American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Optimizing 3-objective portfolio selection with equality constraints and analyzing the effect of varying constraints on the efficient sets
  • JIMO Home
  • This Issue
  • Next Article
    A lattice method for option evaluation with regime-switching asset correlation structure
doi: 10.3934/jimo.2020116

Channel leadership and recycling channel in closed-loop supply chain: The case of recycling price by the recycling party

Zhidan Wu 1, , Xiaohu Qian 2, , Min Huang 3,, , Wai-Ki Ching 4, , Hanbin Kuang 3, and  Xingwei Wang 5,

1. 

College of Information Science and Engineering, Northeastern University, Fundamental Teaching Department of Computer and Mathematics, Shenyang Normal University, Shenyang, Liaoning, 110034, China
2. 

Research Institute of Business Analytics and Supply Chain Management, College of Management, Shenzhen University, Shenzhen, 518060, China
3. 

College of Information Science and Engineering, State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, Liaoning, 110819, China
4. 

Department of Mathematics, The University of Hong Kong, Pokfulam, Hong Kong, China
5. 

College of Computer Science and Engineering, Northeastern University, Shenyang, Liaoning, 110819, China

* Corresponding author: Min Huang

Received  June 2019 Revised  March 2020 Published  June 2020

Due to the fast growing of the waste electrical and electronic equipment (WEEE), the business values of closed-loop supply chains (CLSCs) have been well recognized. In this paper, we investigate the performance of the CLSCs under different combinations of the recycling channel and the channel leadership when the recycling price is determined by the recycling party. Specially, we consider a CLSC consisting of two channel members, i.e., a manufacturer and a retailer. Each member acting as the channel leader has three different channels to collect the used products, and they are (ⅰ) the manufacturer (M-channel), (ⅱ) the retailer (R-channel) and (ⅲ) the third-party (T-channel). Given the recycling party determines the recycling price, mathematical models are developed to investigate the performance of the CLSC under different combinations of the channel leadership and the recycling channel. Through a comparison analysis, we find that M-channel is the most effective recycling channel. Moreover, once the M-channel be adopted, the retailer-led structure is as good as manufacture-led structure. We find that the recycling channel structure could be more important than the channel leadership in the CLSC. Finally, we illustrate that the CLSC can be coordinated by a two-part tariff contract.

Keywords: Closed-loop supply chain, channel leadership, recycling channel, pricing the recycling price, coordination.
Mathematics Subject Classification: Primary: 90B50, 91B24; Secondary: 91B99.
Citation: Zhidan Wu, Xiaohu Qian, Min Huang, Wai-Ki Ching, Hanbin Kuang, Xingwei Wang. Channel leadership and recycling channel in closed-loop supply chain: The case of recycling price by the recycling party. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020116
References:
[1]

E. Almehdawe and B. Matin, Vendor managed inventory with a capacitated manufacturer and multiple retailer: Retailer versus manufacturer leadership, Internat. J. Prod. Econ., 128 (2010), 292-302.  doi: 10.1016/j.ijpe.2010.07.029.  Google Scholar

[2]

A. Atasu, V. D. R. Guide and L. N. Van Wassenhove, Product reuse economics in closed-loop supply chain research, Prod. Oper. Manag., 17 (2010), 483-496.  doi: 10.3401/poms.1080.0051.  Google Scholar

[3]

A. Atasu, L. 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

[4]

M. Bhattacharyya and S. S. Sana, A mathematical model on eco-friendly manufacturing system under probabilistic demand, RAIRO Oper. Res., 53 (2019), 1899-1913.  doi: 10.1051/ro/2018120.  Google Scholar

[5]

G. P. Cachon and A. G. Kök, Competing manufacturers in a retail supply chain: On contractual form and coordination, Manag. Sci., 56 (2010), 571-589.  doi: 10.1287/mnsc.1090.1122.  Google Scholar

[6]

J.-M. Chen and C.-I. Chang, The co-operative strategy of a closed-loop supply chain with remanufacturing, Transpor. Res. Part E, 48 (2012), 387-400.  doi: 10.1016/j.tre.2011.10.001.  Google Scholar

[7]

T.-M. Choi, Y. Li and L. Xu, Channel leadership, performance and coordination in closed loop supply chains, Internat. J. Prod. Econ., 146 (2013), 371-380.  doi: 10.1016/j.ijpe.2013.08.002.  Google Scholar

[8]

C.-H. Chuang, C. X. Wang and Y. Zhao, Closed-loop supply chain models for a high-tech product under alternative reverse channel and collection cost structures, Internat. J. Prod. Econ., 156 (2014), 108-123.  doi: 10.1016/j.ijpe.2014.05.008.  Google Scholar

[9]

P. De 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.  Google Scholar

[10]

V. D. R. Guide and L. N. Van Wassenhove, The evolution of closed-loop supply chain research, Oper. Res., 57 (2009), 10-18.   Google Scholar

[11]

G. Ertek and P. M. Griffin, Supplier-and buyer-driven channels in a two-stage supply chain, IIE Transactions, 34 (2002), 691-700.  doi: 10.1023/A:1014920510164.  Google Scholar

[12]

L. Feng, K. Govindan and C. Li, Strategic planning: Design and coordination for dual-recycling channel reverse supply chain considering consumer behavior, European J. Oper. Res., 260 (2017), 601-612.  doi: 10.1016/j.ejor.2016.12.050.  Google Scholar

[13]

H. Garg, Fuzzy inventory models for deteriorating items under different types of lead-time distributions, in Intelligent Techniques in Engineering Management, Intelligent Systems Reference Library, 87, Springer, Cham, 2015,247–274. doi: 10.1007/978-3-319-17906-3_11.  Google Scholar

[14]

V. D. R. Guide, R. H. Teunter and L. N. Van Wassenhove, Matching demand and supply to maximize profits from remanufacturing, Manufac. Service Oper. Manag., 5 (2003), 303-316.  doi: 10.1287/msom.5.4.303.24883.  Google Scholar

[15]

X. Hong, Z. Wang and H. Zhang, Decision models of closed-loop supply chain with remanufacturing under hybrid dual-channel collection, Internat. J. Advanced Manufac. Tech., 68 (2013), 1851-1865.  doi: 10.1007/s00170-013-4982-1.  Google Scholar

[16]

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

[17]

A. P. Jeuland and S. M. Shugan, Managing channel profits, Marketing Science, 2 (1983), 239-272.  doi: 10.1287/mksc.2.3.239.  Google Scholar

[18]

I. Karakayali, H. Emir-Farinas and E. Akcal, An analysis of decentralized collection and processing of end-of-life products, J. Oper. Manag., 25 (2007), 1161-1183.  doi: 10.1016/j.jom.2007.01.017.  Google Scholar

[19]

Y. Liang, S. Pokharel and G. H. Lim, Pricing used products for remanufacturing, European J. Oper. Res., 193 (2009), 390-395.  doi: 10.1016/j.ejor.2007.11.029.  Google Scholar

[20]

H. Liu, M. Lei, H. Deng, G. K. 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

[21]

P. Majumder and A. Srinivasan, Leadership and competition in network supply chains, Manag. Science, 54 (2008), 1189-1204.  doi: 10.1287/mnsc.1070.0752.  Google Scholar

[22]

T. W. McGuire and R. Staelin, An industry equilibrium analysis of downstream vertical integration, Marketing Science, 2 (1983), 161-190.  doi: 10.1287/mksc.2.2.161.  Google Scholar

[23]

P. R. Messinger and C. Narasimhan, Has power shifted in the grocery channel?, Marketing Science, 14 (1995), 189-223.   Google Scholar

[24]

S. Mitra, Revenue management for remanufactured products, Omega, 35 (2007), 553-562.  doi: 10.1016/j.omega.2005.10.003.  Google Scholar

[25]

S. K. Mukhopadhyay, D.-Q. Yao and X. Yue, Information sharing of value-adding retailer in a mixed channel hi-tech supply chain, J. Business Res., 61 (2008), 950-958.  doi: 10.1016/j.jbusres.2006.10.027.  Google Scholar

[26]

I. E. Nielsen, S. Majumder, S. S. Sana and S. Saha, Comparative analysis of government incentives and game structures on single and two-period green supply chain, J. Cleaner Prod., 235 (2019), 1371-1398.  doi: 10.1016/j.jclepro.2019.06.168.  Google Scholar

[27]

A. Örsdemir, E. Kemahlioğlu-Ziya and A. K. Parlaktürk, Competitive quality choice and remanufacturing, Prod. and Oper. Manag., 23 (2014), 48-64.  doi: 10.1111/poms.12040.  Google Scholar

[28]

S. Saha, N. M. Modak, S. Panda and S. S. Sana, Managing a retailer's dual-channel supply chain under price- and delivery time-sensitive demand, J. Modelling Manag., 13 (2018), 351-374.  doi: 10.1108/JM2-10-2016-0089.  Google Scholar

[29]

S. Saha, N. M. Modak, S. Panda and S. S. Sana, Promotional coordination mechanisms with demand dependent on price and sales efforts, J. Industrial Prod. Engrg., 36 (2019), 13-31.  doi: 10.1080/21681015.2019.1565451.  Google Scholar

[30]

S. S. Sana, J. Ferro-Correa, A. Quintero and R. Amaya, A system dynamics model of financial flow in supply chains: A case study, RAIRO Oper. Res., 52 (2018), 187-204.  doi: 10.1051/ro/2017025.  Google Scholar

[31]

R. C. Savaskan, S. Bhattacharya and L. N. Van Wassenhove, Closed-loop supply chain models with product remanufacturing, Manag. Science, 50 (2004), 239-252.  doi: 10.1287/mnsc.1030.0186.  Google Scholar

[32]

R. C. Savaskan and L. N. Van Wassenhove, Reverse channel design: The case of competing retailers, Manag. Science, 52 (2006), 1-14.  doi: 10.1287/mnsc.1050.0454.  Google Scholar

[33]

J. Shi, G. Zhang and J. Sha, Optimal production and pricing policy for a closed loop system, Resources Conservation Recycling, 55 (2011), 639-647.  doi: 10.1016/j.resconrec.2010.05.016.  Google Scholar

[34]

S. Tiwari, C. K. Jaggi and S. S. Sana, Integrated supply chain of supplier and retailer for stochastic demand, Math. Model. Anal., 23 (2018), 582-595.  doi: 10.3846/mma.2018.035.  Google Scholar

[35]

A. A. Taleizadeh, M. S. Moshtagh and I. Moon, Pricing, product quality, and collection optimization in a decentralized closed-loop supply chain with different channel structures: Game theoretical approach, J. Cleaner Prod., 189 (2018), 406-431.  doi: 10.1016/j.jclepro.2018.02.209.  Google Scholar

[36]

R. H. Teunter, Determining optimal disassembly and recovery strategies, Omega, 34 (2006), 533-537.  doi: 10.1016/j.omega.2005.01.014.  Google Scholar

[37]

M. Thierry, M. Salomon and N. L. V. Wassenhove, Strategies issues in product recovery management, California Manag. Review, 37 (1995), 114-135.  doi: 10.2307/41165792.  Google Scholar

[38]

A. A. Tsay and N. Agrawal, Channel dynamics under price and service competition, Manufacturing and Service Oper. Manag., 2 (2000), 93-110.  doi: 10.1287/msom.2.4.372.12342.  Google Scholar

[39]

J. Vorasayan and S. M. Ryan, Optimal price and quantity of refurbished products, Prod. Oper. Manag., 15 (2006), 369-383.  doi: 10.1111/j.1937-5956.2006.tb00251.x.  Google Scholar

[40]

Z. Wang, B. Zhang, J. Yin and X. Zhang, Willingness and behavior towards e-waste recycling for residents in Beijing city, China, J. Cleaner Prod., 19 (2011), 977-984.  doi: 10.1016/j.jclepro.2010.09.016.  Google Scholar

[41]

W. Wang, Y. Zhang, K. Zhang, T. Bai and J. Shang, Reward-penalty mechanism for closed-loop supply chains under responsibility-sharing and different power structures, Internat. J. Prod. Econ., 170 (2015), 178-190.  doi: 10.1016/j.ijpe.2015.09.003.  Google Scholar

[42]

D.-Q. Yao and J. J. Liu, Competitive pricing of mixed retail and e-tail distribution channels, OMEGA, 33 (2005), 235-247.  doi: 10.1016/j.omega.2004.04.007.  Google Scholar

show all references

References:
[1]

E. Almehdawe and B. Matin, Vendor managed inventory with a capacitated manufacturer and multiple retailer: Retailer versus manufacturer leadership, Internat. J. Prod. Econ., 128 (2010), 292-302.  doi: 10.1016/j.ijpe.2010.07.029.  Google Scholar

[2]

A. Atasu, V. D. R. Guide and L. N. Van Wassenhove, Product reuse economics in closed-loop supply chain research, Prod. Oper. Manag., 17 (2010), 483-496.  doi: 10.3401/poms.1080.0051.  Google Scholar

[3]

A. Atasu, L. 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

[4]

M. Bhattacharyya and S. S. Sana, A mathematical model on eco-friendly manufacturing system under probabilistic demand, RAIRO Oper. Res., 53 (2019), 1899-1913.  doi: 10.1051/ro/2018120.  Google Scholar

[5]

G. P. Cachon and A. G. Kök, Competing manufacturers in a retail supply chain: On contractual form and coordination, Manag. Sci., 56 (2010), 571-589.  doi: 10.1287/mnsc.1090.1122.  Google Scholar

[6]

J.-M. Chen and C.-I. Chang, The co-operative strategy of a closed-loop supply chain with remanufacturing, Transpor. Res. Part E, 48 (2012), 387-400.  doi: 10.1016/j.tre.2011.10.001.  Google Scholar

[7]

T.-M. Choi, Y. Li and L. Xu, Channel leadership, performance and coordination in closed loop supply chains, Internat. J. Prod. Econ., 146 (2013), 371-380.  doi: 10.1016/j.ijpe.2013.08.002.  Google Scholar

[8]

C.-H. Chuang, C. X. Wang and Y. Zhao, Closed-loop supply chain models for a high-tech product under alternative reverse channel and collection cost structures, Internat. J. Prod. Econ., 156 (2014), 108-123.  doi: 10.1016/j.ijpe.2014.05.008.  Google Scholar

[9]

P. De 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.  Google Scholar

[10]

V. D. R. Guide and L. N. Van Wassenhove, The evolution of closed-loop supply chain research, Oper. Res., 57 (2009), 10-18.   Google Scholar

[11]

G. Ertek and P. M. Griffin, Supplier-and buyer-driven channels in a two-stage supply chain, IIE Transactions, 34 (2002), 691-700.  doi: 10.1023/A:1014920510164.  Google Scholar

[12]

L. Feng, K. Govindan and C. Li, Strategic planning: Design and coordination for dual-recycling channel reverse supply chain considering consumer behavior, European J. Oper. Res., 260 (2017), 601-612.  doi: 10.1016/j.ejor.2016.12.050.  Google Scholar

[13]

H. Garg, Fuzzy inventory models for deteriorating items under different types of lead-time distributions, in Intelligent Techniques in Engineering Management, Intelligent Systems Reference Library, 87, Springer, Cham, 2015,247–274. doi: 10.1007/978-3-319-17906-3_11.  Google Scholar

[14]

V. D. R. Guide, R. H. Teunter and L. N. Van Wassenhove, Matching demand and supply to maximize profits from remanufacturing, Manufac. Service Oper. Manag., 5 (2003), 303-316.  doi: 10.1287/msom.5.4.303.24883.  Google Scholar

[15]

X. Hong, Z. Wang and H. Zhang, Decision models of closed-loop supply chain with remanufacturing under hybrid dual-channel collection, Internat. J. Advanced Manufac. Tech., 68 (2013), 1851-1865.  doi: 10.1007/s00170-013-4982-1.  Google Scholar

[16]

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

[17]

A. P. Jeuland and S. M. Shugan, Managing channel profits, Marketing Science, 2 (1983), 239-272.  doi: 10.1287/mksc.2.3.239.  Google Scholar

[18]

I. Karakayali, H. Emir-Farinas and E. Akcal, An analysis of decentralized collection and processing of end-of-life products, J. Oper. Manag., 25 (2007), 1161-1183.  doi: 10.1016/j.jom.2007.01.017.  Google Scholar

[19]

Y. Liang, S. Pokharel and G. H. Lim, Pricing used products for remanufacturing, European J. Oper. Res., 193 (2009), 390-395.  doi: 10.1016/j.ejor.2007.11.029.  Google Scholar

[20]

H. Liu, M. Lei, H. Deng, G. K. 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

[21]

P. Majumder and A. Srinivasan, Leadership and competition in network supply chains, Manag. Science, 54 (2008), 1189-1204.  doi: 10.1287/mnsc.1070.0752.  Google Scholar

[22]

T. W. McGuire and R. Staelin, An industry equilibrium analysis of downstream vertical integration, Marketing Science, 2 (1983), 161-190.  doi: 10.1287/mksc.2.2.161.  Google Scholar

[23]

P. R. Messinger and C. Narasimhan, Has power shifted in the grocery channel?, Marketing Science, 14 (1995), 189-223.   Google Scholar

[24]

S. Mitra, Revenue management for remanufactured products, Omega, 35 (2007), 553-562.  doi: 10.1016/j.omega.2005.10.003.  Google Scholar

[25]

S. K. Mukhopadhyay, D.-Q. Yao and X. Yue, Information sharing of value-adding retailer in a mixed channel hi-tech supply chain, J. Business Res., 61 (2008), 950-958.  doi: 10.1016/j.jbusres.2006.10.027.  Google Scholar

[26]

I. E. Nielsen, S. Majumder, S. S. Sana and S. Saha, Comparative analysis of government incentives and game structures on single and two-period green supply chain, J. Cleaner Prod., 235 (2019), 1371-1398.  doi: 10.1016/j.jclepro.2019.06.168.  Google Scholar

[27]

A. Örsdemir, E. Kemahlioğlu-Ziya and A. K. Parlaktürk, Competitive quality choice and remanufacturing, Prod. and Oper. Manag., 23 (2014), 48-64.  doi: 10.1111/poms.12040.  Google Scholar

[28]

S. Saha, N. M. Modak, S. Panda and S. S. Sana, Managing a retailer's dual-channel supply chain under price- and delivery time-sensitive demand, J. Modelling Manag., 13 (2018), 351-374.  doi: 10.1108/JM2-10-2016-0089.  Google Scholar

[29]

S. Saha, N. M. Modak, S. Panda and S. S. Sana, Promotional coordination mechanisms with demand dependent on price and sales efforts, J. Industrial Prod. Engrg., 36 (2019), 13-31.  doi: 10.1080/21681015.2019.1565451.  Google Scholar

[30]

S. S. Sana, J. Ferro-Correa, A. Quintero and R. Amaya, A system dynamics model of financial flow in supply chains: A case study, RAIRO Oper. Res., 52 (2018), 187-204.  doi: 10.1051/ro/2017025.  Google Scholar

[31]

R. C. Savaskan, S. Bhattacharya and L. N. Van Wassenhove, Closed-loop supply chain models with product remanufacturing, Manag. Science, 50 (2004), 239-252.  doi: 10.1287/mnsc.1030.0186.  Google Scholar

[32]

R. C. Savaskan and L. N. Van Wassenhove, Reverse channel design: The case of competing retailers, Manag. Science, 52 (2006), 1-14.  doi: 10.1287/mnsc.1050.0454.  Google Scholar

[33]

J. Shi, G. Zhang and J. Sha, Optimal production and pricing policy for a closed loop system, Resources Conservation Recycling, 55 (2011), 639-647.  doi: 10.1016/j.resconrec.2010.05.016.  Google Scholar

[34]

S. Tiwari, C. K. Jaggi and S. S. Sana, Integrated supply chain of supplier and retailer for stochastic demand, Math. Model. Anal., 23 (2018), 582-595.  doi: 10.3846/mma.2018.035.  Google Scholar

[35]

A. A. Taleizadeh, M. S. Moshtagh and I. Moon, Pricing, product quality, and collection optimization in a decentralized closed-loop supply chain with different channel structures: Game theoretical approach, J. Cleaner Prod., 189 (2018), 406-431.  doi: 10.1016/j.jclepro.2018.02.209.  Google Scholar

[36]

R. H. Teunter, Determining optimal disassembly and recovery strategies, Omega, 34 (2006), 533-537.  doi: 10.1016/j.omega.2005.01.014.  Google Scholar

[37]

M. Thierry, M. Salomon and N. L. V. Wassenhove, Strategies issues in product recovery management, California Manag. Review, 37 (1995), 114-135.  doi: 10.2307/41165792.  Google Scholar

[38]

A. A. Tsay and N. Agrawal, Channel dynamics under price and service competition, Manufacturing and Service Oper. Manag., 2 (2000), 93-110.  doi: 10.1287/msom.2.4.372.12342.  Google Scholar

[39]

J. Vorasayan and S. M. Ryan, Optimal price and quantity of refurbished products, Prod. Oper. Manag., 15 (2006), 369-383.  doi: 10.1111/j.1937-5956.2006.tb00251.x.  Google Scholar

[40]

Z. Wang, B. Zhang, J. Yin and X. Zhang, Willingness and behavior towards e-waste recycling for residents in Beijing city, China, J. Cleaner Prod., 19 (2011), 977-984.  doi: 10.1016/j.jclepro.2010.09.016.  Google Scholar

[41]

W. Wang, Y. Zhang, K. Zhang, T. Bai and J. Shang, Reward-penalty mechanism for closed-loop supply chains under responsibility-sharing and different power structures, Internat. J. Prod. Econ., 170 (2015), 178-190.  doi: 10.1016/j.ijpe.2015.09.003.  Google Scholar

[42]

D.-Q. Yao and J. J. Liu, Competitive pricing of mixed retail and e-tail distribution channels, OMEGA, 33 (2005), 235-247.  doi: 10.1016/j.omega.2004.04.007.  Google Scholar

Figure 1.  The manufacturer's tradeoff between the channel leadership and the recycling channel
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 2.  The retailer's tradeoff between the channel leadership and the recycling channel
Figure Options

Download full-size image

Download as PowerPoint slide

Table 1.  Notations
Symbol Description
Parameters
$c_{m}$ Unit producing cost from original materials
$c_{0}$ Unit producing cost from returns
$\delta$ Unit saving cost by recovery, $\delta=c_{m}-c_{0}$
$A$ The size of the market
$\alpha$ Sensitivity of the consumers for the retail price, $\alpha>0$
$k$ The basic recovery quantity, which represents the level of
environmental awareness of consumers
$h$ Sensitivity of the customers for the recycling price, $h>0$
Decision variables
$p$ The unit retail price
$w$ The unit wholesale price
$b$ The unit recycling price in centralized decision system
$b_{j}$ The unit recycling price of the recycling party $j$, subscript
$j=t, r, m$ denotes the recycling by the third-party, the
retailer and the manufacturer, respectively
$b_{mj}$ The unit transfer price, $j=r, t$, denotes R-channel and
T-channel, respectively
Derived function
$D(p)$ The demand of the products
$R(b_{j})$ The amount of the recycling products
$\pi_{m}$ The profits of the manufacturer
$\pi_{r}$ The profits of the retailer
$\pi_{t}$ The profits of the third-party
$\Pi$ The profits of the system
Table Options

Download as excel

Symbol Description
Parameters
$c_{m}$ Unit producing cost from original materials
$c_{0}$ Unit producing cost from returns
$\delta$ Unit saving cost by recovery, $\delta=c_{m}-c_{0}$
$A$ The size of the market
$\alpha$ Sensitivity of the consumers for the retail price, $\alpha>0$
$k$ The basic recovery quantity, which represents the level of
environmental awareness of consumers
$h$ Sensitivity of the customers for the recycling price, $h>0$
Decision variables
$p$ The unit retail price
$w$ The unit wholesale price
$b$ The unit recycling price in centralized decision system
$b_{j}$ The unit recycling price of the recycling party $j$, subscript
$j=t, r, m$ denotes the recycling by the third-party, the
retailer and the manufacturer, respectively
$b_{mj}$ The unit transfer price, $j=r, t$, denotes R-channel and
T-channel, respectively
Derived function
$D(p)$ The demand of the products
$R(b_{j})$ The amount of the recycling products
$\pi_{m}$ The profits of the manufacturer
$\pi_{r}$ The profits of the retailer
$\pi_{t}$ The profits of the third-party
$\Pi$ The profits of the system
Table 2.  Main results of the M-led models
Model MM Model MR Model MT
$p^*$ $p^{MM*}=\frac{3A+\alpha c_m}{4\alpha}$ $p^{MR*}=\frac{3A+\alpha c_m}{4\alpha}$ $p^{MT*}=\frac{3A+\alpha c_m}{4\alpha}$
$b^*_i$ $b^{MM*}_m=\frac{h\delta -k}{2h}$ $b^{MR*}_r=\frac{h\delta -3k}{4h}$ $b^{MT*}_t=\frac{h\delta -3k}{4h}$
$w^*$ $w^{MM*}=\frac{A+\alpha c_m}{2\alpha}$ $w^{MR*}=\frac{A+\alpha c_m}{2\alpha}$ $w^{MT*}=\frac{A+\alpha c_m}{2\alpha}$
$b^*_{mj}$ N/A $b^{MR*}_{mr}=\frac{h\delta -k}{2h}$ $b^{MT*}_{mt}=\frac{h\delta -k}{2h}$
$\pi^*_m$ $\pi^{MM*}_m=\frac{P_f}{2}+P_r$ $\pi^{MR*}_m=\frac{P_f+P_r}{2}$ $\pi^{MT*}_m=\frac{P_f}{2}+\frac{P_r}{2}$
$\pi^*_r$ $\pi^{MM*}_r=\frac{P_f}{4}$ $\pi^{MR*}_r=\frac{P_f+P_r}{4}$ $\pi^{MT*}_r=\frac{P_f}{4}$
$\pi^*_t$ N/A N/A $\pi^{MT*}_t=\frac{P_r}{4}$
$\Pi^*$ $\Pi^{MM*}=\frac{3P_f}{4}+P_r$ $\Pi^{MR*}=\frac{3(P_f+P_r)}{4}$ $\Pi^{MT*}=\frac{3(P_f+P_r)}{4}$
Table Options

Download as excel

Model MM Model MR Model MT
$p^*$ $p^{MM*}=\frac{3A+\alpha c_m}{4\alpha}$ $p^{MR*}=\frac{3A+\alpha c_m}{4\alpha}$ $p^{MT*}=\frac{3A+\alpha c_m}{4\alpha}$
$b^*_i$ $b^{MM*}_m=\frac{h\delta -k}{2h}$ $b^{MR*}_r=\frac{h\delta -3k}{4h}$ $b^{MT*}_t=\frac{h\delta -3k}{4h}$
$w^*$ $w^{MM*}=\frac{A+\alpha c_m}{2\alpha}$ $w^{MR*}=\frac{A+\alpha c_m}{2\alpha}$ $w^{MT*}=\frac{A+\alpha c_m}{2\alpha}$
$b^*_{mj}$ N/A $b^{MR*}_{mr}=\frac{h\delta -k}{2h}$ $b^{MT*}_{mt}=\frac{h\delta -k}{2h}$
$\pi^*_m$ $\pi^{MM*}_m=\frac{P_f}{2}+P_r$ $\pi^{MR*}_m=\frac{P_f+P_r}{2}$ $\pi^{MT*}_m=\frac{P_f}{2}+\frac{P_r}{2}$
$\pi^*_r$ $\pi^{MM*}_r=\frac{P_f}{4}$ $\pi^{MR*}_r=\frac{P_f+P_r}{4}$ $\pi^{MT*}_r=\frac{P_f}{4}$
$\pi^*_t$ N/A N/A $\pi^{MT*}_t=\frac{P_r}{4}$
$\Pi^*$ $\Pi^{MM*}=\frac{3P_f}{4}+P_r$ $\Pi^{MR*}=\frac{3(P_f+P_r)}{4}$ $\Pi^{MT*}=\frac{3(P_f+P_r)}{4}$
Table 3.  Main results of the R-led models
Model RM Model RR Model RT
$p^*$ $p^{RM*}=\frac{3A+\alpha c_m}{4\alpha}$ $p^{RR*}=\frac{3A+\alpha c_m}{4\alpha}$ $p^{RT*}=\frac{3A+\alpha c_m}{4\alpha}$
$b^*_i$ $b^{RM*}_m=\frac{h\delta -k}{2h}$ $b^{RR*}_r=\frac{h\delta -3k}{4h}$ $b^{RT*}_t=\frac{h\delta -3k}{4h}$
$w^*$ $w^{RM*}=\frac{A+3\alpha c_m}{4\alpha}$ $w^{RR*}=\frac{A+3\alpha c_m}{4\alpha}$ $w^{RT*}=\frac{A+3\alpha c_m}{4\alpha}$
$b^*_{mj}$ N/A $b^{RR*}_{mr}=\frac{3h\delta -k}{4h}$ $b^{RT*}_{mt}=\frac{h\delta -k}{2h}$
$\pi^*_m$ $\pi^{RM*}_m=\frac{P_f}{4}+P_r$ $\pi^{RR*}_m=\frac{P_f+P_r}{4}$ $\pi^{RT*}_m=\frac{P_f}{4}+\frac{P_r}{2}$
$\pi^*_r$ $\pi^{RM*}_r=\frac{P_f}{2}$ $\pi^{RR*}_r=\frac{P_f+P_r}{2}$ $\pi^{RT*}_r=\frac{P_f}{2}$
$\pi^*_t$ N/A N/A $\pi^{RT*}_t=\frac{P_r}{4}$
$\Pi^*$ $\Pi^{RM*}=\frac{3P_f}{4}+P_r$ $\Pi^{RR*}=\frac{3(P_f+P_r)}{4}$ $\Pi^{RT*}=\frac{3(P_f+P_r)}{4}$
Table Options

Download as excel

Model RM Model RR Model RT
$p^*$ $p^{RM*}=\frac{3A+\alpha c_m}{4\alpha}$ $p^{RR*}=\frac{3A+\alpha c_m}{4\alpha}$ $p^{RT*}=\frac{3A+\alpha c_m}{4\alpha}$
$b^*_i$ $b^{RM*}_m=\frac{h\delta -k}{2h}$ $b^{RR*}_r=\frac{h\delta -3k}{4h}$ $b^{RT*}_t=\frac{h\delta -3k}{4h}$
$w^*$ $w^{RM*}=\frac{A+3\alpha c_m}{4\alpha}$ $w^{RR*}=\frac{A+3\alpha c_m}{4\alpha}$ $w^{RT*}=\frac{A+3\alpha c_m}{4\alpha}$
$b^*_{mj}$ N/A $b^{RR*}_{mr}=\frac{3h\delta -k}{4h}$ $b^{RT*}_{mt}=\frac{h\delta -k}{2h}$
$\pi^*_m$ $\pi^{RM*}_m=\frac{P_f}{4}+P_r$ $\pi^{RR*}_m=\frac{P_f+P_r}{4}$ $\pi^{RT*}_m=\frac{P_f}{4}+\frac{P_r}{2}$
$\pi^*_r$ $\pi^{RM*}_r=\frac{P_f}{2}$ $\pi^{RR*}_r=\frac{P_f+P_r}{2}$ $\pi^{RT*}_r=\frac{P_f}{2}$
$\pi^*_t$ N/A N/A $\pi^{RT*}_t=\frac{P_r}{4}$
$\Pi^*$ $\Pi^{RM*}=\frac{3P_f}{4}+P_r$ $\Pi^{RR*}=\frac{3(P_f+P_r)}{4}$ $\Pi^{RT*}=\frac{3(P_f+P_r)}{4}$
[1]

Xiao-Xu Chen, Peng Xu, Jiao-Jiao Li, Thomas Walker, Guo-Qiang Yang. Decision-making in a retailer-led closed-loop supply chain involving a third-party logistics provider. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2021014
[2]

Xi Zhao, Teng Niu. Impacts of horizontal mergers on dual-channel supply chain. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020173
[3]

Zonghong Cao, Jie Min. Selection and impact of decision mode of encroachment and retail service in a dual-channel supply chain. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020167
[4]

Hongxia Sun, Yao Wan, Yu Li, Linlin Zhang, Zhen Zhou. Competition in a dual-channel supply chain considering duopolistic retailers with different behaviours. Journal of Industrial & Management Optimization, 2021, 17 (2) : 601-631. doi: 10.3934/jimo.2019125
[5]

Simon Hochgerner. Symmetry actuated closed-loop Hamiltonian systems. Journal of Geometric Mechanics, 2020, 12 (4) : 641-669. doi: 10.3934/jgm.2020030
[6]

Sushil Kumar Dey, Bibhas C. Giri. Coordination of a sustainable reverse supply chain with revenue sharing contract. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020165
[7]

Jingrui Sun, Hanxiao Wang. Mean-field stochastic linear-quadratic optimal control problems: Weak closed-loop solvability. Mathematical Control & Related Fields, 2021, 11 (1) : 47-71. doi: 10.3934/mcrf.2020026
[8]

Wei Chen, Yongkai Ma, Weihao Hu. Electricity supply chain coordination with carbon abatement technology investment under the benchmarking mechanism. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020175
[9]

Linfeng Mei, Feng-Bin Wang. Dynamics of phytoplankton species competition for light and nutrient with recycling in a water column. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020359
[10]

Honglin Yang, Jiawu Peng. Coordinating a supply chain with demand information updating. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020181
[11]

Wenyan Zhuo, Honglin Yang, Leopoldo Eduardo Cárdenas-Barrón, Hong Wan. Loss-averse supply chain decisions with a capital constrained retailer. Journal of Industrial & Management Optimization, 2021, 17 (2) : 711-732. doi: 10.3934/jimo.2019131
[12]

Feimin Zhong, Jinxing Xie, Yuwei Shen. Bargaining in a multi-echelon supply chain with power structure: KS solution vs. Nash solution. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020172
[13]

Puneet Pasricha, Anubha Goel. Pricing power exchange options with hawkes jump diffusion processes. Journal of Industrial & Management Optimization, 2021, 17 (1) : 133-149. doi: 10.3934/jimo.2019103
[14]

Editorial Office. Retraction: Xiao-Qian Jiang and Lun-Chuan Zhang, Stock price fluctuation prediction method based on time series analysis. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 915-915. doi: 10.3934/dcdss.2019061
[15]

Musen Xue, Guowei Zhu. Partial myopia vs. forward-looking behaviors in a dynamic pricing and replenishment model for perishable items. Journal of Industrial & Management Optimization, 2021, 17 (2) : 633-648. doi: 10.3934/jimo.2019126
[16]

Jiannan Zhang, Ping Chen, Zhuo Jin, Shuanming Li. Open-loop equilibrium strategy for mean-variance portfolio selection: A log-return model. Journal of Industrial & Management Optimization, 2021, 17 (2) : 765-777. doi: 10.3934/jimo.2019133
[17]

Mahir Demir, Suzanne Lenhart. A spatial food chain model for the Black Sea Anchovy, and its optimal fishery. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 155-171. doi: 10.3934/dcdsb.2020373
[18]

Editorial Office. Retraction: Xiao-Qian Jiang and Lun-Chuan Zhang, A pricing option approach based on backward stochastic differential equation theory. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 969-969. doi: 10.3934/dcdss.2019065
[19]

Lei Liu, Li Wu. Multiplicity of closed characteristics on $ P $-symmetric compact convex hypersurfaces in $ \mathbb{R}^{2n} $. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020378

2019 Impact Factor: 1.366

Tools

Article outline

Figures and Tables

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences