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doi: 10.3934/jimo.2021117
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Collection decisions and coordination in a closed-loop supply chain under recovery price and service competition

College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou, 310023, China

* Corresponding author: zhangxiaofeng@zjut.edu.cn (Xiaofeng Zhang)

Received  December 2020 Revised  April 2021 Early access July 2021

Fund Project: The first author is supported by the Natural Science Foundation of Zhejiang Province, China (No. LY18G010019) and Zhejiang Province Public Welfare Technology Application Research Project (No. 2015C33014)

With the increasing growth of consumers' request for recovery channels, in addition to collecting price, the collecting service has gradually become a competitive point for collectors to collect used products. Focusing on a closed-loop supply chain (CLSC) with recovery competition (on collecting price and collecting service) and distinguishing collecting quality, we propose two models (decentralized and centralized models) to study the collection strategies and profits of the CLSC. Moreover, we analyze the impact of the collecting competition and quality on the CLSC. Finally, a revenue-cost sharing contract (RCSC) is introduced to coordinate the supply chain. And a numerical example is illustrated to verify the contract's efficiency. It is found that the collected quantities and profits of the CLSC members are positively correlated with the remanufacturable ratio. The collecting competition dampens consumers' enthusiasm for recycling, which is not conducive to collectors to carry out collecting activity, resulting in the reduction of the CLSC's profit. The collectors appropriately improving collecting prices and service levels can increase the collected quantities, but to cope with the increasing competition, increasing collecting price is the main means for collectors to attract consumers to recycle. In addition, the designed RCSC can effectively improve the CLSC's efficiency and increase the profits of each party.

Citation: Dingzhong Feng, Xiaofeng Zhang, Ye Zhang. Collection decisions and coordination in a closed-loop supply chain under recovery price and service competition. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021117
References:
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Y. Liu and T. Xiao, Pricing and collection rate decisions and reverse channel choice in a socially responsible supply chain with green consumers, IEEE Trans. Eng. Manag., 67 (2020), 483-495.  doi: 10.1109/TEM.2018.2887118.  Google Scholar

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[25]

R. Lotfi, Z. Yadegari, S. H. Hosseini, A. H. Khameneh, E. B. Tirkolaee and G.-W. Weber, A robust time-cost-quality-energy-environment trade-off with resource-constrained in project management: A case study for a bridge construction project, J. Ind. Manag. Optim., 13 (2020). doi: 10.3934/jimo.2020158.  Google Scholar

[26]

D. Mangun and D. L. Thurston, Incorporating component reuse, remanufacture, and recycle into product portfolio design, IEEE Trans. Eng. Manag., 49 (2002), 479-490.  doi: 10.1109/TEM.2002.807292.  Google Scholar

[27]

N. M. ModakN. Kazemi and L. E. Cárdenas-Barrón, Investigating structure of a two-echelon closed-loop supply chain using social work donation as a Corporate Social Responsibility practice, Int. J. Prod. Econ., 207 (2019), 19-33.  doi: 10.1016/j.ijpe.2018.10.009.  Google Scholar

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J. Nie, Z. Huang, Y. Zhao and Y. Shi, Collective recycling responsibility in closed-loop fashion supply chains with a third party: Financial sharing or physical sharing?, Math. Probl. Eng., 2013 (2013), Article ID 176130. doi: 10.1155/2013/176130.  Google Scholar

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S. PandaN. M. Modak and L. E. Cárdenas-Barrón, Coordinating a socially responsible closed-loop supply chain with product recycling, Int. J. Prod. Econ., 188 (2017), 11-21.  doi: 10.1016/j.ijpe.2017.03.010.  Google Scholar

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Y. ShiJ. NieT. QuL.-K. Chu and D. Sculli, Choosing reverse channels under collection responsibility sharing in a closed-loop supply chain with re-manufacturing, J. Intell. Manuf., 26 (2015), 387-402.  doi: 10.1007/s10845-013-0797-z.  Google Scholar

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N. WangQ. He and B. Jiang, Hybrid closed-loop supply chains with competition in recycling and product markets, Int. J. Prod. Econ., 217 (2019), 246-258.  doi: 10.1016/j.ijpe.2018.01.002.  Google Scholar

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N. Wang, Y. Song, Q. He and T. Jia, Competitive dual-collecting regarding consumer behavior and coordination in closed-loop supply chain, Comput. Ind. Eng., 144 (2020). doi: 10.1016/j.cie.2020.106481.  Google Scholar

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W. Wang, S. Zhou, M. Zhang, H. Sun and L. He, A closed-loop supply chain with competitive dual collection channel under asymmetric information and reward-penalty mechanism, Sustain., 10 (2018). doi: 10.3390/su10072131.  Google Scholar

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J. WeiK. GovindanY. Li and J. Zhao, Pricing and collecting decisions in a closed-loop supply chain with symmetric and asymmetric information, Comput. Oper. Res., 54 (2015), 257-265.  doi: 10.1016/j.cor.2013.11.021.  Google Scholar

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[39]

C.-H. Wu, Price and service competition between new and remanufactured products in a two-echelon supply chain, Int. J. Prod. Econ., 140 (2012), 496-507.  doi: 10.1016/j.ijpe.2012.06.034.  Google Scholar

[40]

J. XieL. LiangL. Liu and P. Ieromonachou, Coordination contracts of dual-channel with cooperation advertising in closed-loop supply chains, Int. J. Prod. Econ., 183 (2017), 528-538.  doi: 10.1016/j.ijpe.2016.07.026.  Google Scholar

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J. XieW. ZhangL. LiangY. XiaJ. Yin and G. Yang, The revenue and cost sharing contract of pricing and servicing policies in a dual-channel closed-loop supply chain, J. Clean. Prod., 191 (2018), 361-383.  doi: 10.1016/j.jclepro.2018.04.223.  Google Scholar

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C. Xu, B. Li, Y. Lan and Y. Tang, A closed-loop supply chain problem with retailing and recycling competition, Abstr. Appl. Anal., 2014 (2014), Article ID 509825. doi: 10.1155/2014/509825.  Google Scholar

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A. Yenipazarli, Managing new and remanufactured products to mitigate environmental damage under emissions regulation, Eur. J. Oper. Res., 249 (2016), 117-130.  doi: 10.1016/j.ejor.2015.08.020.  Google Scholar

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show all references

References:
[1]

A. AtasuL. B. Toktay and L. N. Van Wassenhove, How collection cost structure drives a manufacturer's reverse channel choice, Prod. Oper. Manag., 22 (2013), 1089-1102.  doi: 10.1111/j.1937-5956.2012.01426.x.  Google Scholar

[2]

P. De Giovanni, Environmental collaboration in a closed-loop supply chain with a reverse revenue sharing contract, Ann. Oper. Res., 220 (2014), 135-157.  doi: 10.1007/s10479-011-0912-5.  Google Scholar

[3]

G. Ferrer and J. M. Swaminathan, Managing new and remanufactured products, Manage. Sci., 52 (2006). doi: 10.1287/mnsc.1050.0465.  Google Scholar

[4]

G. Ferrer and J. M. Swaminathan, Managing new and differentiated remanufactured products, Eur. J. Oper. Res., 203 (2010), 370-379.  doi: 10.1016/j.ejor.2009.08.007.  Google Scholar

[5]

S.-S. GanI. N. PujawanSu parno and B. Widodo, Pricing decision for new and remanufactured product in a closed-loop supply chain with separate sales-channel, Int. J. Prod. Econ., 190 (2017), 120-132.  doi: 10.1016/j.ijpe.2016.08.016.  Google Scholar

[6]

J. GaoH. HanL. Hou and H. Wang, Pricing and effort decisions in a closed-loop supply chain under different channel power structures, J. Clean. Prod., 112 (2016), 2043-2057.  doi: 10.1016/j.jclepro.2015.01.066.  Google Scholar

[7]

A. GoliH. K. ZareR. Tavakkoli-Moghaddam and A. Sadegheih, Multiobjective fuzzy mathematical model for a financially constrained closed-loop supply chain with labor employment, Comput. Intell., 36 (2020), 4-34.  doi: 10.1111/coin.12228.  Google Scholar

[8]

K. GovindanH. Soleimani and D. Kannan, Reverse logistics and closed-loop supply chain: A comprehensive review to explore the future, Eur. J. Oper. Res., 240 (2015), 603-626.  doi: 10.1016/j.ejor.2014.07.012.  Google Scholar

[9]

Q. GuJ. Ji and T. Gao, Pricing management for a closed-loop supply chain, J. Revenue Pricing Manag., 7 (2008), 45-60.  doi: 10.1057/palgrave.rpm.5160122.  Google Scholar

[10]

P. HeY. He and H. Xu, Channel structure and pricing in a dual-channel closed-loop supply chain with government subsidy, Int. J. Prod. Econ., 213 (2019), 108-123.  doi: 10.1016/j.ijpe.2019.03.013.  Google Scholar

[11]

Q. HeN. WangZ. YangZ. He and B. Jiang, Competitive collection under channel inconvenience in closed-loop supply chain, Eur. J. Oper. Res., 275 (2019), 155-166.  doi: 10.1016/j.ejor.2018.11.034.  Google Scholar

[12]

I.-H. Hong and J.-S. Yeh, Modeling closed-loop supply chains in the electronics industry: A retailer collection application, Transp. Res. Part E: Logist. Transp. Rev., 48 (2012), 817-829.  doi: 10.1016/j.tre.2012.01.006.  Google Scholar

[13]

X. HongL. XuP. Du and W. Wang, Joint advertising, pricing and collection decisions in a closed-loop supply chain, Int. J. Prod. Econ., 167 (2015), 12-22.  doi: 10.1016/j.ijpe.2015.05.001.  Google Scholar

[14]

M. HuangM. SongL. H. Lee and W. K. Ching, Analysis for strategy of closed-loop supply chain with dual recycling channel, Int. J. Prod. Econ., 144 (2013), 510-520.  doi: 10.1016/j.ijpe.2013.04.002.  Google Scholar

[15]

Y. HuangB. Zheng and Z. Wang, Advertisement vs. Monetary Subsidy: Which is Better for Remanufacturing?, J. Syst. Sci. Syst. Eng., 29 (2020), 344-359.  doi: 10.1007/s11518-019-5447-3.  Google Scholar

[16]

S. K. Jena and S. P. Sarmah, Price and service co-opetiton under uncertain demand and condition of used items in a remanufacturing system, Int. J. Prod. Econ., 173 (2016), 1-21.  doi: 10.1016/j.ijpe.2015.11.019.  Google Scholar

[17]

M. Klausner and C. T. Hendrickson, Reverse-logistics strategy for product take-back, INFORMS Journal on Applied Analytics, 30 (2000), 156-165.  doi: 10.1287/inte.30.3.156.11657.  Google Scholar

[18]

L. KongZ. LiuY. PanJ. Xie and G. Yang, Pricing and service decision of dual-channel operations in an O2O closed-loop supply chain, Ind. Manag. Data Syst., 117 (2017), 1567-1588.  doi: 10.1108/IMDS-12-2016-0544.  Google Scholar

[19]

K. LiY. LiQ. Gu and A. Ingersoll, Joint effects of remanufacturing channel design and after-sales service pricing: An analytical study, Int. J. Prod. Res., 57 (2019), 1066-1081.  doi: 10.1080/00207543.2018.1500722.  Google Scholar

[20]

L. LiangJ. XieL. Liu and Y. Xia, Revenue sharing contract coordination of wind turbine order policy and aftermarket service based on joint effort, Ind. Manag. Data Syst., 117 (2017), 320-345.  doi: 10.1108/IMDS-03-2016-0088.  Google Scholar

[21]

H. LiuM. LeiH. DengG. Keong Leong and T. Huang, A dual channel, quality-based price competition model for the WEEE recycling market with government subsidy, Omega, 59 (2016), 290-302.  doi: 10.1016/j.omega.2015.07.002.  Google Scholar

[22]

L. LiuZ. WangL. XuX. Hong and K. Govindan, Collection effort and reverse channel choices in a closed-loop supply chain, J. Clean. Prod., 144 (2017), 492-500.  doi: 10.1016/j.jclepro.2016.12.126.  Google Scholar

[23]

Y. Liu and T. Xiao, Pricing and collection rate decisions and reverse channel choice in a socially responsible supply chain with green consumers, IEEE Trans. Eng. Manag., 67 (2020), 483-495.  doi: 10.1109/TEM.2018.2887118.  Google Scholar

[24]

Z. LiuJ. TangB. -yi Li and Z. Wang, Trade-off between remanufacturing and recycling of WEEE and the environmental implication under the Chinese Fund Policy, J. Clean. Prod., 167 (2017), 97-109.  doi: 10.1016/j.jclepro.2017.08.137.  Google Scholar

[25]

R. Lotfi, Z. Yadegari, S. H. Hosseini, A. H. Khameneh, E. B. Tirkolaee and G.-W. Weber, A robust time-cost-quality-energy-environment trade-off with resource-constrained in project management: A case study for a bridge construction project, J. Ind. Manag. Optim., 13 (2020). doi: 10.3934/jimo.2020158.  Google Scholar

[26]

D. Mangun and D. L. Thurston, Incorporating component reuse, remanufacture, and recycle into product portfolio design, IEEE Trans. Eng. Manag., 49 (2002), 479-490.  doi: 10.1109/TEM.2002.807292.  Google Scholar

[27]

N. M. ModakN. Kazemi and L. E. Cárdenas-Barrón, Investigating structure of a two-echelon closed-loop supply chain using social work donation as a Corporate Social Responsibility practice, Int. J. Prod. Econ., 207 (2019), 19-33.  doi: 10.1016/j.ijpe.2018.10.009.  Google Scholar

[28]

J. Nie, Z. Huang, Y. Zhao and Y. Shi, Collective recycling responsibility in closed-loop fashion supply chains with a third party: Financial sharing or physical sharing?, Math. Probl. Eng., 2013 (2013), Article ID 176130. doi: 10.1155/2013/176130.  Google Scholar

[29]

I. C. Nnorom and O. Osibanjo, Overview of prospects in adopting remanufacturing of end-of-life electronic products in the developing countries, Int. J. Innov. Manag. Technol., 1 (2010), 328. Google Scholar

[30]

S. PandaN. M. Modak and L. E. Cárdenas-Barrón, Coordinating a socially responsible closed-loop supply chain with product recycling, Int. J. Prod. Econ., 188 (2017), 11-21.  doi: 10.1016/j.ijpe.2017.03.010.  Google Scholar

[31]

R. C. Savaskan, S. Bhattacharya and L. N. Van Wassenhove, Closed-loop supply chain models with product remanufacturing, Manage. Sci., 50 (2004). doi: 10.1287/mnsc.1030.0186.  Google Scholar

[32]

Y. ShiJ. NieT. QuL.-K. Chu and D. Sculli, Choosing reverse channels under collection responsibility sharing in a closed-loop supply chain with re-manufacturing, J. Intell. Manuf., 26 (2015), 387-402.  doi: 10.1007/s10845-013-0797-z.  Google Scholar

[33]

T. P. Wagner, Compact fluorescent lights and the impact of convenience and knowledge on household recycling rates, Waste Manag., 31 (2011), 1300-1306.  doi: 10.1016/j.wasman.2011.01.017.  Google Scholar

[34]

N. WangQ. He and B. Jiang, Hybrid closed-loop supply chains with competition in recycling and product markets, Int. J. Prod. Econ., 217 (2019), 246-258.  doi: 10.1016/j.ijpe.2018.01.002.  Google Scholar

[35]

N. Wang, Y. Song, Q. He and T. Jia, Competitive dual-collecting regarding consumer behavior and coordination in closed-loop supply chain, Comput. Ind. Eng., 144 (2020). doi: 10.1016/j.cie.2020.106481.  Google Scholar

[36]

W. Wang, S. Zhou, M. Zhang, H. Sun and L. He, A closed-loop supply chain with competitive dual collection channel under asymmetric information and reward-penalty mechanism, Sustain., 10 (2018). doi: 10.3390/su10072131.  Google Scholar

[37]

J. WeiK. GovindanY. Li and J. Zhao, Pricing and collecting decisions in a closed-loop supply chain with symmetric and asymmetric information, Comput. Oper. Res., 54 (2015), 257-265.  doi: 10.1016/j.cor.2013.11.021.  Google Scholar

[38]

D. Wen, T. Xiao and M. Dastani, Pricing and collection rate decisions in a closed-loop supply chain considering consumers' environmental responsibility, J. Clean. Prod., 262 (2020). doi: 10.1016/j.jclepro.2020.121272.  Google Scholar

[39]

C.-H. Wu, Price and service competition between new and remanufactured products in a two-echelon supply chain, Int. J. Prod. Econ., 140 (2012), 496-507.  doi: 10.1016/j.ijpe.2012.06.034.  Google Scholar

[40]

J. XieL. LiangL. Liu and P. Ieromonachou, Coordination contracts of dual-channel with cooperation advertising in closed-loop supply chains, Int. J. Prod. Econ., 183 (2017), 528-538.  doi: 10.1016/j.ijpe.2016.07.026.  Google Scholar

[41]

J. XieW. ZhangL. LiangY. XiaJ. Yin and G. Yang, The revenue and cost sharing contract of pricing and servicing policies in a dual-channel closed-loop supply chain, J. Clean. Prod., 191 (2018), 361-383.  doi: 10.1016/j.jclepro.2018.04.223.  Google Scholar

[42]

Y. XiongQ. Zhao and Y. Zhou, Manufacturer-remanufacturing vs supplier-remanufacturing in a closed-loop supply chain, Int. J. Prod. Econ., 176 (2016), 21-28.  doi: 10.1016/j.ijpe.2016.03.001.  Google Scholar

[43]

C. Xu, B. Li, Y. Lan and Y. Tang, A closed-loop supply chain problem with retailing and recycling competition, Abstr. Appl. Anal., 2014 (2014), Article ID 509825. doi: 10.1155/2014/509825.  Google Scholar

[44]

A. Yenipazarli, Managing new and remanufactured products to mitigate environmental damage under emissions regulation, Eur. J. Oper. Res., 249 (2016), 117-130.  doi: 10.1016/j.ejor.2015.08.020.  Google Scholar

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C.-T. Zhang and M.-L. Ren, Closed-loop supply chain coordination strategy for the remanufacture of patented products under competitive demand, Appl. Math. Model., 40 (2016), 6243-6255.  doi: 10.1016/j.apm.2016.02.006.  Google Scholar

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Figure 1.  Decentralized model (DM)
Figure 2.  Centralized model (CM)
Figure 3.  Influence of $ \rho $ on the CLSC members' optimal collection decisions and profits
Figure 4.  Influence of $ n_b $ on the CLSC members' optimal collection decisions and profits
Figure 5.  Influence of $ n_S $ on the CLSC members' optimal collection decisions and profits
Figure 6.  Influence of $ m_b $ on the CLSC members' optimal collected quantities and profits
Figure 7.  Influence of $ m_S $ on the CLSC members' optimal collected quantities and profits
Figure 8.  Influence of sharing ratio $ \theta $ on chain members' profits
Table 1.  Comparison between our research and related literatures
References Collecting channel Pricing on Service on Collecting competition on Collecting quality Coordination mechanism
Single channel dual-channel Sales Collection Sales Collection Price Service
Ferrer and Swaminathan (2010)
Wei et al. (2015)
Gao et al. (2016) LPSS
Gan et al. (2017)
P. He et al. (2019)
Modak et al. (2019) TPTC
Wen et al. (2020)
Savaskan et al. (2004) WPC
Hong and Yeh (2012)
Atasu et al. (2013)
Shi et al. (2015)
Liu and Xiao (2020)
Huang et al. (2013)
L. Liu et al. (2017)
Liu et al. (2016)
Wang et al. (2018) RPM
Q. He et al. (2019) TPTC, AM
Wang et al. (2019)
Wu (2012)
Hong et al. (2015) CA, TPTC
Zhang et al. (2015)
Jena and Sarmah (2016) QDC
Kong et al. (2017)
Zhao et al. (2019)
Li et al. (2019)
Huang et al. (2020)
De Giovanni (2014) WPC, RRSC
Panda et al. (2017) RSC
Liang et al. (2017) RSC
Xie et al. (2017) RSC
Xie et al. (2018) RSC, RCSC
Zheng et al. (2019) SVM, NSM, ESM
Wang et al. (2020) RSC, TPTC
This research RCSC
LPPS: Low Price Promotion Strategy, TPTC: Two Part Tariff Contract, WPC: Wholesale Price Contract, RPM: Reward-Penalty Mechanism, CA: Cooperative advertising, QDC: Quantity Discount Contract, RSC: Revenue Sharing Contract, RRSC: Reverse Revenue Sharing Contract, RCSC: Revenue and Cost Sharing Contract, AM: Authorization Mechanism, SVM: Shapley Value Mechanism, NSM: Nucleolus Solution Mechanism, ESM: Equal Satisfaction Mechanism.
References Collecting channel Pricing on Service on Collecting competition on Collecting quality Coordination mechanism
Single channel dual-channel Sales Collection Sales Collection Price Service
Ferrer and Swaminathan (2010)
Wei et al. (2015)
Gao et al. (2016) LPSS
Gan et al. (2017)
P. He et al. (2019)
Modak et al. (2019) TPTC
Wen et al. (2020)
Savaskan et al. (2004) WPC
Hong and Yeh (2012)
Atasu et al. (2013)
Shi et al. (2015)
Liu and Xiao (2020)
Huang et al. (2013)
L. Liu et al. (2017)
Liu et al. (2016)
Wang et al. (2018) RPM
Q. He et al. (2019) TPTC, AM
Wang et al. (2019)
Wu (2012)
Hong et al. (2015) CA, TPTC
Zhang et al. (2015)
Jena and Sarmah (2016) QDC
Kong et al. (2017)
Zhao et al. (2019)
Li et al. (2019)
Huang et al. (2020)
De Giovanni (2014) WPC, RRSC
Panda et al. (2017) RSC
Liang et al. (2017) RSC
Xie et al. (2017) RSC
Xie et al. (2018) RSC, RCSC
Zheng et al. (2019) SVM, NSM, ESM
Wang et al. (2020) RSC, TPTC
This research RCSC
LPPS: Low Price Promotion Strategy, TPTC: Two Part Tariff Contract, WPC: Wholesale Price Contract, RPM: Reward-Penalty Mechanism, CA: Cooperative advertising, QDC: Quantity Discount Contract, RSC: Revenue Sharing Contract, RRSC: Reverse Revenue Sharing Contract, RCSC: Revenue and Cost Sharing Contract, AM: Authorization Mechanism, SVM: Shapley Value Mechanism, NSM: Nucleolus Solution Mechanism, ESM: Equal Satisfaction Mechanism.
Table 2.  Notations
Symbol Description
Parameters
$ c_m $ Production costs via new raw materials
$ c_r $ Production costs via collected products
$ \Delta $ The cost-savings provided by remanufacturing. Note that $ \Delta={c_m}-{c_r} $
$ \rho $ Remanufacturable ratio of the collected products
$ r $ The revenue by disassembling collected products
$ q_R $ Quantity of used product collected by the retailer
$ q_T $ Quantity of used product collected by the third-party collector
$ m_b $ Collecting price sensitivity coefficient
$ n_b $ Collecting price competition coefficient
$ m_S $ Collecting service sensitivity coefficient
$ n_S $ Collecting service competition coefficient
$ A $ Cost index of reverse channel investment
$ d $ Product demand. Note that $ d=\alpha-\ \beta p $
Decision variables
$ p $ Selling price of products
$ w $ Wholesale price
$ B $ The transfer price that the manufacturer pays to the retailer or the third-party collector
$ S_R $ The retailer's collecting service level
$ S_T $ The third-party collector's collecting service level
$ b_R $ Collecting price to market given by the retailer
$ b_T $ Collecting price to market given by the third-party collector
Other notations
$ M $ The manufacturer
$ R $ The retailer
$ T $ The third-party collector
$ \pi_C $ The total profit of the supply chain
$ \pi_M $ The profit of the manufacturer
$ \pi_R $ The profit of the retailer
$ \pi_T $ The profit of the third-party collector
CM The centralized model
DM The decentralized model
Note that $ p>w>{c_m}>{c_r}>0 $, $ \Delta>B>{b_i}>0 $, $ {S_i}>0 $, $ i=\{R,T\} $.
Symbol Description
Parameters
$ c_m $ Production costs via new raw materials
$ c_r $ Production costs via collected products
$ \Delta $ The cost-savings provided by remanufacturing. Note that $ \Delta={c_m}-{c_r} $
$ \rho $ Remanufacturable ratio of the collected products
$ r $ The revenue by disassembling collected products
$ q_R $ Quantity of used product collected by the retailer
$ q_T $ Quantity of used product collected by the third-party collector
$ m_b $ Collecting price sensitivity coefficient
$ n_b $ Collecting price competition coefficient
$ m_S $ Collecting service sensitivity coefficient
$ n_S $ Collecting service competition coefficient
$ A $ Cost index of reverse channel investment
$ d $ Product demand. Note that $ d=\alpha-\ \beta p $
Decision variables
$ p $ Selling price of products
$ w $ Wholesale price
$ B $ The transfer price that the manufacturer pays to the retailer or the third-party collector
$ S_R $ The retailer's collecting service level
$ S_T $ The third-party collector's collecting service level
$ b_R $ Collecting price to market given by the retailer
$ b_T $ Collecting price to market given by the third-party collector
Other notations
$ M $ The manufacturer
$ R $ The retailer
$ T $ The third-party collector
$ \pi_C $ The total profit of the supply chain
$ \pi_M $ The profit of the manufacturer
$ \pi_R $ The profit of the retailer
$ \pi_T $ The profit of the third-party collector
CM The centralized model
DM The decentralized model
Note that $ p>w>{c_m}>{c_r}>0 $, $ \Delta>B>{b_i}>0 $, $ {S_i}>0 $, $ i=\{R,T\} $.
Table 3.  The comparisons between the optimal collection decisions and profits of the two models
$ p $ $ b_R $ $ b_T $ $ S_R $ $ S_T $ $ q_R $ $ q_T $ $ q_C $ $ \pi_C $
DM 39.5 0.76 0.76 0.38 0.38 9.44 9.44 18.89 707.17
CM 29 1.35 1.35 0.61 0.61 16.36 16.36 32.72 937.63
$ p $ $ b_R $ $ b_T $ $ S_R $ $ S_T $ $ q_R $ $ q_T $ $ q_C $ $ \pi_C $
DM 39.5 0.76 0.76 0.38 0.38 9.44 9.44 18.89 707.17
CM 29 1.35 1.35 0.61 0.61 16.36 16.36 32.72 937.63
Table 4.  The comparison between the profits of the CLSC with coordination and that without coordination
Profit $ \pi_T $ $ \pi_R $ $ \pi_M $ $ \pi $ Supply chain efficiency
Without coordination 6.78 227.28 473.11 707.17 75.42%
With coordination 8.86 367.21 561.44 937.51 99.99%
Profit $ \pi_T $ $ \pi_R $ $ \pi_M $ $ \pi $ Supply chain efficiency
Without coordination 6.78 227.28 473.11 707.17 75.42%
With coordination 8.86 367.21 561.44 937.51 99.99%
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