12.126. [34] C. L. Martins and M. V. Pato, Supply chain sustainability: A tertiary literature review, Journal of Cleaner Production, 225 (2019), 995-1016.  doi: 10.1016/j.jclepro.2019.03.250. [35] M. Reimann, Y. Xiong and Y. Zhou, Managing a closed-loop supply chain with process innovation for remanufacturing, European Journal of Operational Research, 276 (2019), 510-518.  doi: 10.1016/j.ejor.2019.01.028. [36] P. Rogetzer, L. Silbermayr and W. Jammernegg, Sustainable sourcing of strategic raw materials by integrating recycled materials, Flexible Services and Manufacturing Journal, 30 (2018), 421-451.  doi: 10.1007/s10696-017-9288-4. [37] R. Sadeghi, A. A. Taleizadeh, F. T. S. Chen and J. Heydari, Coordinating and pricing decisions in two competitive reverse supply chains with different channel structures, International Journal of Production Research, 57 (2019), 2601-2625.  doi: 10.1080/00207543.2018.1551637. [38] S. Saha, S. P. Sarmah and I. Moon, Dual channel closed-loop supply chain coordination with a reward-driven remanufacturing policy, International Journal of Production Research, 54 (2016), 1503-1517.  doi: 10.1080/00207543.2015.1090031. [39] H. Song and X. Gao, Green supply chain game model and analysis under revenue-sharing contract, Journal of Cleaner Production, 170 (2018), 183-192.  doi: 10.1016/j.jclepro.2017.09.138. [40] A. A. Taleizadeh and R. Sadeghi, Pricing strategies in the competitive reverse supply chains with traditional and e-channels: A game theoretic approach, International Journal of Production Economics, 215 (2019), 48-60.  doi: 10.1016/j.ijpe.2018.06.011. [41] W. Wang, P. Zhang, J. Ding, J. Li, H. Sun and L. He, Closed-loop supply chain network equilibrium model with retailer-collection under legislation, Journal of Industrial and Management Optimization, 15 (2019), 199-219.  doi: 10.3934/jimo.2018039. [42] D. Weraikat, M. K. Zanjani and N. Lehoux, Two-echelon pharmaceutical reverse supply chain coordination with customers incentives, International Journal of Production Economics, 176 (2016), 41-52.  doi: 10.1016/j.ijpe.2016.03.003. [43] W. Xie, B. Chen, F. Huang and J. He, Coordination of a Supply Chain with a Loss-averse retailer under supply uncertainty and marketing effort, Journal of Industrial and Management Optimization, http://dx.doi.org/10.3934/jimo.2020125. [44] A. Z. Zeng, Coordination mechanisms for a three-stage reverse supply chain to increase profitable returns, Naval Research Logistics, 60 (2012), 31-45.  doi: 10.1002/nav.21517. [45] A. Z. Zeng and J. Hou, Procurement and coordination under imperfect quality and uncertain demand in reverse mobile phone supply chain, International Journal of Production Economics, 209 (2019), 346-359. [46] B. Zheng, C. Yang, J. Yang and M. Zhang, Pricing, collecting and contract design in a reverse supply chain with incomplete information, Computers and Industrial Engineering, 111 (2017), 109-122.  doi: 10.1016/j.cie.2017.07.004.

show all references

##### References:
 [1] B. Ageron, A. Gunasekaran and A. Spalanzani, Sustainable supply management: An empirical study, International Journal of Production Economics, 140 (2012), 168-182.  doi: 10.1016/j.ijpe.2011.04.007. [2] L. Aramyan, R. Hoste, W. Van Den Broek, J. Groot, H. Soethoudt, T. L. Nguyen, J. Hermansen and J. van der Vorst, Towards sustainable food production: A scenario study of the European pork sector, Journal on Chain and Network Science, 11 (2011), 177-189.  doi: 10.3920/JCNS2011.Qpork8. [3] A. N. Arnette, B. L. Brewer and T. Choal, Design for sustainability (DFS): The intersection of supply chain and environment, Journal of Cleaner Production, 83 (2004), 374-390.  doi: 10.1016/j.jclepro.2014.07.021. [4] Q. Bai, M. 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. [5] Z. Basiri and J. Heydari, A mathematical model for green supply chain coordination with sustainable products, Journal of Cleaner Production, 145 (2017), 232-249. [6] Y. Bouchery, A. Ghaffari, Z. Jemai and J. Fransoo, Sustainable transportation and order quantity: Insights from multi-objective optimization, Flexible Services and Manufacturing Journal, 28 (2016), 367-396. [7] G. P. 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. [8] O. Capraz, O. Polat and A. Gungor, Planning of waste electrical and electronic equipment(WEEE) recycling facilities: MILP modelling and case study investigation, Flexible Services and Manufacturing Journal, 27 (2015), 479-508.  doi: 10.1007/s10696-015-9217-3. [9] X. Chen, H. Zhang, M. Zhang and J. Chen, Optimal decisions in a retailer Stackelberg supply chain, International Journal of Production Economics, 187 (2017), 260-270.  doi: 10.1016/j.ijpe.2017.03.002. [10] B. Chen, W. Xie, F. Huang and J. He, Quality competition and coordination in a VMI supply chain with two risk-averse manufacturers, Journal of Industrial and Management Optimization, http://dx.doi.org/10.3934/jimo.2020100. [11] D. Chen, J. Ignatis, D. Sun, S. Zhan, C. Zhou, M. Marra and M. Demirbag, Reverse logistics pricing strategy for a green supply chain: A view of customer's environmental awareness, International Journal of Production Economics, 217 (2019), 197-210.  doi: 10.1016/j.ijpe.2018.08.031. [12] K. Das and AH. Chowdhury, Designing a reverse logistics network for optimal collection, recovery and quality-based product-mix planning, International Journal of Production Economics, 135 (2012), 209-221.  doi: 10.1016/j.ijpe.2011.07.010. [13] M. Eskandarpour, P. Dejax, J. Miemczyk and O. Péton, Sustainable supply chain network design: An optimization-oriented review, Omega, 54 (2015), 11-32. [14] B. C. Giri and B. R. Sarker, Coordinating a multi-echelon supply chain under production disruption and price-sensitive stochastic demand, Journal of Industrial and Management Optimization, 15 (2019), 1631-1651.  doi: 10.3934/jimo.2018115. [15] B. C. Giri and S. K. Dey, Game theoretic analysis of a closed-loop supply chain with backup supplier under dual channel recycling, Computers and Industrial Engineering, 129 (2019), 179-191.  doi: 10.1016/j.cie.2019.01.035. [16] K. Govindan, S. G. Azevedo, H. Carvalho and V. Cruz-Machado, Impact of Supply chain Management practices on sustainability, Journal of Cleaner Production, 85 (2014), 212-225.  doi: 10.1016/j.jclepro.2014.05.068. [17] K. Govindan and M. N. Popiuc, Reverse supply chain coordination by revenue sharing contract: A case for the personal computers industry, European Journal of Operational Research, 233 (2014), 326-336.  doi: 10.1016/j.ejor.2013.03.023. [18] K. W. Green, P. J. Zelbst, J. Meacham and V. S. Bhadauria, Green supply chain management practices: Impact on performance, Supply Chain Management: An International Journal, 17 (2012), 290-305.  doi: 10.1108/13598541211227126. [19] J. Heydari, K. Govindan and A. Jafari, Reverse and closed loop supply chain coordination by considering government role, Transportation Research Part D: Transport and Environment, 52 (2017), 379-398.  doi: 10.1016/j.trd.2017.03.008. [20] J. Heydari and M. Ghasemi, A revenue sharing contract for reverse supply chain coordination under stochastic quality of returned products and uncertain remanufacturing capacity, Journal of Cleaner Production, 197 (2018), 607-615.  doi: 10.1016/j.jclepro.2018.06.206. [21] J. Heydari, K. Govindan and R. Sadeghi, Reverse supply chain coordination under stochastic remanufacturing capacity, International Journal of Production Economics, 202 (2018), 1-11.  doi: 10.1016/j.ijpe.2018.04.024. [22] S. Hu, Y. Dai, Z. J. Ma and Y. S. Ye, Designing contracts for a reverse supply chainwith strategic recycling behavior of consumers, International Journal of Production Economics, 180 (2016), 16-24. [23] B. Hu and Y. Feng, Optimization and coordination of supply chain with revenue sharing contracts and service requirement under supply and demand uncertainty, International Journal of Production Economics, 183 (2017), 185-193. [24] G. Hua, S. Wang and T. C. E. Cheng, Price and lead time decisions in dual-channel supply chains, European Journal of Operational Research, 205 (2010), 113-126.  doi: 10.1016/j.ejor.2009.12.012. [25] F. Huang, J. He and J. Wang, Coordination of VMI supply chain with a loss-averse manufacturer under quality-dependency and marketing-dependency, Journal of Industrial and Management Optimization, 15 (2019), 1753-1772.  doi: 10.3934/jimo.2018121. [26] F. Huang, J. He and Q. Lai, Coordination in a retailer-dominated supply chain with a risk-averse manufacturer under marketing dependency, International Transactions in Operational Research, 27 (2020), 3056-3078.  doi: 10.1111/itor.12520. [27] H. Jafari, S. R. Hejazi and R. B. Morteza, Sustainable development by waste recycling under a three-echelon supply chain: A game-theoretic approach, Journal of Cleaner Production, 142 (2017), 2252-2261. [28] H. S. Kilic, U. Cebeci and M. B. Ayhan, Reverse logistics system design for the waste of electrical and electronic equipment (WEEE) in Turkey, Resource Conservation and Recycling, 95 (2015), 120-132.  doi: 10.1016/j.resconrec.2014.12.010. [29] K. Kim, B. Jeong and H. Jung, Supply chain surplus: Comparing conventional and sustainable supply chains, Flexible Services and Manufacturing Journal, 26 (2014), 5-23.  doi: 10.1007/s10696-012-9163-2. [30] S. Kushwaha, A. Ghosh and A. K. Rao, Collection activity channels selection in a reverse supply chain a carbon cap-and-trade regulation, Journal of Cleaner Production, 260 (2020), 121034. doi: 10.1016/j.jclepro.2020.121034. [31] Y. Li, F. Xu and X. Zhao, Governance mechanisms of dual-channel reverse supply chains with informal collection channel, Journal of Cleaner Production, 155 (2017), 125-140.  doi: 10.1016/j.jclepro.2016.09.084. [32] T. Li, R. Zhang, S. Zhao and B. Liu, Low carbon strategy analysis under revenue-sharing and cost-sharing contracts, Journal of Cleaner Production, 212 (2019), 1462-1477.  doi: 10.1016/j.jclepro.2018.11.282. [33] L. Liu, Z. Wang, L. Xu, X. Hong and K. Govindan, Collection effort and reverse channel choices in a closed-loop supply chain, Journal of Cleaner Production, 144 (2017), 492-500.  doi: 10.1016/j.jclepro.2016.12.126. [34] C. L. Martins and M. V. Pato, Supply chain sustainability: A tertiary literature review, Journal of Cleaner Production, 225 (2019), 995-1016.  doi: 10.1016/j.jclepro.2019.03.250. [35] M. Reimann, Y. Xiong and Y. Zhou, Managing a closed-loop supply chain with process innovation for remanufacturing, European Journal of Operational Research, 276 (2019), 510-518.  doi: 10.1016/j.ejor.2019.01.028. [36] P. Rogetzer, L. Silbermayr and W. Jammernegg, Sustainable sourcing of strategic raw materials by integrating recycled materials, Flexible Services and Manufacturing Journal, 30 (2018), 421-451.  doi: 10.1007/s10696-017-9288-4. [37] R. Sadeghi, A. A. Taleizadeh, F. T. S. Chen and J. Heydari, Coordinating and pricing decisions in two competitive reverse supply chains with different channel structures, International Journal of Production Research, 57 (2019), 2601-2625.  doi: 10.1080/00207543.2018.1551637. [38] S. Saha, S. P. Sarmah and I. Moon, Dual channel closed-loop supply chain coordination with a reward-driven remanufacturing policy, International Journal of Production Research, 54 (2016), 1503-1517.  doi: 10.1080/00207543.2015.1090031. [39] H. Song and X. Gao, Green supply chain game model and analysis under revenue-sharing contract, Journal of Cleaner Production, 170 (2018), 183-192.  doi: 10.1016/j.jclepro.2017.09.138. [40] A. A. Taleizadeh and R. Sadeghi, Pricing strategies in the competitive reverse supply chains with traditional and e-channels: A game theoretic approach, International Journal of Production Economics, 215 (2019), 48-60.  doi: 10.1016/j.ijpe.2018.06.011. [41] W. Wang, P. Zhang, J. Ding, J. Li, H. Sun and L. He, Closed-loop supply chain network equilibrium model with retailer-collection under legislation, Journal of Industrial and Management Optimization, 15 (2019), 199-219.  doi: 10.3934/jimo.2018039. [42] D. Weraikat, M. K. Zanjani and N. Lehoux, Two-echelon pharmaceutical reverse supply chain coordination with customers incentives, International Journal of Production Economics, 176 (2016), 41-52.  doi: 10.1016/j.ijpe.2016.03.003. [43] W. Xie, B. Chen, F. Huang and J. He, Coordination of a Supply Chain with a Loss-averse retailer under supply uncertainty and marketing effort, Journal of Industrial and Management Optimization, http://dx.doi.org/10.3934/jimo.2020125. [44] A. Z. Zeng, Coordination mechanisms for a three-stage reverse supply chain to increase profitable returns, Naval Research Logistics, 60 (2012), 31-45.  doi: 10.1002/nav.21517. [45] A. Z. Zeng and J. Hou, Procurement and coordination under imperfect quality and uncertain demand in reverse mobile phone supply chain, International Journal of Production Economics, 209 (2019), 346-359. [46] B. Zheng, C. Yang, J. Yang and M. Zhang, Pricing, collecting and contract design in a reverse supply chain with incomplete information, Computers and Industrial Engineering, 111 (2017), 109-122.  doi: 10.1016/j.cie.2017.07.004.
Diagram of the supply chain model
Proposed supply chain model under revenue sharing contract
Concavity of $E(\Pi)$ w.r.to $p$ and $r$
$L$ vs. profits of the SC and its entities
$b$ vs. profits of the SC and its entities
$r^{max}$ vs. profits of the SC and its entities
Optimal results
 Model $r^{*}$ $p^{*}$ $1-\phi$ $\phi_{1}+\phi_{2}$ $E(\Pi_{c})$ $E(\Pi_{m})$ $E(\Pi_{s})$ $E(\Pi)$ Centralized 26.67 437 - - - - - 143535 Decentralized 46.67 463 - - 6505 122018 10355 138878 RS-I 26.67 437 .01 - 7662 125518 10355 143535 RS-II 26.67 437 - 0.03 - 124536 - 143535
 Model $r^{*}$ $p^{*}$ $1-\phi$ $\phi_{1}+\phi_{2}$ $E(\Pi_{c})$ $E(\Pi_{m})$ $E(\Pi_{s})$ $E(\Pi)$ Centralized 26.67 437 - - - - - 143535 Decentralized 46.67 463 - - 6505 122018 10355 138878 RS-I 26.67 437 .01 - 7662 125518 10355 143535 RS-II 26.67 437 - 0.03 - 124536 - 143535
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