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doi: 10.3934/jimo.2021187
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## Two-sided vertical competition considering product quality in a manufacturing-remanufacturing system

 School of Management, Hefei University of Technology, Hefei, China Key Laboratory of Process Optimization and Intelligent Decision-making, Ministry of Education, Hefei, China

* Corresponding author: Yan Li

Received  April 2021 Revised  August 2021 Early access November 2021

We study two-sided vertical competition between a manufacturer and a supplier. The problem is formulated as a dynamic game where the supplier has more pricing power than the manufacturer. Based on the one-sided vertical competition modes with different recyclers as benchmarks, we derive optimal pricing and production decisions of manufacturer and supplier and further study the impacts of product quality on those decisions under the two-sided vertical competition mode. A key finding is that manufacturer/supplier prefers to be a follower rather than the first one to engage in recycling activities. Specifically, when the manufacturer/supplier has engaged in recycling activities, the supplier/manufacturer has an incentive to participate in recycling activities as well. We also find that high-quality remanufactured components/products can benefit manufacturer, supplier and consumers at the same time.

Citation: Kai Li, Yan Li, Jing Liu, Nenggui Zhao. Two-sided vertical competition considering product quality in a manufacturing-remanufacturing system. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2021187
##### References:
 [1] A. Atasu, M. Sarvary and L. N. Van Wassenhove, Remanufacturing as a marketing strategy, Management Science, 54 (2008), 1731-1746.  doi: 10.1287/mnsc.1080.0893. [2] 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. [3] J. D. Abbey, J. D. Blackburn and V. D. R. Guide Jr, Optimal pricing for new and remanufactured products, Journal of Operations Management, 36 (2015), 130-146.  doi: 10.1016/j.jom.2015.03.007. [4] J. D. Abbey, R. Kleber, G. C. Souza and G. Voigt, The role of perceived quality risk in pricing remanufactured products, Production and Operations Management, 26 (2017), 100-115.  doi: 10.1111/poms.12628. [5] P. Assarzadegan and M. Rasti-Barzoki, A game theoretic approach for pricing under a return policy and a money back guarantee in a closed loop supply chain, International Journal of Production Economics, 222 (2020), 107486.  doi: 10.1016/j.ijpe.2019.09.007. [6] S. C. Bulmus, S. X. Zhu and R. Teunter, Competition for cores in remanufacturing, European J. Oper. Res., 233 (2014), 105-113.  doi: 10.1016/j.ejor.2013.08.025. [7] Q. Chai, Z. Xiao, K.-h. Lai and G. Zhou, Can carbon cap and trade mechanism be beneficial for remanufacturing?, International Journal of Production Economics, 203 (2018), 311-321.  doi: 10.1016/j.ijpe.2018.07.004. [8] K. Govindan, B. Jiménez-Parra, S. Rubio and M.-A. Vicente-Molina, Marketing issues for remanufactured products, Journal of Cleaner Production, 227 (2019), 890-899.  doi: 10.1016/j.jclepro.2019.03.305. [9] P. D. Giovanni and G. Zaccour, A two-period game of a closed-loop supply chain, European J. Oper. Res., 232 (2014), 22-40.  doi: 10.1016/j.ejor.2013.06.032. [10] X. Hong, K. Govindan, L. Xu and P. Du, Quantity and collection decisions in a closed-loop supply chain with technology licensing, European J. Oper. Res., 256 (2017), 820-829.  doi: 10.1016/j.ejor.2016.06.051. [11] B. Jiang and B. Yang, Quality and pricing decisions in a market with consumer information sharing, Management Science, 65 (2019), 272-285. [12] S. K. Jena, S. P. Sarmah and S. C. Sarin, Price competition between high and low brand products considering coordination strategy, Computers & Industrial Engineering, 130 (2019), 500-511.  doi: 10.1016/j.cie.2019.03.008. [13] R. Kleber, M. Reimann, G. C. Souza and W. Zhang, Two-sided competition with vertical differentiation in both acquisition and sales in remanufacturing, European J. Oper. Res., 284 (2020), 572-587.  doi: 10.1016/j.ejor.2020.01.012. [14] K. Li, J. Liu, H. Fu and B. Liu, Acquisition and pricing strategies in hybrid manufacturing-remanufacturing systems, Journal of Manufacturing Systems, 57 (2020), 217-230.  doi: 10.1016/j.jmsy.2020.09.006. [15] P. Ma, Y. Gong and P. Mirchandani, Trade-in for remanufactured products: Pricing with double reference effects, International Journal of Production Economics, 230 (2020), 107800. [16] T. Maiti and B. 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. [17] F. E. Ouardighi, J. Sim and B. Kim, Pollution accumulation and abatement policies in two supply chains under vertical and horizontal competition and strategy types, Omega, 98 (2021), 102108.  doi: 10.1016/j.omega.2019.102108. [18] R. C. Savaskan, S. Bhattacharya and L. N. Van Wassenhove, Closed-loop supply chain models with product remanufacturing, Management Science, 50 (2004), 239-252.  doi: 10.1287/mnsc.1030.0186. [19] 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. [20] C.-H. Wu, Price and service competition between new and remanufactured products in a two-echelon supply chain, International Journal of Production Economics, 140 (2012), 496-507.  doi: 10.1016/j.ijpe.2012.06.034. [21] C.-H. Wu, Oem product design in a price competition with remanufactured product, Omega, 41 (2013), 287-298. [22] C.-H. Wu, Strategic and operational decisions under sales competition and collection competition for end-of-use products in remanufacturing, International Journal of Production Economics, 169 (2015), 11-20. [23] C.-H. Wu, C.-W. Chen and C.-C. Hsieh, Competitive pricing decisions in a two-echelon supply chain with horizontal and vertical competition, International Journal of Production Economics, 135 (2012), 265-274.  doi: 10.1016/j.ijpe.2011.07.020. [24] C.-H. Wu and H.-H. Wu, Competitive remanufacturing strategy and take-back decision with oem remanufacturing, Computers & Industrial Engineering, 98 (2016), 149-163.  doi: 10.1016/j.cie.2016.05.033. [25] J. Wei and J. Zhao, Pricing and remanufacturing decisions in two competing supply chains, International Journal of Production Research, 53 (2015), 258-278.  doi: 10.1080/00207543.2014.951088. [26] J. Wei and J. Zhao, Pricing decisions for substitutable products with horizontal and vertical competition in fuzzy environments, Ann. Oper. Res., 242 (2016), 505-528.  doi: 10.1007/s10479-014-1541-6. [27] X. Wu and Y. Zhou, The optimal reverse channel choice under supply chain competition, European J. Oper. Res., 259 (2017), 63-66.  doi: 10.1016/j.ejor.2016.09.027. [28] T. Xiao, D. Yang and H. Shen, Coordinating a supply chain with a quality assurance policy via a revenue-sharing contract, International Journal of Production Research, 49 (2011), 99-120.  doi: 10.1080/00207543.2010.508936. [29] A. Yenipazarli, Managing new and remanufactured products to mitigate environmental damage under emissions regulation, European J. Oper. Res., 249 (2016), 117-130.  doi: 10.1016/j.ejor.2015.08.020. [30] L. Yang, Y. Hu and L. Huang, Collecting mode selection in a remanufacturing supply chain under cap-and-trade regulation, European J. Oper. Res., 287 (2020), 480-496.  doi: 10.1016/j.ejor.2020.04.006. [31] J. Zhao, J. 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. [32] M. Ziari and M. S. Sajadieh, A behavior-based pricing model in retail systems considering vertical and horizontal competition, Computers & Industrial Engineering, 152 (2021), 107054. [33] P. Zhang, Y. Xiong, Z. Xiong and W. Yan, Designing contracts for a closed-loop supply chain under information asymmetry, Oper. Res. Lett., 42 (2014), 150-155.  doi: 10.1016/j.orl.2014.01.004. [34] S. Zhao, Q. Zhu and L. Cui, A decision-making model for remanufacturers: Considering both consumers' environmental preference and the government subsidy policy, Resources, Conservation and Recycling, 128 (2018), 176-186.  doi: 10.1016/j.resconrec.2016.07.005.

show all references

##### References:
 [1] A. Atasu, M. Sarvary and L. N. Van Wassenhove, Remanufacturing as a marketing strategy, Management Science, 54 (2008), 1731-1746.  doi: 10.1287/mnsc.1080.0893. [2] 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. [3] J. D. Abbey, J. D. Blackburn and V. D. R. Guide Jr, Optimal pricing for new and remanufactured products, Journal of Operations Management, 36 (2015), 130-146.  doi: 10.1016/j.jom.2015.03.007. [4] J. D. Abbey, R. Kleber, G. C. Souza and G. Voigt, The role of perceived quality risk in pricing remanufactured products, Production and Operations Management, 26 (2017), 100-115.  doi: 10.1111/poms.12628. [5] P. Assarzadegan and M. Rasti-Barzoki, A game theoretic approach for pricing under a return policy and a money back guarantee in a closed loop supply chain, International Journal of Production Economics, 222 (2020), 107486.  doi: 10.1016/j.ijpe.2019.09.007. [6] S. C. Bulmus, S. X. Zhu and R. Teunter, Competition for cores in remanufacturing, European J. Oper. Res., 233 (2014), 105-113.  doi: 10.1016/j.ejor.2013.08.025. [7] Q. Chai, Z. Xiao, K.-h. Lai and G. Zhou, Can carbon cap and trade mechanism be beneficial for remanufacturing?, International Journal of Production Economics, 203 (2018), 311-321.  doi: 10.1016/j.ijpe.2018.07.004. [8] K. Govindan, B. Jiménez-Parra, S. Rubio and M.-A. Vicente-Molina, Marketing issues for remanufactured products, Journal of Cleaner Production, 227 (2019), 890-899.  doi: 10.1016/j.jclepro.2019.03.305. [9] P. D. Giovanni and G. Zaccour, A two-period game of a closed-loop supply chain, European J. Oper. Res., 232 (2014), 22-40.  doi: 10.1016/j.ejor.2013.06.032. [10] X. Hong, K. Govindan, L. Xu and P. Du, Quantity and collection decisions in a closed-loop supply chain with technology licensing, European J. Oper. Res., 256 (2017), 820-829.  doi: 10.1016/j.ejor.2016.06.051. [11] B. Jiang and B. Yang, Quality and pricing decisions in a market with consumer information sharing, Management Science, 65 (2019), 272-285. [12] S. K. Jena, S. P. Sarmah and S. C. Sarin, Price competition between high and low brand products considering coordination strategy, Computers & Industrial Engineering, 130 (2019), 500-511.  doi: 10.1016/j.cie.2019.03.008. [13] R. Kleber, M. Reimann, G. C. Souza and W. Zhang, Two-sided competition with vertical differentiation in both acquisition and sales in remanufacturing, European J. Oper. Res., 284 (2020), 572-587.  doi: 10.1016/j.ejor.2020.01.012. [14] K. Li, J. Liu, H. Fu and B. Liu, Acquisition and pricing strategies in hybrid manufacturing-remanufacturing systems, Journal of Manufacturing Systems, 57 (2020), 217-230.  doi: 10.1016/j.jmsy.2020.09.006. [15] P. Ma, Y. Gong and P. Mirchandani, Trade-in for remanufactured products: Pricing with double reference effects, International Journal of Production Economics, 230 (2020), 107800. [16] T. Maiti and B. 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. [17] F. E. Ouardighi, J. Sim and B. Kim, Pollution accumulation and abatement policies in two supply chains under vertical and horizontal competition and strategy types, Omega, 98 (2021), 102108.  doi: 10.1016/j.omega.2019.102108. [18] R. C. Savaskan, S. Bhattacharya and L. N. Van Wassenhove, Closed-loop supply chain models with product remanufacturing, Management Science, 50 (2004), 239-252.  doi: 10.1287/mnsc.1030.0186. [19] 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. [20] C.-H. Wu, Price and service competition between new and remanufactured products in a two-echelon supply chain, International Journal of Production Economics, 140 (2012), 496-507.  doi: 10.1016/j.ijpe.2012.06.034. [21] C.-H. Wu, Oem product design in a price competition with remanufactured product, Omega, 41 (2013), 287-298. [22] C.-H. Wu, Strategic and operational decisions under sales competition and collection competition for end-of-use products in remanufacturing, International Journal of Production Economics, 169 (2015), 11-20. [23] C.-H. Wu, C.-W. Chen and C.-C. Hsieh, Competitive pricing decisions in a two-echelon supply chain with horizontal and vertical competition, International Journal of Production Economics, 135 (2012), 265-274.  doi: 10.1016/j.ijpe.2011.07.020. [24] C.-H. Wu and H.-H. Wu, Competitive remanufacturing strategy and take-back decision with oem remanufacturing, Computers & Industrial Engineering, 98 (2016), 149-163.  doi: 10.1016/j.cie.2016.05.033. [25] J. Wei and J. Zhao, Pricing and remanufacturing decisions in two competing supply chains, International Journal of Production Research, 53 (2015), 258-278.  doi: 10.1080/00207543.2014.951088. [26] J. Wei and J. Zhao, Pricing decisions for substitutable products with horizontal and vertical competition in fuzzy environments, Ann. Oper. Res., 242 (2016), 505-528.  doi: 10.1007/s10479-014-1541-6. [27] X. Wu and Y. Zhou, The optimal reverse channel choice under supply chain competition, European J. Oper. Res., 259 (2017), 63-66.  doi: 10.1016/j.ejor.2016.09.027. [28] T. Xiao, D. Yang and H. Shen, Coordinating a supply chain with a quality assurance policy via a revenue-sharing contract, International Journal of Production Research, 49 (2011), 99-120.  doi: 10.1080/00207543.2010.508936. [29] A. Yenipazarli, Managing new and remanufactured products to mitigate environmental damage under emissions regulation, European J. Oper. Res., 249 (2016), 117-130.  doi: 10.1016/j.ejor.2015.08.020. [30] L. Yang, Y. Hu and L. Huang, Collecting mode selection in a remanufacturing supply chain under cap-and-trade regulation, European J. Oper. Res., 287 (2020), 480-496.  doi: 10.1016/j.ejor.2020.04.006. [31] J. Zhao, J. 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. [32] M. Ziari and M. S. Sajadieh, A behavior-based pricing model in retail systems considering vertical and horizontal competition, Computers & Industrial Engineering, 152 (2021), 107054. [33] P. Zhang, Y. Xiong, Z. Xiong and W. Yan, Designing contracts for a closed-loop supply chain under information asymmetry, Oper. Res. Lett., 42 (2014), 150-155.  doi: 10.1016/j.orl.2014.01.004. [34] S. Zhao, Q. Zhu and L. Cui, A decision-making model for remanufacturers: Considering both consumers' environmental preference and the government subsidy policy, Resources, Conservation and Recycling, 128 (2018), 176-186.  doi: 10.1016/j.resconrec.2016.07.005.
Closed-loop supply chain structures
The profits of manufacturer and supplier vs. $\delta$
The profits of manufacturer and supplier vs. $q_{n}$
The profits of manufacturer and supplier vs. $q_{r}$
The profits of manufacturer and supplier under different competition modes vs. $\delta$
The profits of manufacturer and supplier under different competition modes vs. $q_{n}$
The profits of manufacturer and supplier under different competition modes vs. $q_{r}$
Basic symbols in models
 Symbol Definition $v$ The consumer's willingness to pay for the new products $\delta$ The consumer value discount for remanufactured products $\phi$ The percentage of used products that manufacturer recycles $c_{n}/c_{r}$ The unit cost when using the new/remanufactured component $p_{n}/p_{r}$ The unit price of new/remanufactured product $q_{n}/q_{r}$ The quality of new/remanufactured component $d_{n}/d_{r}$ The quantity of new/remanufactured products $w/f$ The price of new/ remanufactured component $U_{n}/U_{r}$ The net utility obtained by consumers when they purchase new/remanufactured product
 Symbol Definition $v$ The consumer's willingness to pay for the new products $\delta$ The consumer value discount for remanufactured products $\phi$ The percentage of used products that manufacturer recycles $c_{n}/c_{r}$ The unit cost when using the new/remanufactured component $p_{n}/p_{r}$ The unit price of new/remanufactured product $q_{n}/q_{r}$ The quality of new/remanufactured component $d_{n}/d_{r}$ The quantity of new/remanufactured products $w/f$ The price of new/ remanufactured component $U_{n}/U_{r}$ The net utility obtained by consumers when they purchase new/remanufactured product
The effect of $q_{n}$ and $q_{r}$ on optimal decisions under vertical competition Ⅰ mode
 Symbol $p_{n}^{{\rm{NC}}}$ $p_{r}^{{\rm{NC}}}$ ${w^{{\rm{NC}}}}$ ${f^{{\rm{NC}}}}$ $q_{n}$ $+$ $/$ $+$ $/$ $q_{r}$ $/$ $+$ $/$ $+$
 Symbol $p_{n}^{{\rm{NC}}}$ $p_{r}^{{\rm{NC}}}$ ${w^{{\rm{NC}}}}$ ${f^{{\rm{NC}}}}$ $q_{n}$ $+$ $/$ $+$ $/$ $q_{r}$ $/$ $+$ $/$ $+$
The effect of $q_{n}$ and $q_{r}$ on optimal decisions under vertical competition Ⅱ mode
 Symbol $p_{n}^{{\rm{VC}}}$ $p_{r}^{{\rm{VC}}}$ ${w^{{\rm{VC}}}}$ $q_{n}$ $+$ $/$ $+$ $q_{r}$ $\mp$ $+$ $\mp$
 Symbol $p_{n}^{{\rm{VC}}}$ $p_{r}^{{\rm{VC}}}$ ${w^{{\rm{VC}}}}$ $q_{n}$ $+$ $/$ $+$ $q_{r}$ $\mp$ $+$ $\mp$
The effect of $q_{n}$, $q_{r}$ and $\phi$ on optimal decisions under two-sided vertical competition mode
 Symbol $p_{n}^{{\rm{NC}}}$ $p_{r}^{{\rm{NC}}}$ ${w^{{\rm{NC}}}}$ ${f^{{\rm{NC}}}}$ $q_{n}$ $+$ $/$ $+$ $/$ $q_{r}$ $/$ $+$ $/$ $+\left(0 <\phi<\frac{1}{2}\right),-\left(\frac{1}{2}<\phi<1\right)$ $\phi$ $/$ $/$ $/$ Shown in proposition 7
 Symbol $p_{n}^{{\rm{NC}}}$ $p_{r}^{{\rm{NC}}}$ ${w^{{\rm{NC}}}}$ ${f^{{\rm{NC}}}}$ $q_{n}$ $+$ $/$ $+$ $/$ $q_{r}$ $/$ $+$ $/$ $+\left(0 <\phi<\frac{1}{2}\right),-\left(\frac{1}{2}<\phi<1\right)$ $\phi$ $/$ $/$ $/$ Shown in proposition 7

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