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September  2021, 17(5): 2475-2503. doi: 10.3934/jimo.2020078

Optimal production and emission reduction policies for a remanufacturing firm considering deferred payment strategy

Qianru li , Weida chen , and  Yongming zhang

School of Economics and Management, Southeast University, Nanjing, P.R. China

* Corresponding author: Weida Chen

Received  June 2019 Revised  December 2019 Published  September 2021 Early access  April 2020

Fund Project: This work was supported by the National Natural Science Foundation of China (NSFC) under Grants 71571042, 71971058

Carbon emission reduction is regarded as an effective way to protect the environment, which requires a large amount of capital. Thus, for a remanufacturing firm with limited initial capital, trade credits act as an effective financing method in supporting production and emission reductions. In this study, under the cap-and-trade and government's subsidy policies, a joint decision on recycling, remanufacturing and emission reduction by a financially constrained remanufacturer with considering deferred payment to a third-party recycler is analyzed. On the basis, optimization models are established to derive the optimal recycling quantity, carbon reduction rate and government subsidy rate by using a backward induction. Furthermore, an analytical comparison is provided between the cases of base model, carbon abatement investment model and deferred payment model. Numerical experiment results indicate that the remanufacturer can always make use of the investment option to further decrease its carbon emissions and gain more profit. We also find that deferred payment can effectively mitigate carbon emissions only when the degree of emission efforts is more than a certain critical value, and it also plays a positive role in the third-party recycler's revenue, especially for the case with higher initial capital. Some other managerial implications are further discussed.

Keywords: Recycling, remanufacturing, carbon abatement investment, deferred payment, government abatement subsidy.
Mathematics Subject Classification: Primary: 90B50, 90C30; Secondary: 90B30.
Citation: Qianru li, Weida chen, Yongming zhang. Optimal production and emission reduction policies for a remanufacturing firm considering deferred payment strategy. Journal of Industrial and Management Optimization, 2021, 17 (5) : 2475-2503. doi: 10.3934/jimo.2020078
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]

V. Babich and C. S. Tang, Managing opportunistic supplier product adulteration: Deferred payments, inspection, and combined mechanisms, Manufac. Service Oper. Management, 14 (2012), 301-314.  doi: 10.1287/msom.1110.0366.

[3]

K. Biel and C. H. Glock, Prerequisites of efficient decentralized waste heat recovery and energy storage in production planning, J. Business Econ., 87 (2017), 41-72.  doi: 10.1007/s11573-016-0804-x.

[4]

K. Biel and C. H. Glock, Systematic literature review of decision support models for energy-efficient production planning, Comput. Industrial Engineering, 101 (2016), 243-259.  doi: 10.1016/j.cie.2016.08.021.

[5]

S. Benjaafar, Y. Li and M. Daskin, Carbon footprint and the management of supply chains: Insights from simple models, IEEE Transac. Automat. Science Engineering, 10 (2013), 99-116.  doi: 10.1109/TASE.2012.2203304.

[6]

J. Cao, X. Chen, X. Zhang, Y. Gao, X. Zhang and S. Kumar, Overview of remanufacturing industry in China: Government policies, enterprise, and public awareness, J. Cleaner Produc., 242 (2019). doi: 10.1016/j.jclepro.2019.118450.

[7]

X. Chang, H. Xia, H. Zhu, T. Fan and H. Zhao, Production decisions in a hybrid manufacturing–remanufacturing system with carbon cap and trade mechanism, Internat. J. Produc. Econ., 162 (2015), 160-173.  doi: 10.1016/j.ijpe.2015.01.020.

[8]

X. Chen, S. Benjaafar and A. Elomri, The carbon-constrained EOQ, Oper. Res. Lett., 41 (2013), 172-179.  doi: 10.1016/j.orl.2012.12.003.

[9]

X. Chen, Z. Luo and X. Wang, Impact of efficiency, investment, and competition on low carbon manufacturing, J. Cleaner Produc., 143 (2017), 388-400.  doi: 10.1016/j.jclepro.2016.12.095.

[10]

W. Chen, L. Wei and Y. Li, Fuzzy multicycle manufacturing/remanufacturing production decisions considering inflation and the time value of money, J. Cleaner Produc., 198 (2018), 1494-1502.  doi: 10.1016/j.jclepro.2018.07.004.

[11]

J. Chod, Inventory, risk shifting, and trade credit, Management Science, 63 (2016), 3207-3225.  doi: 10.1287/mnsc.2016.2515.

[12]

S. Devalkar and H. Krishnan, The impact of negative demand shocks on trade credit and supply chain cohesion, SSRN Electronic J., (2014). doi: 10.2139/ssrn.2437739.

[13]

C. Dong, B. Shen, P.-S. Chow, L. Yang and C. T. Ng, Sustainability investment under cap-and-trade regulation, Ann. Oper. Res., 240 (2016), 509-531.  doi: 10.1007/s10479-013-1514-1.

[14]

D. F. Drake, P. R. Kleindorfer and L. N. Van Wassenhove, Technology choice and capacity portfolios under emissions regulation, Produc. Oper. Management, 25 (2016), 1006-1025.  doi: 10.1111/poms.12523.

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D. Esty and A. Winston, Green to Gold: How Smart Companies Use Environmental Strategy to Innovate, Create Value, and Build Competitive Advantage, John Wiley & Sons, 2009.

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H. Golpîra, S. A. R. Khan and Y. Zhang, Robust Smart Energy Efficient Production Planning for a general Job-Shop Manufacturing System under combined demand and supply uncertainty in the presence of grid-connected microgrid, J. Cleaner Produc., 202 (2018), 649-665.  doi: 10.1016/j.jclepro.2018.08.151.

[17]

Y. Jiang and D. Klabjan, Optimal emissions reduction investment under greenhouse gas emissions regulations, Ph.D thesis, Northwestern University in Evanston, 2012.

[18]

Z. Luo, X. Chen, X and X. Wang, The role of co-opetition in low carbon manufacturing, European J. Oper. Res., 253 (2016), 392–403. doi: 10.1016/j.ejor.2016.02.030.

[19]

C. H. Lee and B. D. Rhee, Trade credit for supply chain coordination, European J. Oper. Res., 214 (2011), 136-146.  doi: 10.1016/j.ejor.2011.04.004.

[20]

Q. Li, Optimal core pricing and financing strategies for remanufacturers, 2018 Chinese Control and Decision Conference (CCDC), IEEE, 2018. doi: 10.1109/CCDC.2018.8407445.

[21]

H. Peura, S. A. Yang and G. Lai, Trade credit in competition: A horizontal benefit, Manufac. Service Oper. Management, 19 (2017), 263-289.  doi: 10.1287/msom.2016.0608.

[22]

L. D. Qiu and Z. Tao, Policy on international R&D cooperation: Subsidy or tax?, European Econ. Rev., 42 (1998), 1727-1750.  doi: 10.1016/S0014-2921(97)00097-4.

[23]

H. Rui and G. Lai, Sourcing with deferred payment and inspection under supplier product adulteration risk, Produc. Oper. Management, 24 (2015), 934-946.  doi: 10.1111/poms.12313.

[24]

H. Sun, W. Chen, Z. Ren and B. Liu, Optimal policy in a hybrid manufacturing/remanufacturing system with financial hedging, Internat. J. Produc. Res., 55 (2017), 5728-5742.  doi: 10.1080/00207543.2017.1330570.

[25]

A. Toptal, H. Özlü and D. Konur, Joint decisions on inventory replenishment and emission reduction investment under different emission regulations, Internat. J. Produc. Res., 52 (2014), 243-269.  doi: 10.1080/00207543.2013.836615.

[26]

T. I. Tunca and W. Zhu, Buyer intermediation in supplier finance, Management Science, 64 (2017), 5631-5650.  doi: 10.1287/mnsc.2017.2863.

[27]

Y.-C. Tsao, Channel coordination under two-level trade credits and demand uncertainty, Appl. Math. Model., 52 (2017), 160-173.  doi: 10.1016/j.apm.2017.07.046.

[28]

E. Van der Laan and M. Salomon, Production planning and inventory control with remanufacturing and disposal, European J. Oper. res., 102 (1997), 264-278.  doi: 10.1016/S0377-2217(97)00108-2.

[29]

J. Wang, Y. Wang, S. Zhang and M. Zhang, Effects of fund policy incorporating Extended Producer Responsibility for WEEE dismantling industry in China, Resources Conservation Recycling, 130 (2018), 44-50.  doi: 10.1016/j.resconrec.2017.11.016.

[30]

Y. Wang and W. Chen, Effects of emissions constraint on manufacturing/remanufacturing decisions considering capital constraint and financing, Atmospheric Pollution Res., 8 (2017), 455-464.  doi: 10.1016/j.apr.2016.11.006.

[31]

Y. Wang, W. Chen and B. Liu, Manufacturing/remanufacturing decisions for a capital-constrained manufacturer considering carbon emission cap and trade, J. Cleaner Produc., 140 (2017), 1118-1128.  doi: 10.1016/j.jclepro.2016.10.058.

[32]

S. Xiao, S. P. Sethi, M. Liu and S. Ma, Coordinating contracts for a financially constrained supply chain, Omega, 72 (2017), 71-86.  doi: 10.1016/j.omega.2016.11.005.

[33]

B. Yalabik and R. J. Fairchild, Customer, regulatory, and competitive pressure as drivers of environmental innovation, Internat. J. Produc. Econ., 131 (2011), 519-527.  doi: 10.1016/j.ijpe.2011.01.020.

[34]

L. Yang, G. Wang and C. Ke, Remanufacturing and promotion in dual-channel supply chains under cap-and-trade regulation, J. Cleaner Produc., 204 (2018), 939-957.  doi: 10.1016/j.jclepro.2018.08.297.

[35]

L. Yang, Q. Zhang and J. Ji, Pricing and carbon emission reduction decisions in supply chains with vertical and horizontal cooperation, Internat. J. Produc. Econ., 191 (2017), 286-297.  doi: 10.1016/j.ijpe.2017.06.021.

[36]

S. A. Yang and J. R. Birge, Trade credit in supply chains: Multiple creditors and priority rules, 2011. Available from: https://ssrn.com/abstract=1840663. doi: 10.2139/ssrn.1840663.

[37]

S. A. Yang and J. R. Birge, Trade credit, risk sharing, and inventory financing portfolios, Management Science, 64 (2017), 3667-3689.  doi: 10.1287/mnsc.2017.2799.

[38]

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.

[39]

Y. Yu, X. Han and G. Hu, Optimal production for manufacturers considering consumer environmental awareness and green subsidies, Internat. J. Produc. Econ., 182 (2016), 397-408.  doi: 10.1016/j.ijpe.2016.09.014.

[40]

J. Zhou, Q. Deng and T. Li, Optimal acquisition and remanufacturing policies considering the effect of quality uncertainty on carbon emissions, J. Cleaner Produc., 186 (2018), 180-190.  doi: 10.1016/j.jclepro.2018.03.150.

[41]

L. Zhou, J. Li, F. Li, Q. Meng, J. Li and X. Xu, Energy consumption model and energy efficiency of machine tools: A comprehensive literature review, J. Cleaner Produc., 112 (2016), 3721-3734.  doi: 10.1016/j.jclepro.2015.05.093.

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]

V. Babich and C. S. Tang, Managing opportunistic supplier product adulteration: Deferred payments, inspection, and combined mechanisms, Manufac. Service Oper. Management, 14 (2012), 301-314.  doi: 10.1287/msom.1110.0366.

[3]

K. Biel and C. H. Glock, Prerequisites of efficient decentralized waste heat recovery and energy storage in production planning, J. Business Econ., 87 (2017), 41-72.  doi: 10.1007/s11573-016-0804-x.

[4]

K. Biel and C. H. Glock, Systematic literature review of decision support models for energy-efficient production planning, Comput. Industrial Engineering, 101 (2016), 243-259.  doi: 10.1016/j.cie.2016.08.021.

[5]

S. Benjaafar, Y. Li and M. Daskin, Carbon footprint and the management of supply chains: Insights from simple models, IEEE Transac. Automat. Science Engineering, 10 (2013), 99-116.  doi: 10.1109/TASE.2012.2203304.

[6]

J. Cao, X. Chen, X. Zhang, Y. Gao, X. Zhang and S. Kumar, Overview of remanufacturing industry in China: Government policies, enterprise, and public awareness, J. Cleaner Produc., 242 (2019). doi: 10.1016/j.jclepro.2019.118450.

[7]

X. Chang, H. Xia, H. Zhu, T. Fan and H. Zhao, Production decisions in a hybrid manufacturing–remanufacturing system with carbon cap and trade mechanism, Internat. J. Produc. Econ., 162 (2015), 160-173.  doi: 10.1016/j.ijpe.2015.01.020.

[8]

X. Chen, S. Benjaafar and A. Elomri, The carbon-constrained EOQ, Oper. Res. Lett., 41 (2013), 172-179.  doi: 10.1016/j.orl.2012.12.003.

[9]

X. Chen, Z. Luo and X. Wang, Impact of efficiency, investment, and competition on low carbon manufacturing, J. Cleaner Produc., 143 (2017), 388-400.  doi: 10.1016/j.jclepro.2016.12.095.

[10]

W. Chen, L. Wei and Y. Li, Fuzzy multicycle manufacturing/remanufacturing production decisions considering inflation and the time value of money, J. Cleaner Produc., 198 (2018), 1494-1502.  doi: 10.1016/j.jclepro.2018.07.004.

[11]

J. Chod, Inventory, risk shifting, and trade credit, Management Science, 63 (2016), 3207-3225.  doi: 10.1287/mnsc.2016.2515.

[12]

S. Devalkar and H. Krishnan, The impact of negative demand shocks on trade credit and supply chain cohesion, SSRN Electronic J., (2014). doi: 10.2139/ssrn.2437739.

[13]

C. Dong, B. Shen, P.-S. Chow, L. Yang and C. T. Ng, Sustainability investment under cap-and-trade regulation, Ann. Oper. Res., 240 (2016), 509-531.  doi: 10.1007/s10479-013-1514-1.

[14]

D. F. Drake, P. R. Kleindorfer and L. N. Van Wassenhove, Technology choice and capacity portfolios under emissions regulation, Produc. Oper. Management, 25 (2016), 1006-1025.  doi: 10.1111/poms.12523.

[15]

D. Esty and A. Winston, Green to Gold: How Smart Companies Use Environmental Strategy to Innovate, Create Value, and Build Competitive Advantage, John Wiley & Sons, 2009.

[16]

H. Golpîra, S. A. R. Khan and Y. Zhang, Robust Smart Energy Efficient Production Planning for a general Job-Shop Manufacturing System under combined demand and supply uncertainty in the presence of grid-connected microgrid, J. Cleaner Produc., 202 (2018), 649-665.  doi: 10.1016/j.jclepro.2018.08.151.

[17]

Y. Jiang and D. Klabjan, Optimal emissions reduction investment under greenhouse gas emissions regulations, Ph.D thesis, Northwestern University in Evanston, 2012.

[18]

Z. Luo, X. Chen, X and X. Wang, The role of co-opetition in low carbon manufacturing, European J. Oper. Res., 253 (2016), 392–403. doi: 10.1016/j.ejor.2016.02.030.

[19]

C. H. Lee and B. D. Rhee, Trade credit for supply chain coordination, European J. Oper. Res., 214 (2011), 136-146.  doi: 10.1016/j.ejor.2011.04.004.

[20]

Q. Li, Optimal core pricing and financing strategies for remanufacturers, 2018 Chinese Control and Decision Conference (CCDC), IEEE, 2018. doi: 10.1109/CCDC.2018.8407445.

[21]

H. Peura, S. A. Yang and G. Lai, Trade credit in competition: A horizontal benefit, Manufac. Service Oper. Management, 19 (2017), 263-289.  doi: 10.1287/msom.2016.0608.

[22]

L. D. Qiu and Z. Tao, Policy on international R&D cooperation: Subsidy or tax?, European Econ. Rev., 42 (1998), 1727-1750.  doi: 10.1016/S0014-2921(97)00097-4.

[23]

H. Rui and G. Lai, Sourcing with deferred payment and inspection under supplier product adulteration risk, Produc. Oper. Management, 24 (2015), 934-946.  doi: 10.1111/poms.12313.

[24]

H. Sun, W. Chen, Z. Ren and B. Liu, Optimal policy in a hybrid manufacturing/remanufacturing system with financial hedging, Internat. J. Produc. Res., 55 (2017), 5728-5742.  doi: 10.1080/00207543.2017.1330570.

[25]

A. Toptal, H. Özlü and D. Konur, Joint decisions on inventory replenishment and emission reduction investment under different emission regulations, Internat. J. Produc. Res., 52 (2014), 243-269.  doi: 10.1080/00207543.2013.836615.

[26]

T. I. Tunca and W. Zhu, Buyer intermediation in supplier finance, Management Science, 64 (2017), 5631-5650.  doi: 10.1287/mnsc.2017.2863.

[27]

Y.-C. Tsao, Channel coordination under two-level trade credits and demand uncertainty, Appl. Math. Model., 52 (2017), 160-173.  doi: 10.1016/j.apm.2017.07.046.

[28]

E. Van der Laan and M. Salomon, Production planning and inventory control with remanufacturing and disposal, European J. Oper. res., 102 (1997), 264-278.  doi: 10.1016/S0377-2217(97)00108-2.

[29]

J. Wang, Y. Wang, S. Zhang and M. Zhang, Effects of fund policy incorporating Extended Producer Responsibility for WEEE dismantling industry in China, Resources Conservation Recycling, 130 (2018), 44-50.  doi: 10.1016/j.resconrec.2017.11.016.

[30]

Y. Wang and W. Chen, Effects of emissions constraint on manufacturing/remanufacturing decisions considering capital constraint and financing, Atmospheric Pollution Res., 8 (2017), 455-464.  doi: 10.1016/j.apr.2016.11.006.

[31]

Y. Wang, W. Chen and B. Liu, Manufacturing/remanufacturing decisions for a capital-constrained manufacturer considering carbon emission cap and trade, J. Cleaner Produc., 140 (2017), 1118-1128.  doi: 10.1016/j.jclepro.2016.10.058.

[32]

S. Xiao, S. P. Sethi, M. Liu and S. Ma, Coordinating contracts for a financially constrained supply chain, Omega, 72 (2017), 71-86.  doi: 10.1016/j.omega.2016.11.005.

[33]

B. Yalabik and R. J. Fairchild, Customer, regulatory, and competitive pressure as drivers of environmental innovation, Internat. J. Produc. Econ., 131 (2011), 519-527.  doi: 10.1016/j.ijpe.2011.01.020.

[34]

L. Yang, G. Wang and C. Ke, Remanufacturing and promotion in dual-channel supply chains under cap-and-trade regulation, J. Cleaner Produc., 204 (2018), 939-957.  doi: 10.1016/j.jclepro.2018.08.297.

[35]

L. Yang, Q. Zhang and J. Ji, Pricing and carbon emission reduction decisions in supply chains with vertical and horizontal cooperation, Internat. J. Produc. Econ., 191 (2017), 286-297.  doi: 10.1016/j.ijpe.2017.06.021.

[36]

S. A. Yang and J. R. Birge, Trade credit in supply chains: Multiple creditors and priority rules, 2011. Available from: https://ssrn.com/abstract=1840663. doi: 10.2139/ssrn.1840663.

[37]

S. A. Yang and J. R. Birge, Trade credit, risk sharing, and inventory financing portfolios, Management Science, 64 (2017), 3667-3689.  doi: 10.1287/mnsc.2017.2799.

[38]

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.

[39]

Y. Yu, X. Han and G. Hu, Optimal production for manufacturers considering consumer environmental awareness and green subsidies, Internat. J. Produc. Econ., 182 (2016), 397-408.  doi: 10.1016/j.ijpe.2016.09.014.

[40]

J. Zhou, Q. Deng and T. Li, Optimal acquisition and remanufacturing policies considering the effect of quality uncertainty on carbon emissions, J. Cleaner Produc., 186 (2018), 180-190.  doi: 10.1016/j.jclepro.2018.03.150.

[41]

L. Zhou, J. Li, F. Li, Q. Meng, J. Li and X. Xu, Energy consumption model and energy efficiency of machine tools: A comprehensive literature review, J. Cleaner Produc., 112 (2016), 3721-3734.  doi: 10.1016/j.jclepro.2015.05.093.

Figure 1.  Framework of the remanufacturing system with limited capital
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Figure 2.  Framework of the game model of Model Ⅱ
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Figure 3.  The sequence of the events
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Figure 4.  Comparison of emission differences under different models for varying values of $\xi $ when $c_{m} = 4$
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Figure 5.  Comparison of profit differences of the remanufacturer under different models for varying values of $\xi $ when $c_{m} = 4$
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Figure 6.  Comparison of profit differences of the third-party recycler under different models for varying values of $\xi$ when $c_{m} = 4$
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Figure 7.  Comparison of emission differences under different models when $ c_{m} = 8 $
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Figure 8.  Comparison of profit differences of the third-party recycler under different models when $ c_{m} = 8 $
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Figure 9.  Comparison of profit differences of the third-party recycler under different models when $ c_{m} = 8 $
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Table 1.  Carbon abatement investment related research
Research object Carbon abatement investment method Carbon emission regulation Tax or subsidy Consumer environmental awareness references
Supply chain Offset investment
Technology investment		 Cap-and-offset, carbon tax,
cap-and-trade policy
cap-and-trade policy		 No Benjaafar et al.(2013)
Dong et al. (2016),
Yang et al. (2017)
Individual firm — — Yes No Qiu and Tao (1998),
Wang et al. (2018)
— — Yes Yes Yu et al. (2016)
Offset investment Cap-and-offset, carbon tax,
cap-and-trade policy		 No Chen et al.(2013)
Technology investment — No No Chen et al. (2017),
Cap-and-trade Luo et al. (2016)
Carbon cap, carbon tax,
cap-and-trade policy		 Jiang and Klabjan (2012),
Toptal et al.(2014)
— Yes Yes Yalabik and Fairchild (2011)
Remanufacturing firm Technology investment Cap-and-trade Yes Yes Our paper
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Research object Carbon abatement investment method Carbon emission regulation Tax or subsidy Consumer environmental awareness references
Supply chain Offset investment
Technology investment		 Cap-and-offset, carbon tax,
cap-and-trade policy
cap-and-trade policy		 No Benjaafar et al.(2013)
Dong et al. (2016),
Yang et al. (2017)
Individual firm — — Yes No Qiu and Tao (1998),
Wang et al. (2018)
— — Yes Yes Yu et al. (2016)
Offset investment Cap-and-offset, carbon tax,
cap-and-trade policy		 No Chen et al.(2013)
Technology investment — No No Chen et al. (2017),
Cap-and-trade Luo et al. (2016)
Carbon cap, carbon tax,
cap-and-trade policy		 Jiang and Klabjan (2012),
Toptal et al.(2014)
— Yes Yes Yalabik and Fairchild (2011)
Remanufacturing firm Technology investment Cap-and-trade Yes Yes Our paper
Table 2.  Trade credit related research
Research object Financing method Supply chain coordination Default risk references
Supply chain Bank loan & trade credit No No Chod (2016)
Yes Yes Xiao et al. (2017),
Yang and Birge (2017)
Trade credit No No Peura et al. (2017),
Tunca and Zhu (2017)
No Yes Babich and Tang (2012),
Rui and Lai (2015)
Yes No Tsao and Yu-Chung (2017),
Lee and Rhee (2011)
Yes Yes Devalkar and Krishnan (2014),
Yang and Birge (2011)
Remanufact-uring system Bank loan No No Li (2018),
Sun et al. (2017),
Wang et al. (2017),
Wang and Chen (2017)
Trade credit Our paper
Table Options

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Research object Financing method Supply chain coordination Default risk references
Supply chain Bank loan & trade credit No No Chod (2016)
Yes Yes Xiao et al. (2017),
Yang and Birge (2017)
Trade credit No No Peura et al. (2017),
Tunca and Zhu (2017)
No Yes Babich and Tang (2012),
Rui and Lai (2015)
Yes No Tsao and Yu-Chung (2017),
Lee and Rhee (2011)
Yes Yes Devalkar and Krishnan (2014),
Yang and Birge (2011)
Remanufact-uring system Bank loan No No Li (2018),
Sun et al. (2017),
Wang et al. (2017),
Wang and Chen (2017)
Trade credit Our paper
Table 3.  Notation
Indices
$ i $ Index for the case of Model $ j, i= $ 1, 2, 3 for Model I, II, III respectively.
$ j $ Index for model, $ j= $ I, II, III.
Parameters
$ c $ Unit remanufacturing cost.
$ c_{0} $ Unit disposal cost.
$ h $ Unit stock-holding cost.
$ s $ Unit shortage cost.
$ v_{t} $ Unit acquisition price by the third-party recycler.
$ a $ Unit recycling price by the remanufacturer.
$ p $ Unit sales price, $ p>s>c. $
$ \xi $ Remanufacturing rate.
$ D $ Stochastic demand with support on [0, $ +\infty $), CDF $ F $ (), PDF $ f $ (). Suppose it obey the uniform distribution on [$ \alpha, \beta $], $ F (\alpha) =0 $, $ F (\beta) =1 $.
$ q_{i} $ Production quantity for Model $ j $, $ q_{i} =R_{i} \ast \xi $.
$ t $ Consumers' low carbon preference coefficient.
$ \delta $ Environmental benefit coefficient.
$ c_{m} $ Unit carbon trading price.
$ e_{0} $ Initial unit carbon emissions.
$ \Delta e_{i} $ Unit carbon emission reduction for Model $ j $.
$ m $ Cost coefficient of emission reduction.
$ E_{g} $ Carbon emission quota.
$ B $ Initial capital by the remanufacturer.
$ T_{1}, T_{2} $ Recycling period and production period.
$ M $ Sales period/credit period.
$ k $ Sensitivity to deferred payment length.
$ \pi_{ri}, \pi_{ti} $ The profit by the remanufacturer and the third-party recycler for Model $ j, $ respectively.
Decision variables
$ R_{i} $ Recycling quantity of Model $ j $ by the remanufacturer.
$ \tau_{i} $ Carbon reduction rate of Model $ j $, $ \tau_{i} =\Delta e_{i}/e_{0} $.
$ f_{i} $ Government subsidy rate for carbon emission reduction of Model $ j $.
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Indices
$ i $ Index for the case of Model $ j, i= $ 1, 2, 3 for Model I, II, III respectively.
$ j $ Index for model, $ j= $ I, II, III.
Parameters
$ c $ Unit remanufacturing cost.
$ c_{0} $ Unit disposal cost.
$ h $ Unit stock-holding cost.
$ s $ Unit shortage cost.
$ v_{t} $ Unit acquisition price by the third-party recycler.
$ a $ Unit recycling price by the remanufacturer.
$ p $ Unit sales price, $ p>s>c. $
$ \xi $ Remanufacturing rate.
$ D $ Stochastic demand with support on [0, $ +\infty $), CDF $ F $ (), PDF $ f $ (). Suppose it obey the uniform distribution on [$ \alpha, \beta $], $ F (\alpha) =0 $, $ F (\beta) =1 $.
$ q_{i} $ Production quantity for Model $ j $, $ q_{i} =R_{i} \ast \xi $.
$ t $ Consumers' low carbon preference coefficient.
$ \delta $ Environmental benefit coefficient.
$ c_{m} $ Unit carbon trading price.
$ e_{0} $ Initial unit carbon emissions.
$ \Delta e_{i} $ Unit carbon emission reduction for Model $ j $.
$ m $ Cost coefficient of emission reduction.
$ E_{g} $ Carbon emission quota.
$ B $ Initial capital by the remanufacturer.
$ T_{1}, T_{2} $ Recycling period and production period.
$ M $ Sales period/credit period.
$ k $ Sensitivity to deferred payment length.
$ \pi_{ri}, \pi_{ti} $ The profit by the remanufacturer and the third-party recycler for Model $ j, $ respectively.
Decision variables
$ R_{i} $ Recycling quantity of Model $ j $ by the remanufacturer.
$ \tau_{i} $ Carbon reduction rate of Model $ j $, $ \tau_{i} =\Delta e_{i}/e_{0} $.
$ f_{i} $ Government subsidy rate for carbon emission reduction of Model $ j $.
Table 4.  The impact of m on the total emission (k = 0.2)
m 1200 1400 1600 1800 2000
$ E_{2}^{\ast} $ 19.9770 41.8060 53.7053 61.0017 65.8504
$ E_{3}^{(1)} $ 37.5510 40.3498 42.4490 44.0816 45.3878
$ E_{3}^{(2)} $ 29.5592 46.1639 55.1360 60.5937 64.1942
Notes: carbon emission unit: kilo
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m 1200 1400 1600 1800 2000
$ E_{2}^{\ast} $ 19.9770 41.8060 53.7053 61.0017 65.8504
$ E_{3}^{(1)} $ 37.5510 40.3498 42.4490 44.0816 45.3878
$ E_{3}^{(2)} $ 29.5592 46.1639 55.1360 60.5937 64.1942
Notes: carbon emission unit: kilo
Table 5.  The impact of m on the total emission (k = 0.6)
m 1200 1400 1600 1800 2000
$ E_{2}^{\ast} $ 19.9770 41.8060 53.7053 61.0017 65.8504
$ E_{3}^{(1)} $ 37.551 40.3498 42.4490 44.0816 45.3878
$ E_{3}^{(2)} $ 34.0743 34.1072 33.8873 33.6214 33.3659
Notes: carbon emission unit: kilo
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m 1200 1400 1600 1800 2000
$ E_{2}^{\ast} $ 19.9770 41.8060 53.7053 61.0017 65.8504
$ E_{3}^{(1)} $ 37.551 40.3498 42.4490 44.0816 45.3878
$ E_{3}^{(2)} $ 34.0743 34.1072 33.8873 33.6214 33.3659
Notes: carbon emission unit: kilo
Table 6.  Present values for the base parameters ($ vt = 1 $)
Parameter $ p $ $ c $ $ a $ $ c_{0} $ $ h $ $ s $ $ v_{t} $
(RMB) (RMB) (RMB) (RMB) (RMB) (RMB) (RMB)
Present value 40 8 2 1 2 1.6 1
Parameter $ \xi $ $ [\alpha, \beta] $ $ e_{0} $ $ c_{m} $ $ \delta $ $ t $ $ E $
— — (kilo) (RMB) — (RMB) (kilo)
Present value 0.8 [0, 100] 2 6 0.6 1 60
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Parameter $ p $ $ c $ $ a $ $ c_{0} $ $ h $ $ s $ $ v_{t} $
(RMB) (RMB) (RMB) (RMB) (RMB) (RMB) (RMB)
Present value 40 8 2 1 2 1.6 1
Parameter $ \xi $ $ [\alpha, \beta] $ $ e_{0} $ $ c_{m} $ $ \delta $ $ t $ $ E $
— — (kilo) (RMB) — (RMB) (kilo)
Present value 0.8 [0, 100] 2 6 0.6 1 60
Table 7.  Comparison of the optimal solutions for varying values of $ k $ under two different self-owned capital strategies
$ B $ $ k $ $ R $ $ \tau $ $ f $ $ E $ $ \Delta E $ $ I $ $ \pi_{r} $ $ \pi_{t} $ sw
(RMB) (RMB) — — (kilo) (kilo) (RMB) (RMB) (RMB) (RMB)
$ B<\min (B_{1}, B_{2}) , B_{1}= $ 414.2992, $ B_{2}= $ 583.7571
200 0.2 23.8095 0.1829 0.0833 31.1292 6.9660 22.9878 543.7939 62.9580 1365.8837
300 0.2 35.7143 0.2743 0.0833 41.4694 15.6735 51.7224 633.6119 94.4371 1365.8837
400 0.2 47.6190 0.3657 0.0833 48.3265 27.8639 91.9510 695.3773 125.9161 1523.7365
400 0.6 47.6190 0.3657 0.0833 48.3265 27.8639 91.9510 292.7556 528.5379 1121.1148
$ B>\max (B_{2}, B_{3}), B_{2}= $ 586.0089, $ B_{3}= $ 645.6875
700 0.2 69.7630 0.5408 0.0919 51.2557 60.3650 199.2045 737.4973 184.4698 1573.5686
800 0.2 69.7630 0.5408 0.0919 51.2557 60.3650 199.2045 737.4973 184.4698 1573.5686
900 0.2 69.7630 0.5408 0.0919 51.2557 60.3650 199.2045 737.4973 184.4698 1573.5686
900 0.6 26.6087 0.2011 0.0687 34.0100 8.5639 28.2608 342.0076 295.3374 1165.0597
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$ B $ $ k $ $ R $ $ \tau $ $ f $ $ E $ $ \Delta E $ $ I $ $ \pi_{r} $ $ \pi_{t} $ sw
(RMB) (RMB) — — (kilo) (kilo) (RMB) (RMB) (RMB) (RMB)
$ B<\min (B_{1}, B_{2}) , B_{1}= $ 414.2992, $ B_{2}= $ 583.7571
200 0.2 23.8095 0.1829 0.0833 31.1292 6.9660 22.9878 543.7939 62.9580 1365.8837
300 0.2 35.7143 0.2743 0.0833 41.4694 15.6735 51.7224 633.6119 94.4371 1365.8837
400 0.2 47.6190 0.3657 0.0833 48.3265 27.8639 91.9510 695.3773 125.9161 1523.7365
400 0.6 47.6190 0.3657 0.0833 48.3265 27.8639 91.9510 292.7556 528.5379 1121.1148
$ B>\max (B_{2}, B_{3}), B_{2}= $ 586.0089, $ B_{3}= $ 645.6875
700 0.2 69.7630 0.5408 0.0919 51.2557 60.3650 199.2045 737.4973 184.4698 1573.5686
800 0.2 69.7630 0.5408 0.0919 51.2557 60.3650 199.2045 737.4973 184.4698 1573.5686
900 0.2 69.7630 0.5408 0.0919 51.2557 60.3650 199.2045 737.4973 184.4698 1573.5686
900 0.6 26.6087 0.2011 0.0687 34.0100 8.5639 28.2608 342.0076 295.3374 1165.0597
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