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Closed-loop supply chain network equilibrium model with retailer-collection under legislation
1. | School of Management, China University of Mining and Technology, Xuzhou 221116, China |
2. | College of Engineering, Nanjing Agricultural University, Nanjing 210031, China |
3. | School of Business, Qingdao University, Qingdao 266071, China |
This paper examines the waste of electrical and electronic equipments (WEEE) and draws on variational inequalities to model the closed-loop supply chain network. The network consists of manufacturers, retailers and consumer markets engaging in a Cournot-Nash game. Retailers are responsible for collecting WEEE in the network. It is assumed that the price of the remanufactured goods is different from that of the newly manufactured ones. The network equilibrium occurs when all players agree on volumes and prices. Several properties of the model are examined and the modified projection method is utilized to obtain the optimal solutions. Numerical examples are provided to illustrate the impact of CLSC parameters on the profits of channel members and consumer benefits, and to provide policy support for governments. We find that it is necessary to regulate a medium collection rate and a certain minimum recovery rate. This is also advantageous to manufacturers in producing new manufactured products. The impact of collection rate and recovery rate on manufacturers are greater than that on retailers. Consumers can benefit from the increase of the recovery rate as well as the collection rate.
References:
[1] |
P. Calcott and M. Walls,
Waste, recycling, and Design for Environment: Roles for markets and policy instruments, Resource and Energy Economics, 27 (2005), 287-305.
doi: 10.1016/j.reseneeco.2005.02.001. |
[2] |
S. C. Choi,
Price competition in a channel structure with a common retailer, Marketing Science, 10 (1991), 271-296.
doi: 10.1287/mksc.10.4.271. |
[3] |
S. C. Choi,
Price competition in a duopoly common retailer channel, Journal of Retailing, 72 (1996), 117-134.
doi: 10.1016/S0022-4359(96)90010-X. |
[4] |
J. M. Cruz,
Dynamics of supply chain networks with corporate social responsibility through integrated environmental decision-making, European Journal of Operational Research, 184 (2008), 1005-1031.
doi: 10.1016/j.ejor.2006.12.012. |
[5] |
P. Georgiadis and D. Vlachos,
The effect of environmental parameters on product recovery, European Journal of Operational Research, 157 (2004), 449-464.
doi: 10.1016/S0377-2217(03)00203-0. |
[6] |
K. Govindan, H. Soleimani and D. Kannan,
Reverse logistics and closed-loop supply chain: A comprehensive review to explore the future, European Journal of Operational Research, 240 (2015), 603-626.
doi: 10.1016/j.ejor.2014.07.012. |
[7] |
V. D. R. Guide, T. P. Harrison and L. N. Van Wassenhove,
The challenge of closed-loop supply chains, Interfaces, 33 (2003), 3-6.
|
[8] |
Y. Hamdouch, Q. P. Qiang and K. Ghoudi,
A closed-loop supply chain equilibrium model with random and price-sensitive demand and return, Networks and Spatial Economics, 17 (2017), 459-503.
|
[9] |
D. Hammond and P. Beullens,
Closed-loop supply chain network equilibrium under legislation, European Journal of Operational Research, 183 (2007), 895-908.
doi: 10.1016/j.ejor.2006.10.033. |
[10] |
Y. Hotta, C. Visvanathan and M. Kojima,
Recycling rate and target setting: challenges for standardized measurement, Journal of Material Cycles and Waste Management, 18 (2016), 14-21.
doi: 10.1007/s10163-015-0361-3. |
[11] |
A. Nagurney, Network Economics: A Variational Inequality Approach, Kluwer Academic Publishers, 1993. |
[12] |
A. Nagurney, Supply Chain Network Economics: Dynamics of prices flows and profits, Edward Elgar Publishing Limited, 2006. |
[13] |
A. Nagurney, J. Dong and D. Zhang,
A supply chain network equilibrium model, Transportation Research Part E, 38 (2002), 281-303.
doi: 10.1016/S1366-5545(01)00020-5. |
[14] |
A. Nagurney and F. Toyasaki,
Reserve supply chain management and electronic waste recycling: A multitiered network equilibrium framework for e-cycling, Transportation Research Part E, 41 (2005), 1-28.
|
[15] |
A. Nagurney and F. Toyasaki,
Supply chain supernetworks and environmental criteria, Transportation Research Part D, 8 (2003), 185-213.
doi: 10.1016/S1361-9209(02)00049-4. |
[16] |
V. Padmanabhan and I. P. L. Png,
Manufacturer's returns policies and retail competition, Marketing Science, 16 (1997), 81-94.
|
[17] |
Q. P. Qiang,
The closed-loop supply chain network with competition and design for remanufactureability, Journal of Cleaner Production, 105 (2015), 348-356.
doi: 10.1016/j.jclepro.2014.07.005. |
[18] |
Q. Qiang, K. Ke, T. Anderson and J. Dong,
The closed-loop supply chain network with competition, distribution channel investment, and uncertainties, Omega, 41 (2013), 186-194.
doi: 10.1016/j.omega.2011.08.011. |
[19] |
S. Salhofer, B. Steuer, R. Ramusch and P. Beigl,
WEEE management in Europe and China--A comparison, Waste Management, 57 (2016), 27-35.
|
[20] |
R. C. Savaskan and L. N. Van Wassenhove,
Reverse Channel Design: The case of competing retailers, Management Science, 52 (2006), 1-14.
|
[21] |
R. C. Savaskan, S. Bhattacharya and L. N. Van Wassenhove,
Closed-Loop supply chain models with product remanufacturing, Management Science, 50 (2004), 239-252.
|
[22] |
F. Schultmann, M. Zumkeller and O. Rentz,
Modeling reverse logistic tasks within closed-loop supply chains: An example from the automotive industry, European Journal of Operational Research, 171 (2006), 1033-1050.
|
[23] |
G. C. Souza,
Closed-loop supply chains: A critical review, and future research, Decision Sciences, 44 (2013), 7-38.
doi: 10.1111/j.1540-5915.2012.00394.x. |
[24] |
L. Wang and M. Chen,
Policies and perspective on end-of-life vehicles in China, Journal of Cleaner Production, 44 (2013), 168-176.
doi: 10.1016/j.jclepro.2012.11.036. |
[25] |
S. Webster and S. Mitra,
Competitive strategy in remanufacturing and the impact of take-back laws, Journal of Operations Management, 25 (2007), 1123-1140.
doi: 10.1016/j.jom.2007.01.014. |
[26] |
J. Wei, K. Govindan, Y. Li and J. Zhao,
Pricing and collecting decisions in a closed-loop supply chain with symmetric and asymmetric information, Computers and Operations Research, 54 (2015), 257-265.
doi: 10.1016/j.cor.2013.11.021. |
[27] |
G. Yang, Z. Wang and X. Li,
The optimization of the closed-loop supply chain network, Transportation Research Part E: Logistics and Transportation Review, 45 (2009), 16-28.
doi: 10.1016/j.tre.2008.02.007. |
[28] |
R. Zuidwijk and H. Krikke,
Strategic response to EEE returns: Product eco-design or new recovery processes, European Journal of Operational Research, 191 (2008), 1206-1222.
doi: 10.1016/j.ejor.2007.08.004. |
show all references
References:
[1] |
P. Calcott and M. Walls,
Waste, recycling, and Design for Environment: Roles for markets and policy instruments, Resource and Energy Economics, 27 (2005), 287-305.
doi: 10.1016/j.reseneeco.2005.02.001. |
[2] |
S. C. Choi,
Price competition in a channel structure with a common retailer, Marketing Science, 10 (1991), 271-296.
doi: 10.1287/mksc.10.4.271. |
[3] |
S. C. Choi,
Price competition in a duopoly common retailer channel, Journal of Retailing, 72 (1996), 117-134.
doi: 10.1016/S0022-4359(96)90010-X. |
[4] |
J. M. Cruz,
Dynamics of supply chain networks with corporate social responsibility through integrated environmental decision-making, European Journal of Operational Research, 184 (2008), 1005-1031.
doi: 10.1016/j.ejor.2006.12.012. |
[5] |
P. Georgiadis and D. Vlachos,
The effect of environmental parameters on product recovery, European Journal of Operational Research, 157 (2004), 449-464.
doi: 10.1016/S0377-2217(03)00203-0. |
[6] |
K. Govindan, H. Soleimani and D. Kannan,
Reverse logistics and closed-loop supply chain: A comprehensive review to explore the future, European Journal of Operational Research, 240 (2015), 603-626.
doi: 10.1016/j.ejor.2014.07.012. |
[7] |
V. D. R. Guide, T. P. Harrison and L. N. Van Wassenhove,
The challenge of closed-loop supply chains, Interfaces, 33 (2003), 3-6.
|
[8] |
Y. Hamdouch, Q. P. Qiang and K. Ghoudi,
A closed-loop supply chain equilibrium model with random and price-sensitive demand and return, Networks and Spatial Economics, 17 (2017), 459-503.
|
[9] |
D. Hammond and P. Beullens,
Closed-loop supply chain network equilibrium under legislation, European Journal of Operational Research, 183 (2007), 895-908.
doi: 10.1016/j.ejor.2006.10.033. |
[10] |
Y. Hotta, C. Visvanathan and M. Kojima,
Recycling rate and target setting: challenges for standardized measurement, Journal of Material Cycles and Waste Management, 18 (2016), 14-21.
doi: 10.1007/s10163-015-0361-3. |
[11] |
A. Nagurney, Network Economics: A Variational Inequality Approach, Kluwer Academic Publishers, 1993. |
[12] |
A. Nagurney, Supply Chain Network Economics: Dynamics of prices flows and profits, Edward Elgar Publishing Limited, 2006. |
[13] |
A. Nagurney, J. Dong and D. Zhang,
A supply chain network equilibrium model, Transportation Research Part E, 38 (2002), 281-303.
doi: 10.1016/S1366-5545(01)00020-5. |
[14] |
A. Nagurney and F. Toyasaki,
Reserve supply chain management and electronic waste recycling: A multitiered network equilibrium framework for e-cycling, Transportation Research Part E, 41 (2005), 1-28.
|
[15] |
A. Nagurney and F. Toyasaki,
Supply chain supernetworks and environmental criteria, Transportation Research Part D, 8 (2003), 185-213.
doi: 10.1016/S1361-9209(02)00049-4. |
[16] |
V. Padmanabhan and I. P. L. Png,
Manufacturer's returns policies and retail competition, Marketing Science, 16 (1997), 81-94.
|
[17] |
Q. P. Qiang,
The closed-loop supply chain network with competition and design for remanufactureability, Journal of Cleaner Production, 105 (2015), 348-356.
doi: 10.1016/j.jclepro.2014.07.005. |
[18] |
Q. Qiang, K. Ke, T. Anderson and J. Dong,
The closed-loop supply chain network with competition, distribution channel investment, and uncertainties, Omega, 41 (2013), 186-194.
doi: 10.1016/j.omega.2011.08.011. |
[19] |
S. Salhofer, B. Steuer, R. Ramusch and P. Beigl,
WEEE management in Europe and China--A comparison, Waste Management, 57 (2016), 27-35.
|
[20] |
R. C. Savaskan and L. N. Van Wassenhove,
Reverse Channel Design: The case of competing retailers, Management Science, 52 (2006), 1-14.
|
[21] |
R. C. Savaskan, S. Bhattacharya and L. N. Van Wassenhove,
Closed-Loop supply chain models with product remanufacturing, Management Science, 50 (2004), 239-252.
|
[22] |
F. Schultmann, M. Zumkeller and O. Rentz,
Modeling reverse logistic tasks within closed-loop supply chains: An example from the automotive industry, European Journal of Operational Research, 171 (2006), 1033-1050.
|
[23] |
G. C. Souza,
Closed-loop supply chains: A critical review, and future research, Decision Sciences, 44 (2013), 7-38.
doi: 10.1111/j.1540-5915.2012.00394.x. |
[24] |
L. Wang and M. Chen,
Policies and perspective on end-of-life vehicles in China, Journal of Cleaner Production, 44 (2013), 168-176.
doi: 10.1016/j.jclepro.2012.11.036. |
[25] |
S. Webster and S. Mitra,
Competitive strategy in remanufacturing and the impact of take-back laws, Journal of Operations Management, 25 (2007), 1123-1140.
doi: 10.1016/j.jom.2007.01.014. |
[26] |
J. Wei, K. Govindan, Y. Li and J. Zhao,
Pricing and collecting decisions in a closed-loop supply chain with symmetric and asymmetric information, Computers and Operations Research, 54 (2015), 257-265.
doi: 10.1016/j.cor.2013.11.021. |
[27] |
G. Yang, Z. Wang and X. Li,
The optimization of the closed-loop supply chain network, Transportation Research Part E: Logistics and Transportation Review, 45 (2009), 16-28.
doi: 10.1016/j.tre.2008.02.007. |
[28] |
R. Zuidwijk and H. Krikke,
Strategic response to EEE returns: Product eco-design or new recovery processes, European Journal of Operational Research, 191 (2008), 1206-1222.
doi: 10.1016/j.ejor.2007.08.004. |



352.8712 | 352.8712 | 358.2704 | 383.6992 | 414.7223 | 435.5493 | |
59.8369 | 59.8369 | 71.6460 | 98.1422 | 108.6234 | 106.8103 | |
384.0070 | 384.0070 | 376.6145 | 362.1067 | 359.6196 | 375.6179 | |
402.8527 | 402.8527 | 406.0255 | 421.8723 | 441.8835 | 456.1049 | |
39.8914 | 39.8914 | 47.7639 | 65.4282 | 72.4157 | 71.2072 | |
393.9832 | 393.9832 | 388.5579 | 378.4611 | 377.7207 | 390.6693 |
352.8712 | 352.8712 | 358.2704 | 383.6992 | 414.7223 | 435.5493 | |
59.8369 | 59.8369 | 71.6460 | 98.1422 | 108.6234 | 106.8103 | |
384.0070 | 384.0070 | 376.6145 | 362.1067 | 359.6196 | 375.6179 | |
402.8527 | 402.8527 | 406.0255 | 421.8723 | 441.8835 | 456.1049 | |
39.8914 | 39.8914 | 47.7639 | 65.4282 | 72.4157 | 71.2072 | |
393.9832 | 393.9832 | 388.5579 | 378.4611 | 377.7207 | 390.6693 |
422.8170 | 424.1308 | 427.8478 | 433.8971 | 435.5493 | |
91.0883 | 97.7935 | 103.2339 | 106.4136 | 106.8103 | |
424.1402 | 409.5847 | 394.2371 | 378.9959 | 375.6179 | |
450.0756 | 450.2139 | 451.9405 | 455.1846 | 456.1049 | |
60.7962 | 65.1957 | 68.8227 | 70.9424 | 71.2072 | |
427.1726 | 416.1012 | 404.5575 | 393.1814 | 390.6693 |
422.8170 | 424.1308 | 427.8478 | 433.8971 | 435.5493 | |
91.0883 | 97.7935 | 103.2339 | 106.4136 | 106.8103 | |
424.1402 | 409.5847 | 394.2371 | 378.9959 | 375.6179 | |
450.0756 | 450.2139 | 451.9405 | 455.1846 | 456.1049 | |
60.7962 | 65.1957 | 68.8227 | 70.9424 | 71.2072 | |
427.1726 | 416.1012 | 404.5575 | 393.1814 | 390.6693 |
Total profits | |||||
Manufactures | 13642.876 | 17247.346 | 15531.509 | 12759.803 | 10108.842 |
Retailers | 2995.498 | 2993.549 | 2794.858 | 2376.378 | 1916.658 |
Total profits | |||||
Manufactures | 13642.876 | 17247.346 | 15531.509 | 12759.803 | 10108.842 |
Retailers | 2995.498 | 2993.549 | 2794.858 | 2376.378 | 1916.658 |
Total profits | |||||
Manufactures | 9082.426 | 9616.632 | 9981.219 | 10112.544 | 10108.842 |
Retailers | 1669.838 | 1785.409 | 1944.052 | 2113.821 | 1916.658 |
Total profits | |||||
Manufactures | 9082.426 | 9616.632 | 9981.219 | 10112.544 | 10108.842 |
Retailers | 1669.838 | 1785.409 | 1944.052 | 2113.821 | 1916.658 |
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