
-
Previous Article
Sparse markowitz portfolio selection by using stochastic linear complementarity approach
- JIMO Home
- This Issue
-
Next Article
An improved 2.11-competitive algorithm for online scheduling on parallel machines to minimize total weighted completion time
Integrated recycling-integrated production - distribution planning for decentralized closed-loop supply chain
1. | College of Management, Chongqing University of Technology, NO.69, Hongguang Road, Banan District, Chongqing 400054, China |
2. | School of Economics and Management, Nanchang Hangkong University, NO.696, Fenghenan Road, Honggutan District, Nanchang 330063, China |
Integrated integrated production - distribution planning in traditional forward supply chain has attracted a lot of attention in recent years and its economic advantages are particularly noticeable. However, for closed-loop supply chain, recycling and remanufacturing processes should be taken further into account to the integrated planning. In this paper, we address a planning problem of a multi - echelon decentralized closed-loop supply chain system, which consists of a joint recycling center, multiple manufacturing/remanufacturing factories and multiple distributors decentralized to different regions. For this problem, an integrated recycling-integrated production - distribution multi - level planning model is developed, which considers material flows and decision interactions among members at different echelons in the system, as well as their own operation objectives. And the local interests of members at every echelon would be balanced in order to coordinate the operation of the whole system. According to the characteristics of the planning model, the solution approach is designed by hierarchical iteration strategy based on Self-Adaptive Genetic Algorithm (SAGA). Hierarchical iteration processes, in which SAGA is used to solve every single level model, are corresponding to repeated negotiation behaviors among members at different echelons in closed-loop supply chain. Finally, a numerical example is suggested to demonstrate the applicability and effectiveness of the proposed model and solution approach.
References:
[1] |
R. A. Aliev, B. Fazlollahi and B. G. Guirimov,
Fuzzy-genetic approach to aggregate integrated production - distribution planning in supply chain management, Information Sciences, 177 (2007), 4241-4255.
doi: 10.1016/j.ins.2007.04.012. |
[2] |
S. M. J. M. Al-e-hachem, H. Malekly and M. B. Aryanezhad,
A multi - objective robust optimization model for multi - product multi - site aggregate production planning in a supply chain under uncertainty, International Journal of Production Economics, 134 (2011), 28-42.
|
[3] |
S. H. Amin and G. Q. Zhang,
A proposed mathematical model for closed-loop network configuration based on product life cycle, International Journal of Advanced Manufacturing Technology, 58 (2012), 791-801.
doi: 10.1007/s00170-011-3407-2. |
[4] |
P. Amorim, H. O. Günther and B. Almada-Lobo,
Multi-objective integrated production and distribution planning of perishable products, International Journal of Production Economics, 138 (2012), 89-101.
doi: 10.1016/j.ijpe.2012.03.005. |
[5] |
G. Barbarosolu,
Hierarchical design of an integrated production and 2-echelon distribution system, European Journal of Operational Research, 118 (1999), 464-484.
doi: 10.1016/S0377-2217(98)00317-8. |
[6] |
M. Boudia, M. A. O. Louly and C. Prins,
A reactive GRASP and path relinking for a combined integrated production - distribution problem, Computers & Operations Research, 34 (2007), 3402-3419.
doi: 10.1016/j.cor.2006.02.005. |
[7] |
H. I. Calvete, C. Galé and M. J. Oliveros,
Bilevel model for integrated production - distribution planning solved by using ant colony optimization, Computers & Operations Research, 38 (2011), 320-327.
doi: 10.1016/j.cor.2010.05.007. |
[8] |
F. T. S. Chan, S. H. Chung and S. Wadhwa,
A hybrid genetic algorithm for production and distribution, Omega, 33 (2005), 345-355.
doi: 10.1016/j.omega.2004.05.004. |
[9] |
K. Deb, A. Pratap and S. Agarwal,
A fast and elitist multiobjective genetic algorithm: NSGA-Ⅱ, IEEE Transactions on Evolutionary Computation, 6 (2002), 182-197.
doi: 10.1109/4235.996017. |
[10] |
G. W. Depuy, J. S. Usher and R. L. Walker,
Production planning for remanufactured products, Production Planning & Control, 18 (2007), 573-583.
doi: 10.1080/09537280701542210. |
[11] |
H. H. Doh and D. H. Lee,
Generic production planning model for remanufacturing systems, Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 224 (2010), 159-168.
doi: 10.1243/09544054JEM1543. |
[12] |
E. Gebennini, R. Gamberini and R. Manzini,
An integrated integrated production - distribution model for the dynamic location and allocation problem with safety stock optimization, International Journal of Production Economics, 122 (2009), 286-304.
doi: 10.1016/j.ijpe.2009.06.027. |
[13] |
M. Gen and A. Syarif,
Hybrid genetic algorithm for multi - time period production/distribution planning, Computers & Industrial Engineering, 48 (2005), 799-809.
doi: 10.1016/j.cie.2004.12.012. |
[14] |
B. Golany, J. Yang and G. Yu,
Economic lot-sizing with remanufacturing options, IIE Transactions, 33 (2001), 995-1003.
doi: 10.1080/07408170108936890. |
[15] |
P. Hansen, B. Jaumard and G. Savard,
New branch and bound rules for linear bilevel programming, SIAM Journal on Science and Statistical Computing, 13 (1992), 1194-1217.
doi: 10.1137/0913069. |
[16] |
J. Holland,
Adaptation in Natural and Artificial System, The University of Michigan Press, Ann Arbor, 1975. |
[17] |
M. Y. Jaber and A. M. A. EI Saadany,
The production remanufacture and waste disposal model with lost sale, International Journal of production Economics, 120 (2009), 115-124.
doi: 10.1016/j.ijpe.2008.07.016. |
[18] |
K. Kim, I. Song and J. Kim,
Supply planning model for remanufacturing system in reverse logistics environment, Computers & Industrial Engineering, 51 (2006), 279-287.
doi: 10.1016/j.cie.2006.02.008. |
[19] |
Y. J. Li, J. Zhang and J. Chen,
Optimal solution structure for multi - period production planning with returned products remanufacturing, Asia-Pacific Journal of Operational Research, 27 (2010), 629-648.
doi: 10.1142/S0217595910002910. |
[20] |
Y. J. Li, J. Chen and X. Q. Cai,
Uncapacited production planning with multiple product types, returned product remanufacturing, and demand substitution, OR Spectrum, 28 (2006), 101-125.
doi: 10.1007/s00291-005-0012-5. |
[21] |
Y. J. Li, J. Chen and X. Q. Cai,
Heuristic genetic algorithm for capacitated production planning problems with batch processing and remanufacturing, International Journal of Production Economics, 105 (2007), 301-317.
doi: 10.1016/j.ijpe.2004.11.017. |
[22] |
T. F. Liang and H. W. Cheng,
Application of fuzzy sets to manufacturing/distribution planning decisions with multi - product and multi - time period in supply chains, Expert Systems with Application, 36 (2009), 3367-3377.
doi: 10.1016/j.eswa.2008.01.002. |
[23] |
T. F. Liang,
Fuzzy multi - objective production/distribution planning decisions with multi - product and multi - time period in a supply chain, Computers & Industrial Engineering, 55 (2008), 676-694.
doi: 10.1016/j.cie.2008.02.008. |
[24] |
T. F. Liang,
Application of fuzzy sets to manufacturing/distribution planning decisions in supply chains, Information Science, 18 (2011), 842-854.
doi: 10.1016/j.ins.2010.10.019. |
[25] |
S. S. Liu and L. G. Papageorgiou,
Multiobjective optimisation of production, distribution and capacity planning of global supply chain in the process industry, Omega, 41 (2013), 369-382.
doi: 10.1016/j.omega.2012.03.007. |
[26] |
R. Manzini and E. Gebennini,
Optimization models for the dynamic facility location and allocation problem, International Journal of Production Research, 46 (2008), 2061-2086.
doi: 10.1080/00207540600847418. |
[27] |
L. Özdamar and T. Yazgac,
A hierarchical planning approach for a integrated production - distribution system, International Journal of Production Research, 16 (1999), 3759-3772.
|
[28] |
Z. D. Pan, J. F. Tang and O. Liu,
Capacitated dynamic lot sizing problems in closed-loop supply chain, European Journal of Operational Research, 198 (2009), 810-821.
doi: 10.1016/j.ejor.2008.10.018. |
[29] |
P. Piñeyro and O. Viera,
The economic lot-sizing problem with remanufacturing and one-way substitution, International Journal of Production Economics, 124 (2010), 482-488.
|
[30] |
D. F. Pyke and M. A. Cohen,
Performance characteristics of stochastic integrated integrated production - distribution system, European Journal of Operational Research, 68 (1993), 23-48.
doi: 10.1016/0377-2217(93)90075-X. |
[31] |
D. F. Pyke and M. A. Cohen,
Multiproduct integrated integrated production - distribution system, European Journal of Operational Research, 74 (1994), 18-49.
doi: 10.1016/0377-2217(94)90201-1. |
[32] |
K. Richter and M. Sombrutzki,
Remanufacturing planning for reverse Wagner/Whitin models, European Journal of Operational Research, 121 (2000), 304-315.
doi: 10.1016/S0377-2217(99)00219-2. |
[33] |
K. Richter and J. Weber,
The reverse Wagner/Whitin model with variable manufacturing and remanufacturing cost, International Journal of Production Economics, 71 (2001), 447-456.
doi: 10.1016/S0925-5273(00)00142-0. |
[34] |
N. Rizk, A. Martel and S. D'Amours,
Multi-item dynamic integrated production - distribution planning in process industries with divergent finishing stages, Computers & Operations Research, 33 (2006), 3600-3623.
doi: 10.1016/j.cor.2005.02.047. |
[35] |
T. Schulz,
A new Silver-Meal based heuristic for single-item dynamic lot sizing problem with returns and remanufacturing, International Journal of Production Research, 49 (2011), 2519-2533.
doi: 10.1080/00207543.2010.532916. |
[36] |
H. Selim, C. Araz and I. Ozkarahan,
Collaborative integrated production - distribution planning in supply chain: A fuzzy programming approach, Transportation Research Part E, 44 (2008), 396-419.
doi: 10.1016/j.tre.2006.11.001. |
[37] |
M. Srinivas and L. M. Patnaik,
Adaptive probabilities of crossover and mutation in Genetic Algorithm, IEEE Transaction on Systems, Man and Cybernetics, 24 (1994), 656-667.
doi: 10.1109/21.286385. |
[38] |
R. H. Teunter, Z. P. Bayindir and W. V. D. Heuvel,
Dynamic lot sizing with product returns and remanufacturing, International Journal of Production Research, 44 (2006), 4377-4400.
doi: 10.1080/00207540600693564. |
[39] |
L. N. Vicente, G. Savard and J. J. Judice,
Descent approaches for quadratic bilevel programming, Journal of Optimization Theory and Applications, 81 (1994), 379-399.
doi: 10.1007/BF02191670. |
[40] |
X. P. Wang and L. M. Cao, Genetic Algorithm-Theory, Application and Software Implementation, Xi An Jiao Tong University Press, Shan Xi, 2002. |
[41] |
A. Xanthopoulos and E. Iakovou,
On the optimal design of the disassembly and recovery processes, Waste Management, 29 (2009), 1702-1711.
doi: 10.1016/j.wasman.2008.11.009. |
[42] |
P. Yilmaz and B. Çatay,
Strategic level three-stage production distribution planning with capacity expansion, Computers & Industrial Engineering, 51 (2006), 609-620.
|
[43] |
F. Zaman, S. M. Elsayed and T. Ray,
Configuring two - algorithm-based evolutionary approach for solving dynamic economic dispatch problems, Engineering Applications of Artificial Intelligence, 53 (2016), 105-125.
doi: 10.1016/j.engappai.2016.04.001. |
[44] |
J. Zhang, X. Liu and Y. L. Tu,
A capacitated production planning problem for closed-loop supply chain with remanufacturing, International Journal of Advanced Manufacturing Technology, 54 (2011), 757-766.
doi: 10.1007/s00170-010-2948-0. |
show all references
References:
[1] |
R. A. Aliev, B. Fazlollahi and B. G. Guirimov,
Fuzzy-genetic approach to aggregate integrated production - distribution planning in supply chain management, Information Sciences, 177 (2007), 4241-4255.
doi: 10.1016/j.ins.2007.04.012. |
[2] |
S. M. J. M. Al-e-hachem, H. Malekly and M. B. Aryanezhad,
A multi - objective robust optimization model for multi - product multi - site aggregate production planning in a supply chain under uncertainty, International Journal of Production Economics, 134 (2011), 28-42.
|
[3] |
S. H. Amin and G. Q. Zhang,
A proposed mathematical model for closed-loop network configuration based on product life cycle, International Journal of Advanced Manufacturing Technology, 58 (2012), 791-801.
doi: 10.1007/s00170-011-3407-2. |
[4] |
P. Amorim, H. O. Günther and B. Almada-Lobo,
Multi-objective integrated production and distribution planning of perishable products, International Journal of Production Economics, 138 (2012), 89-101.
doi: 10.1016/j.ijpe.2012.03.005. |
[5] |
G. Barbarosolu,
Hierarchical design of an integrated production and 2-echelon distribution system, European Journal of Operational Research, 118 (1999), 464-484.
doi: 10.1016/S0377-2217(98)00317-8. |
[6] |
M. Boudia, M. A. O. Louly and C. Prins,
A reactive GRASP and path relinking for a combined integrated production - distribution problem, Computers & Operations Research, 34 (2007), 3402-3419.
doi: 10.1016/j.cor.2006.02.005. |
[7] |
H. I. Calvete, C. Galé and M. J. Oliveros,
Bilevel model for integrated production - distribution planning solved by using ant colony optimization, Computers & Operations Research, 38 (2011), 320-327.
doi: 10.1016/j.cor.2010.05.007. |
[8] |
F. T. S. Chan, S. H. Chung and S. Wadhwa,
A hybrid genetic algorithm for production and distribution, Omega, 33 (2005), 345-355.
doi: 10.1016/j.omega.2004.05.004. |
[9] |
K. Deb, A. Pratap and S. Agarwal,
A fast and elitist multiobjective genetic algorithm: NSGA-Ⅱ, IEEE Transactions on Evolutionary Computation, 6 (2002), 182-197.
doi: 10.1109/4235.996017. |
[10] |
G. W. Depuy, J. S. Usher and R. L. Walker,
Production planning for remanufactured products, Production Planning & Control, 18 (2007), 573-583.
doi: 10.1080/09537280701542210. |
[11] |
H. H. Doh and D. H. Lee,
Generic production planning model for remanufacturing systems, Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 224 (2010), 159-168.
doi: 10.1243/09544054JEM1543. |
[12] |
E. Gebennini, R. Gamberini and R. Manzini,
An integrated integrated production - distribution model for the dynamic location and allocation problem with safety stock optimization, International Journal of Production Economics, 122 (2009), 286-304.
doi: 10.1016/j.ijpe.2009.06.027. |
[13] |
M. Gen and A. Syarif,
Hybrid genetic algorithm for multi - time period production/distribution planning, Computers & Industrial Engineering, 48 (2005), 799-809.
doi: 10.1016/j.cie.2004.12.012. |
[14] |
B. Golany, J. Yang and G. Yu,
Economic lot-sizing with remanufacturing options, IIE Transactions, 33 (2001), 995-1003.
doi: 10.1080/07408170108936890. |
[15] |
P. Hansen, B. Jaumard and G. Savard,
New branch and bound rules for linear bilevel programming, SIAM Journal on Science and Statistical Computing, 13 (1992), 1194-1217.
doi: 10.1137/0913069. |
[16] |
J. Holland,
Adaptation in Natural and Artificial System, The University of Michigan Press, Ann Arbor, 1975. |
[17] |
M. Y. Jaber and A. M. A. EI Saadany,
The production remanufacture and waste disposal model with lost sale, International Journal of production Economics, 120 (2009), 115-124.
doi: 10.1016/j.ijpe.2008.07.016. |
[18] |
K. Kim, I. Song and J. Kim,
Supply planning model for remanufacturing system in reverse logistics environment, Computers & Industrial Engineering, 51 (2006), 279-287.
doi: 10.1016/j.cie.2006.02.008. |
[19] |
Y. J. Li, J. Zhang and J. Chen,
Optimal solution structure for multi - period production planning with returned products remanufacturing, Asia-Pacific Journal of Operational Research, 27 (2010), 629-648.
doi: 10.1142/S0217595910002910. |
[20] |
Y. J. Li, J. Chen and X. Q. Cai,
Uncapacited production planning with multiple product types, returned product remanufacturing, and demand substitution, OR Spectrum, 28 (2006), 101-125.
doi: 10.1007/s00291-005-0012-5. |
[21] |
Y. J. Li, J. Chen and X. Q. Cai,
Heuristic genetic algorithm for capacitated production planning problems with batch processing and remanufacturing, International Journal of Production Economics, 105 (2007), 301-317.
doi: 10.1016/j.ijpe.2004.11.017. |
[22] |
T. F. Liang and H. W. Cheng,
Application of fuzzy sets to manufacturing/distribution planning decisions with multi - product and multi - time period in supply chains, Expert Systems with Application, 36 (2009), 3367-3377.
doi: 10.1016/j.eswa.2008.01.002. |
[23] |
T. F. Liang,
Fuzzy multi - objective production/distribution planning decisions with multi - product and multi - time period in a supply chain, Computers & Industrial Engineering, 55 (2008), 676-694.
doi: 10.1016/j.cie.2008.02.008. |
[24] |
T. F. Liang,
Application of fuzzy sets to manufacturing/distribution planning decisions in supply chains, Information Science, 18 (2011), 842-854.
doi: 10.1016/j.ins.2010.10.019. |
[25] |
S. S. Liu and L. G. Papageorgiou,
Multiobjective optimisation of production, distribution and capacity planning of global supply chain in the process industry, Omega, 41 (2013), 369-382.
doi: 10.1016/j.omega.2012.03.007. |
[26] |
R. Manzini and E. Gebennini,
Optimization models for the dynamic facility location and allocation problem, International Journal of Production Research, 46 (2008), 2061-2086.
doi: 10.1080/00207540600847418. |
[27] |
L. Özdamar and T. Yazgac,
A hierarchical planning approach for a integrated production - distribution system, International Journal of Production Research, 16 (1999), 3759-3772.
|
[28] |
Z. D. Pan, J. F. Tang and O. Liu,
Capacitated dynamic lot sizing problems in closed-loop supply chain, European Journal of Operational Research, 198 (2009), 810-821.
doi: 10.1016/j.ejor.2008.10.018. |
[29] |
P. Piñeyro and O. Viera,
The economic lot-sizing problem with remanufacturing and one-way substitution, International Journal of Production Economics, 124 (2010), 482-488.
|
[30] |
D. F. Pyke and M. A. Cohen,
Performance characteristics of stochastic integrated integrated production - distribution system, European Journal of Operational Research, 68 (1993), 23-48.
doi: 10.1016/0377-2217(93)90075-X. |
[31] |
D. F. Pyke and M. A. Cohen,
Multiproduct integrated integrated production - distribution system, European Journal of Operational Research, 74 (1994), 18-49.
doi: 10.1016/0377-2217(94)90201-1. |
[32] |
K. Richter and M. Sombrutzki,
Remanufacturing planning for reverse Wagner/Whitin models, European Journal of Operational Research, 121 (2000), 304-315.
doi: 10.1016/S0377-2217(99)00219-2. |
[33] |
K. Richter and J. Weber,
The reverse Wagner/Whitin model with variable manufacturing and remanufacturing cost, International Journal of Production Economics, 71 (2001), 447-456.
doi: 10.1016/S0925-5273(00)00142-0. |
[34] |
N. Rizk, A. Martel and S. D'Amours,
Multi-item dynamic integrated production - distribution planning in process industries with divergent finishing stages, Computers & Operations Research, 33 (2006), 3600-3623.
doi: 10.1016/j.cor.2005.02.047. |
[35] |
T. Schulz,
A new Silver-Meal based heuristic for single-item dynamic lot sizing problem with returns and remanufacturing, International Journal of Production Research, 49 (2011), 2519-2533.
doi: 10.1080/00207543.2010.532916. |
[36] |
H. Selim, C. Araz and I. Ozkarahan,
Collaborative integrated production - distribution planning in supply chain: A fuzzy programming approach, Transportation Research Part E, 44 (2008), 396-419.
doi: 10.1016/j.tre.2006.11.001. |
[37] |
M. Srinivas and L. M. Patnaik,
Adaptive probabilities of crossover and mutation in Genetic Algorithm, IEEE Transaction on Systems, Man and Cybernetics, 24 (1994), 656-667.
doi: 10.1109/21.286385. |
[38] |
R. H. Teunter, Z. P. Bayindir and W. V. D. Heuvel,
Dynamic lot sizing with product returns and remanufacturing, International Journal of Production Research, 44 (2006), 4377-4400.
doi: 10.1080/00207540600693564. |
[39] |
L. N. Vicente, G. Savard and J. J. Judice,
Descent approaches for quadratic bilevel programming, Journal of Optimization Theory and Applications, 81 (1994), 379-399.
doi: 10.1007/BF02191670. |
[40] |
X. P. Wang and L. M. Cao, Genetic Algorithm-Theory, Application and Software Implementation, Xi An Jiao Tong University Press, Shan Xi, 2002. |
[41] |
A. Xanthopoulos and E. Iakovou,
On the optimal design of the disassembly and recovery processes, Waste Management, 29 (2009), 1702-1711.
doi: 10.1016/j.wasman.2008.11.009. |
[42] |
P. Yilmaz and B. Çatay,
Strategic level three-stage production distribution planning with capacity expansion, Computers & Industrial Engineering, 51 (2006), 609-620.
|
[43] |
F. Zaman, S. M. Elsayed and T. Ray,
Configuring two - algorithm-based evolutionary approach for solving dynamic economic dispatch problems, Engineering Applications of Artificial Intelligence, 53 (2016), 105-125.
doi: 10.1016/j.engappai.2016.04.001. |
[44] |
J. Zhang, X. Liu and Y. L. Tu,
A capacitated production planning problem for closed-loop supply chain with remanufacturing, International Journal of Advanced Manufacturing Technology, 54 (2011), 757-766.
doi: 10.1007/s00170-010-2948-0. |


Variables | Generation interval | Variables | Generation interval |
Variables | Generation interval | Variables | Generation interval |
![]() | A | B-1 | B-2 | C-1 | C-2 | D |
Ⅰ | 1 | 1 | 0 | 4 | 0 | 1 |
Ⅱ | 1 | 0 | 1 | 0 | 4 | 1 |
Ⅲ | 1 | 0 | 1 | 0 | 4 | 1 |
![]() | A | B-1 | B-2 | C-1 | C-2 | D |
Ⅰ | 1 | 1 | 0 | 4 | 0 | 1 |
Ⅱ | 1 | 0 | 1 | 0 | 4 | 1 |
Ⅲ | 1 | 0 | 1 | 0 | 4 | 1 |
1 | 2 | 3 | 4 | 5 | |||||||||||||||
1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | |||||
| 378 | 384 | 400 | 394 | 395 | 396 | 365 | 367 | 389 | 370 | 391 | 405 | 398 | 408 | 423 | ||||
| 387 | 407 | 402 | 380 | 387 | 394 | 376 | 395 | 399 | 368 | 378 | 393 | 409 | 416 | 416 | ||||
| 380 | 397 | 393 | 376 | 391 | 409 | 384 | 389 | 384 | 374 | 397 | 393 | 365 | 367 | 389 | ||||
| 393 | 395 | 390 | 381 | 388 | 391 | 370 | 395 | 383 | 393 | 395 | 390 | 376 | 395 | 399 | ||||
| 398 | 408 | 423 | 370 | 391 | 405 | 381 | 387 | 394 | 394 | 395 | 396 | 374 | 389 | 384 | ||||
| 409 | 416 | 416 | 368 | 378 | 393 | 385 | 386 | 397 | 380 | 387 | 394 | 370 | 395 | 383 |
1 | 2 | 3 | 4 | 5 | |||||||||||||||
1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | |||||
| 378 | 384 | 400 | 394 | 395 | 396 | 365 | 367 | 389 | 370 | 391 | 405 | 398 | 408 | 423 | ||||
| 387 | 407 | 402 | 380 | 387 | 394 | 376 | 395 | 399 | 368 | 378 | 393 | 409 | 416 | 416 | ||||
| 380 | 397 | 393 | 376 | 391 | 409 | 384 | 389 | 384 | 374 | 397 | 393 | 365 | 367 | 389 | ||||
| 393 | 395 | 390 | 381 | 388 | 391 | 370 | 395 | 383 | 393 | 395 | 390 | 376 | 395 | 399 | ||||
| 398 | 408 | 423 | 370 | 391 | 405 | 381 | 387 | 394 | 394 | 395 | 396 | 374 | 389 | 384 | ||||
| 409 | 416 | 416 | 368 | 378 | 393 | 385 | 386 | 397 | 380 | 387 | 394 | 370 | 395 | 383 |
1 | 2 | 3 | 4 | 5 | |||||||||||||||
1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | |||||
157 | 163 | 165 | 158 | 166 | 170 | 168 | 172 | 172 | 158 | 160 | 162 | 158 | 167 | 171 | |||||
| 160 | 162 | 169 | 160 | 162 | 173 | 162 | 163 | 165 | 163 | 169 | 171 | 167 | 170 | 172 | ||||
| 155 | 156 | 160 | 162 | 168 | 175 | 158 | 167 | 171 | 162 | 168 | 175 | 152 | 159 | 166 | ||||
| 162 | 163 | 165 | 156 | 159 | 168 | 167 | 170 | 172 | 156 | 159 | 168 | 158 | 163 | 170 | ||||
| 158 | 160 | 162 | 152 | 159 | 166 | 167 | 174 | 174 | 157 | 163 | 165 | 155 | 156 | 160 | ||||
| 163 | 169 | 171 | 158 | 163 | 170 | 151 | 163 | 166 | 160 | 162 | 169 | 162 | 163 | 165 |
1 | 2 | 3 | 4 | 5 | |||||||||||||||
1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | |||||
157 | 163 | 165 | 158 | 166 | 170 | 168 | 172 | 172 | 158 | 160 | 162 | 158 | 167 | 171 | |||||
| 160 | 162 | 169 | 160 | 162 | 173 | 162 | 163 | 165 | 163 | 169 | 171 | 167 | 170 | 172 | ||||
| 155 | 156 | 160 | 162 | 168 | 175 | 158 | 167 | 171 | 162 | 168 | 175 | 152 | 159 | 166 | ||||
| 162 | 163 | 165 | 156 | 159 | 168 | 167 | 170 | 172 | 156 | 159 | 168 | 158 | 163 | 170 | ||||
| 158 | 160 | 162 | 152 | 159 | 166 | 167 | 174 | 174 | 157 | 163 | 165 | 155 | 156 | 160 | ||||
| 163 | 169 | 171 | 158 | 163 | 170 | 151 | 163 | 166 | 160 | 162 | 169 | 162 | 163 | 165 |
1 | 2 | 3 | 4 | 5 | |||||||||||||||
1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | |||||
186 | 188 | 189 | 186 | 191 | 197 | 191 | 192 | 187 | 184 | 184 | 190 | 187 | 198 | 202 | |||||
| 190 | 198 | 199 | 184 | 195 | 198 | 198 | 193 | 195 | 192 | 195 | 198 | 199 | 207 | 205 | ||||
| 184 | 184 | 190 | 181 | 195 | 195 | 187 | 198 | 202 | 181 | 195 | 195 | 196 | 198 | 205 | ||||
| 192 | 195 | 198 | 197 | 190 | 199 | 199 | 204 | 204 | 197 | 190 | 199 | 182 | 190 | 191 | ||||
| 174 | 198 | 204 | 187 | 179 | 195 | 189 | 184 | 198 | 186 | 191 | 197 | 198 | 193 | 195 | ||||
| 182 | 190 | 191 | 188 | 189 | 191 | 180 | 193 | 194 | 184 | 195 | 198 | 187 | 179 | 195 |
1 | 2 | 3 | 4 | 5 | |||||||||||||||
1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | |||||
186 | 188 | 189 | 186 | 191 | 197 | 191 | 192 | 187 | 184 | 184 | 190 | 187 | 198 | 202 | |||||
| 190 | 198 | 199 | 184 | 195 | 198 | 198 | 193 | 195 | 192 | 195 | 198 | 199 | 207 | 205 | ||||
| 184 | 184 | 190 | 181 | 195 | 195 | 187 | 198 | 202 | 181 | 195 | 195 | 196 | 198 | 205 | ||||
| 192 | 195 | 198 | 197 | 190 | 199 | 199 | 204 | 204 | 197 | 190 | 199 | 182 | 190 | 191 | ||||
| 174 | 198 | 204 | 187 | 179 | 195 | 189 | 184 | 198 | 186 | 191 | 197 | 198 | 193 | 195 | ||||
| 182 | 190 | 191 | 188 | 189 | 191 | 180 | 193 | 194 | 184 | 195 | 198 | 187 | 179 | 195 |
| | |||||||||
1 | 2 | 3 | 4 | 5 | 6 | 1 | 2 | 3 | ||
35 | 30 | 30 | 25 | 25 | 30 | | 1000 | 1200 | 1200 | |
| 10 | 10 | 10 | 5 | 5 | 5 | | 100 | 100 | 100 |
| 0.95 | 0.92 | 0.92 | 0.90 | 0.90 | 0.85 | | 10 | 10 | 10 |
| | |||||||||
1 | 2 | 3 | 4 | 5 | 6 | 1 | 2 | 3 | ||
35 | 30 | 30 | 25 | 25 | 30 | | 1000 | 1200 | 1200 | |
| 10 | 10 | 10 | 5 | 5 | 5 | | 100 | 100 | 100 |
| 0.95 | 0.92 | 0.92 | 0.90 | 0.90 | 0.85 | | 10 | 10 | 10 |
1 | 2 | 3 | |||||||||
1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | |||
25000 | 30000 | 35000 | 25000 | 30000 | 35000 | 25000 | 30000 | 35000 | |||
| 25000 | 30000 | 35000 | 25000 | 30000 | 35000 | 25000 | 30000 | 35000 | ||
| 5900 | 7400 | 7900 | 6000 | 7500 | 8000 | 6050 | 7550 | 8050 | ||
| 5900 | 7400 | 7900 | 6000 | 7500 | 8000 | 6050 | 7550 | 8050 | ||
| 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | ||
| 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 |
1 | 2 | 3 | |||||||||
1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | |||
25000 | 30000 | 35000 | 25000 | 30000 | 35000 | 25000 | 30000 | 35000 | |||
| 25000 | 30000 | 35000 | 25000 | 30000 | 35000 | 25000 | 30000 | 35000 | ||
| 5900 | 7400 | 7900 | 6000 | 7500 | 8000 | 6050 | 7550 | 8050 | ||
| 5900 | 7400 | 7900 | 6000 | 7500 | 8000 | 6050 | 7550 | 8050 | ||
| 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | ||
| 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 |
i= | 1 | 2 | 3 | |||||||||||||||||
c= | 1 | 2 | 3 | 4 | 5 | 6 | 1 | 2 | 3 | 4 | 5 | 6 | 1 | 2 | 3 | 4 | 5 | 6 | ||
SPcit | 25000 | 20000 | 24000 | 15000 | 18000 | 18000 | 25000 | 20000 | 24000 | 15000 | 18000 | 18000 | 25000 | 20000 | 24000 | 15000 | 18000 | 18000 | ||
SRPcit | 10000 | 6000 | 7000 | 5000 | 6000 | 5000 | 10000 | 6000 | 7000 | 5000 | 6000 | 5000 | 10000 | 6000 | 7000 | 5000 | 6000 | 5000 | ||
UPCcit | 3900 | 2400 | 2700 | 70 | 95 | 950 | 4000 | 2500 | 2800 | 75 | 100 | 1000 | 4100 | 2600 | 2900 | 80 | 105 | 1050 | ||
URPCcit | 950 | 550 | 650 | 22 | 28 | 325 | 1000 | 600 | 700 | 25 | 30 | 350 | 1050 | 650 | 750 | 28 | 32 | 375 | ||
ICQCcitf | 10 | 10 | 10 | 5 | 5 | 5 | 10 | 10 | 10 | 5 | 5 | 5 | 10 | 10 | 10 | 5 | 5 | 5 | ||
ICNCcitf | 15 | 15 | 15 | 10 | 10 | 10 | 15 | 15 | 15 | 10 | 10 | 10 | 15 | 15 | 15 | 10 | 10 | 10 | ||
ICRCcitf | 15 | 15 | 15 | 10 | 10 | 10 | 15 | 15 | 15 | 10 | 10 | 10 | 15 | 15 | 15 | 10 | 10 | 10 | ||
UTCacitf | 40 | 30 | 30 | 15 | 15 | 25 | 45 | 35 | 35 | 15 | 15 | 30 | 40 | 30 | 30 | 15 | 15 | 25 | ||
PPCcit | 820 | 520 | 540 | 135 | 135 | 355 | 820 | 520 | 540 | 135 | 135 | 355 | 800 | 500 | 520 | 120 | 120 | 345 | ||
MPci | 2400 | 800 | 1600 | 3200 | 6400 | 2400 | 2400 | 800 | 1600 | 3200 | 6400 | 2400 | 2400 | 800 | 1600 | 3200 | 6400 | 2400 | ||
MRPci | 1050 | 350 | 700 | 1400 | 2800 | 1050 | 1050 | 350 | 700 | 1400 | 2800 | 1050 | 1050 | 350 | 700 | 1400 | 2800 | 1050 |
i= | 1 | 2 | 3 | |||||||||||||||||
c= | 1 | 2 | 3 | 4 | 5 | 6 | 1 | 2 | 3 | 4 | 5 | 6 | 1 | 2 | 3 | 4 | 5 | 6 | ||
SPcit | 25000 | 20000 | 24000 | 15000 | 18000 | 18000 | 25000 | 20000 | 24000 | 15000 | 18000 | 18000 | 25000 | 20000 | 24000 | 15000 | 18000 | 18000 | ||
SRPcit | 10000 | 6000 | 7000 | 5000 | 6000 | 5000 | 10000 | 6000 | 7000 | 5000 | 6000 | 5000 | 10000 | 6000 | 7000 | 5000 | 6000 | 5000 | ||
UPCcit | 3900 | 2400 | 2700 | 70 | 95 | 950 | 4000 | 2500 | 2800 | 75 | 100 | 1000 | 4100 | 2600 | 2900 | 80 | 105 | 1050 | ||
URPCcit | 950 | 550 | 650 | 22 | 28 | 325 | 1000 | 600 | 700 | 25 | 30 | 350 | 1050 | 650 | 750 | 28 | 32 | 375 | ||
ICQCcitf | 10 | 10 | 10 | 5 | 5 | 5 | 10 | 10 | 10 | 5 | 5 | 5 | 10 | 10 | 10 | 5 | 5 | 5 | ||
ICNCcitf | 15 | 15 | 15 | 10 | 10 | 10 | 15 | 15 | 15 | 10 | 10 | 10 | 15 | 15 | 15 | 10 | 10 | 10 | ||
ICRCcitf | 15 | 15 | 15 | 10 | 10 | 10 | 15 | 15 | 15 | 10 | 10 | 10 | 15 | 15 | 15 | 10 | 10 | 10 | ||
UTCacitf | 40 | 30 | 30 | 15 | 15 | 25 | 45 | 35 | 35 | 15 | 15 | 30 | 40 | 30 | 30 | 15 | 15 | 25 | ||
PPCcit | 820 | 520 | 540 | 135 | 135 | 355 | 820 | 520 | 540 | 135 | 135 | 355 | 800 | 500 | 520 | 120 | 120 | 345 | ||
MPci | 2400 | 800 | 1600 | 3200 | 6400 | 2400 | 2400 | 800 | 1600 | 3200 | 6400 | 2400 | 2400 | 800 | 1600 | 3200 | 6400 | 2400 | ||
MRPci | 1050 | 350 | 700 | 1400 | 2800 | 1050 | 1050 | 350 | 700 | 1400 | 2800 | 1050 | 1050 | 350 | 700 | 1400 | 2800 | 1050 |
j= | 1 | 2 | 3 | 4 | 5 | ||||||||||||||
p= | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | ||||
URCCpjt | 1000 | 1150 | 1150 | 1000 | 1150 | 1150 | 1050 | 1200 | 1200 | 1050 | 1200 | 1200 | 1100 | 1250 | 1250 | ||||
URCDpjt | 900 | 1050 | 1050 | 900 | 1050 | 1050 | 950 | 1100 | 1100 | 950 | 1100 | 1100 | 1000 | 1150 | 1150 | ||||
SPNpjt | 18160 | 20670 | 21340 | 18160 | 20665 | 21340 | 18150 | 20680 | 21345 | 18150 | 20680 | 21345 | 18170 | 20690 | 21365 | ||||
SPRpjt | 12570 | 14740 | 15400 | 12570 | 14740 | 15400 | 12580 | 14740 | 15410 | 12580 | 14740 | 15410 | 12590 | 14760 | 15430 | ||||
USNPpjt | 4120 | 4690 | 4840 | 4120 | 4690 | 4840 | 4110 | 4690 | 4840 | 4110 | 4690 | 4840 | 4120 | 4690 | 4850 | ||||
USRPpjt | 2850 | 3340 | 3490 | 2850 | 3340 | 3490 | 2850 | 3340 | 3500 | 2850 | 3340 | 3500 | 2860 | 3350 | 3500 | ||||
UTCpjtda | 30 | 30 | 30 | 35 | 35 | 35 | 30 | 30 | 30 | 35 | 35 | 35 | 30 | 30 | 30 | ||||
ICNPpjtd | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | ||||
ICRMPpjtd | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | ||||
ICRPpjtd | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 |
j= | 1 | 2 | 3 | 4 | 5 | ||||||||||||||
p= | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | ||||
URCCpjt | 1000 | 1150 | 1150 | 1000 | 1150 | 1150 | 1050 | 1200 | 1200 | 1050 | 1200 | 1200 | 1100 | 1250 | 1250 | ||||
URCDpjt | 900 | 1050 | 1050 | 900 | 1050 | 1050 | 950 | 1100 | 1100 | 950 | 1100 | 1100 | 1000 | 1150 | 1150 | ||||
SPNpjt | 18160 | 20670 | 21340 | 18160 | 20665 | 21340 | 18150 | 20680 | 21345 | 18150 | 20680 | 21345 | 18170 | 20690 | 21365 | ||||
SPRpjt | 12570 | 14740 | 15400 | 12570 | 14740 | 15400 | 12580 | 14740 | 15410 | 12580 | 14740 | 15410 | 12590 | 14760 | 15430 | ||||
USNPpjt | 4120 | 4690 | 4840 | 4120 | 4690 | 4840 | 4110 | 4690 | 4840 | 4110 | 4690 | 4840 | 4120 | 4690 | 4850 | ||||
USRPpjt | 2850 | 3340 | 3490 | 2850 | 3340 | 3490 | 2850 | 3340 | 3500 | 2850 | 3340 | 3500 | 2860 | 3350 | 3500 | ||||
UTCpjtda | 30 | 30 | 30 | 35 | 35 | 35 | 30 | 30 | 30 | 35 | 35 | 35 | 30 | 30 | 30 | ||||
ICNPpjtd | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | ||||
ICRMPpjtd | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | ||||
ICRPpjtd | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 |
i | 1 | 2 | 3 | ||||||||||||||
j | 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 | ||
MPN1ijt | 15440 | 15440 | 15460 | 15460 | 15500 | 15840 | 15870 | 15780 | 15780 | 15840 | 16100 | 16070 | 16100 | 16100 | 16070 | ||
MPN2ijt | 17640 | 17640 | 17670 | 17670 | 17720 | 17990 | 18000 | 17980 | 17980 | 17990 | 18290 | 18270 | 18290 | 18290 | 18270 | ||
MPN3ijt | 18220 | 18220 | 18260 | 18260 | 18300 | 18580 | 18600 | 18560 | 18560 | 18580 | 18860 | 18850 | 18860 | 18860 | 18850 | ||
MPR1ijt | 10730 | 10730 | 10770 | 10770 | 10810 | 10970 | 10990 | 10950 | 10950 | 10870 | 11090 | 11070 | 11090 | 11090 | 11070 | ||
MPR2ijt | 12630 | 12630 | 12650 | 12650 | 12690 | 12860 | 12880 | 12840 | 12840 | 12860 | 12970 | 12950 | 12970 | 12970 | 12950 | ||
MPR3ijt | 13200 | 13200 | 13240 | 13240 | 13290 | 13430 | 13450 | 13410 | 13410 | 13430 | 13550 | 13530 | 13550 | 13550 | 13530 | ||
UTCpijtfd | 40 | 40 | 50 | 50 | 60 | 60 | 50 | 40 | 50 | 60 | 60 | 50 | 50 | 40 | 40 |
i | 1 | 2 | 3 | ||||||||||||||
j | 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 | ||
MPN1ijt | 15440 | 15440 | 15460 | 15460 | 15500 | 15840 | 15870 | 15780 | 15780 | 15840 | 16100 | 16070 | 16100 | 16100 | 16070 | ||
MPN2ijt | 17640 | 17640 | 17670 | 17670 | 17720 | 17990 | 18000 | 17980 | 17980 | 17990 | 18290 | 18270 | 18290 | 18290 | 18270 | ||
MPN3ijt | 18220 | 18220 | 18260 | 18260 | 18300 | 18580 | 18600 | 18560 | 18560 | 18580 | 18860 | 18850 | 18860 | 18860 | 18850 | ||
MPR1ijt | 10730 | 10730 | 10770 | 10770 | 10810 | 10970 | 10990 | 10950 | 10950 | 10870 | 11090 | 11070 | 11090 | 11090 | 11070 | ||
MPR2ijt | 12630 | 12630 | 12650 | 12650 | 12690 | 12860 | 12880 | 12840 | 12840 | 12860 | 12970 | 12950 | 12970 | 12970 | 12950 | ||
MPR3ijt | 13200 | 13200 | 13240 | 13240 | 13290 | 13430 | 13450 | 13410 | 13410 | 13430 | 13550 | 13530 | 13550 | 13550 | 13530 | ||
UTCpijtfd | 40 | 40 | 50 | 50 | 60 | 60 | 50 | 40 | 50 | 60 | 60 | 50 | 50 | 40 | 40 |
Algorithm | Running result | Convergence generation | |||||||
Best | Mean | Worst | Proportion of Best Result | Standard Deviation | Best | Mean | Worst | ||
SGA(Pcr = 0:6, Pmu = 0:005) | 103014002 | 102488365 | 102017694 | 36% | 453083 | 712 | 736 | 754 | |
SGA(Pcr = 0:6, Pmu = 0:02) | 104891190 | 103904980 | 103309728 | 20% | 672762 | 616 | 658 | 682 | |
SGA(Pcr = 0:8, Pmu = 0:005) | 103499360 | 103141280 | 102441552 | 46% | 432193 | 658 | 688 | 712 | |
SGA(Pcr = 0:8, Pmu = 0:02) | 104514894 | 103861409 | 103309728 | 42% | 566313 | 724 | 742 | 766 | |
AGA | 106570884 | 106360212 | 105911706 | 54% | 262057 | 458 | 489 | 511 | |
SAGA | 107302078 | 107217562 | 106984452 | 62% | 124847 | 489 | 527 | 557 |
Algorithm | Running result | Convergence generation | |||||||
Best | Mean | Worst | Proportion of Best Result | Standard Deviation | Best | Mean | Worst | ||
SGA(Pcr = 0:6, Pmu = 0:005) | 103014002 | 102488365 | 102017694 | 36% | 453083 | 712 | 736 | 754 | |
SGA(Pcr = 0:6, Pmu = 0:02) | 104891190 | 103904980 | 103309728 | 20% | 672762 | 616 | 658 | 682 | |
SGA(Pcr = 0:8, Pmu = 0:005) | 103499360 | 103141280 | 102441552 | 46% | 432193 | 658 | 688 | 712 | |
SGA(Pcr = 0:8, Pmu = 0:02) | 104514894 | 103861409 | 103309728 | 42% | 566313 | 724 | 742 | 766 | |
AGA | 106570884 | 106360212 | 105911706 | 54% | 262057 | 458 | 489 | 511 | |
SAGA | 107302078 | 107217562 | 106984452 | 62% | 124847 | 489 | 527 | 557 |
Notation | Description |
the index set of periods, | |
the index set of product type, | |
| the index set of component kind, |
| the index set of manufacturing/remanufacturing factory, |
| the index set of distributor, |
| the accumulative leading time of the joint recycling center, manufacturing/remanufacturing factories and distribution centers, respectively |
Notation | Description |
the index set of periods, | |
the index set of product type, | |
| the index set of component kind, |
| the index set of manufacturing/remanufacturing factory, |
| the index set of distributor, |
| the accumulative leading time of the joint recycling center, manufacturing/remanufacturing factories and distribution centers, respectively |
Notation | Description |
the quantity of batches of qualified component | |
| the quantity of batches of return product |
| the binary variable indicating whether return product |
| the quantity of batches of return product |
| the quantity of component |
|
the inventory of return product |
Notation | Description |
the quantity of batches of qualified component | |
| the quantity of batches of return product |
| the binary variable indicating whether return product |
| the quantity of batches of return product |
| the quantity of component |
|
the inventory of return product |
Notation | Description |
the quantity of batches of new and remanufacturing product | |
| the binary variable indicating whether new and remanufacturing product |
| the quantity of batches of new and remanufactured product |
| the binary variable indicating whether component |
| the quantity of batches of component |
| the inventory of new and remanufactured product |
| the inventory of qualified, new and remanufactured component |
| the quantity of one-way substitution for component |
| this notation has occurred in the first level model |
Notation | Description |
the quantity of batches of new and remanufacturing product | |
| the binary variable indicating whether new and remanufacturing product |
| the quantity of batches of new and remanufactured product |
| the binary variable indicating whether component |
| the quantity of batches of component |
| the inventory of new and remanufactured product |
| the inventory of qualified, new and remanufactured component |
| the quantity of one-way substitution for component |
| this notation has occurred in the first level model |
Notation | Description |
the quantity of new and remanufactured product | |
| the quantity of EOL product |
| the inventory of new, remanufactured and return product |
| this natation has occurred in the first level model |
| these notations have occurred in second level model |
Notation | Description |
the quantity of new and remanufactured product | |
| the quantity of EOL product |
| the inventory of new, remanufactured and return product |
| this natation has occurred in the first level model |
| these notations have occurred in second level model |
Notation | Description |
the quantity of qualified component | |
| the quantity of return product |
| the quantity of return product |
| the unit purchase cost of qualified component |
| the unit recycling cost of return product |
| the set-up cost incurred if return product |
| the unit disassembly & tested cost of return product |
| the unit disposing cost of component |
| the unit inventory cost of qualified component |
| the unit transportation cost of qualified component |
| the bill of component |
| the remanufacturable rate of component |
| the maximum inventory level of return products and qualified components at the recycling center, respectively |
| the maximum quantity of return product |
| the maximum quantity of qualified components can be transported from the recycling center to factories in every periods |
Notation | Description |
the quantity of qualified component | |
| the quantity of return product |
| the quantity of return product |
| the unit purchase cost of qualified component |
| the unit recycling cost of return product |
| the set-up cost incurred if return product |
| the unit disassembly & tested cost of return product |
| the unit disposing cost of component |
| the unit inventory cost of qualified component |
| the unit transportation cost of qualified component |
| the bill of component |
| the remanufacturable rate of component |
| the maximum inventory level of return products and qualified components at the recycling center, respectively |
| the maximum quantity of return product |
| the maximum quantity of qualified components can be transported from the recycling center to factories in every periods |
Notation | Description |
the middle price of new and remanufactured product | |
| the quantity of new or remanufactured product |
| the quantity of new and remanufactured product |
| the quantity of component |
| the set-up cost incurred if new and remanufactured product |
| the unit assembly cost of new and remanufactured product |
| the set-up cost incurred if component |
| the unit processing and reprocessing cost of component |
| the unit inventory cost of new and remanufactured product |
| the unit inventory cost of qualified, new and remanufactured component |
| the unit transportation cost of product |
| the maximum inventory level of qualified components, new components, remanufactured components, new products andremanufactured products at factory |
| the maximum quantity of new and remanufactured product |
| the maximum quantity of component |
| the maximum quantity of products can be transported from factory |
| these notations have occurred in the first level model |
Notation | Description |
the middle price of new and remanufactured product | |
| the quantity of new or remanufactured product |
| the quantity of new and remanufactured product |
| the quantity of component |
| the set-up cost incurred if new and remanufactured product |
| the unit assembly cost of new and remanufactured product |
| the set-up cost incurred if component |
| the unit processing and reprocessing cost of component |
| the unit inventory cost of new and remanufactured product |
| the unit inventory cost of qualified, new and remanufactured component |
| the unit transportation cost of product |
| the maximum inventory level of qualified components, new components, remanufactured components, new products andremanufactured products at factory |
| the maximum quantity of new and remanufactured product |
| the maximum quantity of component |
| the maximum quantity of products can be transported from factory |
| these notations have occurred in the first level model |
Notation | Description |
the selling price of new and remanufactured product | |
| the demands of new and remanufactured product |
| the unit recycling cost of EOL product |
| the unit shortage cost of new and remanufactured product |
| the unit inventory cost of new, remanufactured and return product |
| the unit transportation cost of return product |
| the quantity of EOL product |
| the maximum inventory level of new, remanufactured and return products at distributor |
| the maximum quantity of return products can be transported from distributor |
| these notations have occurred in the first level model |
| these notations have occurred in the second level model |
Notation | Description |
the selling price of new and remanufactured product | |
| the demands of new and remanufactured product |
| the unit recycling cost of EOL product |
| the unit shortage cost of new and remanufactured product |
| the unit inventory cost of new, remanufactured and return product |
| the unit transportation cost of return product |
| the quantity of EOL product |
| the maximum inventory level of new, remanufactured and return products at distributor |
| the maximum quantity of return products can be transported from distributor |
| these notations have occurred in the first level model |
| these notations have occurred in the second level model |
[1] |
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 and Management Optimization, 2021, 17 (6) : 3247-3268. doi: 10.3934/jimo.2020116 |
[2] |
Maedeh Agahgolnezhad Gerdrodbari, Fatemeh Harsej, Mahboubeh Sadeghpour, Mohammad Molani Aghdam. A robust multi-objective model for managing the distribution of perishable products within a green closed-loop supply chain. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021107 |
[3] |
Kaveh Keshmiry Zadeh, Fatemeh Harsej, Mahboubeh Sadeghpour, Mohammad Molani Aghdam. Designing a multi-echelon closed-loop supply chain with disruption in the distribution centers under uncertainty. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022057 |
[4] |
Masoud Mohammadzadeh, Alireza Arshadi Khamseh, Mohammad Mohammadi. A multi-objective integrated model for closed-loop supply chain configuration and supplier selection considering uncertain demand and different performance levels. Journal of Industrial and Management Optimization, 2017, 13 (2) : 1041-1064. doi: 10.3934/jimo.2016061 |
[5] |
Guangzhou Yan, Qinyu Song, Yaodong Ni, Xiangfeng Yang. Pricing, carbon emission reduction and recycling decisions in a closed-loop supply chain under uncertain environment. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021181 |
[6] |
Huaqing Cao, Xiaofen Ji. Optimal recycling price strategy of clothing enterprises based on closed-loop supply chain. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2021232 |
[7] |
Fatemeh Kangi, Seyed Hamid Reza Pasandideh, Esmaeil Mehdizadeh, Hamed Soleimani. The optimization of a multi-period multi-product closed-loop supply chain network with cross-docking delivery strategy. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021118 |
[8] |
Wenbin Wang, Peng Zhang, Junfei Ding, Jian Li, Hao Sun, Lingyun He. Closed-loop supply chain network equilibrium model with retailer-collection under legislation. Journal of Industrial and Management Optimization, 2019, 15 (1) : 199-219. doi: 10.3934/jimo.2018039 |
[9] |
Reza Lotfi, Yahia Zare Mehrjerdi, Mir Saman Pishvaee, Ahmad Sadeghieh, Gerhard-Wilhelm Weber. A robust optimization model for sustainable and resilient closed-loop supply chain network design considering conditional value at risk. Numerical Algebra, Control and Optimization, 2021, 11 (2) : 221-253. doi: 10.3934/naco.2020023 |
[10] |
Abdolhossein Sadrnia, Amirreza Payandeh Sani, Najme Roghani Langarudi. Sustainable closed-loop supply chain network optimization for construction machinery recovering. Journal of Industrial and Management Optimization, 2021, 17 (5) : 2389-2414. doi: 10.3934/jimo.2020074 |
[11] |
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 and Management Optimization, 2021 doi: 10.3934/jimo.2021117 |
[12] |
Shuaishuai Fu, Weida Chen, Junfei Ding, Dandan Wang. Optimal financing strategy in a closed-loop supply chain for construction machinery remanufacturing with emissions abatement. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022002 |
[13] |
Benrong Zheng, Xianpei Hong. Effects of take-back legislation on pricing and coordination in a closed-loop supply chain. Journal of Industrial and Management Optimization, 2022, 18 (3) : 1603-1627. doi: 10.3934/jimo.2021035 |
[14] |
Xiaohong Chen, Kui Li, Fuqiang Wang, Xihua Li. Optimal production, pricing and government subsidy policies for a closed loop supply chain with uncertain returns. Journal of Industrial and Management Optimization, 2020, 16 (3) : 1389-1414. doi: 10.3934/jimo.2019008 |
[15] |
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 and Management Optimization, 2022, 18 (2) : 1161-1183. doi: 10.3934/jimo.2021014 |
[16] |
Jia Shu, Jie Sun. Designing the distribution network for an integrated supply chain. Journal of Industrial and Management Optimization, 2006, 2 (3) : 339-349. doi: 10.3934/jimo.2006.2.339 |
[17] |
Jiuping Xu, Pei Wei. Production-distribution planning of construction supply chain management under fuzzy random environment for large-scale construction projects. Journal of Industrial and Management Optimization, 2013, 9 (1) : 31-56. doi: 10.3934/jimo.2013.9.31 |
[18] |
Xiaochen Sun, Fei Hu, Yancong Zhou, Cheng-Chew Lim. Optimal acquisition, inventory and production decisions for a closed-loop manufacturing system with legislation constraint. Journal of Industrial and Management Optimization, 2015, 11 (4) : 1355-1373. doi: 10.3934/jimo.2015.11.1355 |
[19] |
Simon Hochgerner. Symmetry actuated closed-loop Hamiltonian systems. Journal of Geometric Mechanics, 2020, 12 (4) : 641-669. doi: 10.3934/jgm.2020030 |
[20] |
Xia Zhao, Jianping Dou. Bi-objective integrated supply chain design with transportation choices: A multi-objective particle swarm optimization. Journal of Industrial and Management Optimization, 2019, 15 (3) : 1263-1288. doi: 10.3934/jimo.2018095 |
2020 Impact Factor: 1.801
Tools
Metrics
Other articles
by authors
[Back to Top]