Integrated recycling-integrated production - distribution planning for decentralized closed-loop supply chain

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April 2018, 14(2): 511-539. doi: 10.3934/jimo.2017058

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

* Corresponding authorr: Yi Jing

Received May 2015 Published June 2017

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.

Keywords: Recycling-integrated production - distribution planning, closed-loop supply chain, multi - level program, SAGA, hierarchical iteration.

Mathematics Subject Classification: Primary: 90B50; Secondary: 90C10.

Citation: Yi Jing, Wenchuan Li. Integrated recycling-integrated production - distribution planning for decentralized closed-loop supply chain. Journal of Industrial & Management Optimization, 2018, 14 (2) : 511-539. doi: 10.3934/jimo.2017058

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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[14]	B. Golany, J. Yang and G. Yu, Economic lot-sizing with remanufacturing options, IIE Transactions, 33 (2001), 995-1003. doi: 10.1080/07408170108936890. Google Scholar
[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. Google Scholar
[16]	J. Holland, Adaptation in Natural and Artificial System, The University of Michigan Press, Ann Arbor, 1975. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[40]	X. P. Wang and L. M. Cao, Genetic Algorithm-Theory, Application and Software Implementation, Xi An Jiao Tong University Press, Shan Xi, 2002.Google Scholar
[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. Google Scholar
[42]	P. Yilmaz and B. Çatay, Strategic level three-stage production distribution planning with capacity expansion, Computers & Industrial Engineering, 51 (2006), 609-620. Google Scholar
[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. Google Scholar
[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. Google Scholar

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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[14]	B. Golany, J. Yang and G. Yu, Economic lot-sizing with remanufacturing options, IIE Transactions, 33 (2001), 995-1003. doi: 10.1080/07408170108936890. Google Scholar
[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. Google Scholar
[16]	J. Holland, Adaptation in Natural and Artificial System, The University of Michigan Press, Ann Arbor, 1975. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[40]	X. P. Wang and L. M. Cao, Genetic Algorithm-Theory, Application and Software Implementation, Xi An Jiao Tong University Press, Shan Xi, 2002.Google Scholar
[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. Google Scholar
[42]	P. Yilmaz and B. Çatay, Strategic level three-stage production distribution planning with capacity expansion, Computers & Industrial Engineering, 51 (2006), 609-620. Google Scholar
[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. Google Scholar
[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. Google Scholar

Figure 1. Diagrammatic sketch for the two - point crossover

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Figure 2. Diagrammatic sketch for the inverted sequence mutation

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Figure 3. The changes of computational results with the values of $M$ and $N$

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Table 1. The generation intervals of decision variables in encoding

Variables	Generation interval	Variables	Generation interval
$x_{pit} $	$[0, MA_{pi}/ab_{pi}]$	$fdn_{pijt} $	$\displaystyle \left[0, \left(MT_{i}^{f} -\sum\limits_{N_{p} =1}^{p-1}{\sum\limits_{N_{j} =1}^J {fdn_{pijt} \cdot tpb_{p}}} \right. \right. $ $\displaystyle \left. \left. -\sum\limits_{N_{j} =1}^{j-1}{fdn_{pijt} \cdot tpb_{p}} \right)\Bigg/tpb_{p} \right]$
$y_{pit} $	$[0, MRA_{pi}/rab_{pi}]$	$fdr_{pijt} $	$\displaystyle \left[0, \left(MT_{i}^{f} -\sum\limits_{N_{p} =1}^P {\sum\limits_{N_{j} =1}^J {fdn_{pijt} \cdot tpb_{p}}} \right. \right. $ $\displaystyle -\sum\limits_{N_{p} =1}^{p-1}{\sum\limits_{N_{j} =1}^J {fdr_{pijt} \cdot tpb_{p}}} $ $\displaystyle \left. \left.-\sum\limits_{N_{j} =1}^{j-1} {fdr_{pijt} \cdot tpb_{p}} \right)\Bigg/tpb_{p} \right]$
$v_{cit} $	$[0, MP_{ci}/pb_{ci}]$	$subc_{cit} $	$\displaystyle \left[0, {v_{cit} \cdot pb_{c}} -\sum\limits_{p=1}^P {BOC_{pc} \cdot x_{pit} \cdot ab_{p} +\overline \zeta_{ci}^{f}}\right]$
$z_{cit} $	$[0, MRP_{ci}/rpb_{ci}]$

$j=$	1			2			3			4			5
$p=$	1	2	3	1	2	3	1	2	3	1	2	3	1	2	3
$t=1$	378	384	400	394	395	396	365	367	389	370	391	405	398	408	423
$t=2$	387	407	402	380	387	394	376	395	399	368	378	393	409	416	416
$t=3$	380	397	393	376	391	409	384	389	384	374	397	393	365	367	389
$t=4$	393	395	390	381	388	391	370	395	383	393	395	390	376	395	399
$t=5$	398	408	423	370	391	405	381	387	394	394	395	396	374	389	384
$t=6$	409	416	416	368	378	393	385	386	397	380	387	394	370	395	383

	$c$							$p$
	1	2	3	4	5	6		1	2	3
$UDC_{ct} $	35	30	30	25	25	30	$SDT_{pt} $	1000	1200	1200
$ICQC_{ct}^{a} $	10	10	10	5	5	5	$UDTC_{pt} $	100	100	100
$\theta_{ct} $	0.95	0.92	0.92	0.90	0.90	0.85	$ICRP_{pt}^{a} $	10	10	10

$i=$	1			2			3
$p=$	1	2	3	1	2	3	1	2	3
$SA_{pit} $	25000	30000	35000	25000	30000	35000	25000	30000	35000
$SRA_{pit} $	25000	30000	35000	25000	30000	35000	25000	30000	35000
$UAC_{pit} $	5900	7400	7900	6000	7500	8000	6050	7550	8050
$URAC_{pit} $	5900	7400	7900	6000	7500	8000	6050	7550	8050
$ICNP_{pit}^{f} $	20	20	20	20	20	20	20	20	20
$ICRMP_{pit}^{f} $	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
SP_cit	25000	20000	24000	15000	18000	18000	25000	20000	24000	15000	18000	18000	25000	20000	24000	15000	18000	18000
SRP_cit	10000	6000	7000	5000	6000	5000	10000	6000	7000	5000	6000	5000	10000	6000	7000	5000	6000	5000
UPC_cit	3900	2400	2700	70	95	950	4000	2500	2800	75	100	1000	4100	2600	2900	80	105	1050
URPC_cit	950	550	650	22	28	325	1000	600	700	25	30	350	1050	650	750	28	32	375
ICQC_cit^f	10	10	10	5	5	5	10	10	10	5	5	5	10	10	10	5	5	5
ICNC_cit^f	15	15	15	10	10	10	15	15	15	10	10	10	15	15	15	10	10	10
ICRC_cit^f	15	15	15	10	10	10	15	15	15	10	10	10	15	15	15	10	10	10
UTCa_cit^f	40	30	30	15	15	25	45	35	35	15	15	30	40	30	30	15	15	25
PPC_cit	820	520	540	135	135	355	820	520	540	135	135	355	800	500	520	120	120	345
MP_ci	2400	800	1600	3200	6400	2400	2400	800	1600	3200	6400	2400	2400	800	1600	3200	6400	2400
MRP_ci	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
URCC_pjt	1000	1150	1150	1000	1150	1150	1050	1200	1200	1050	1200	1200	1100	1250	1250
URCD_pjt	900	1050	1050	900	1050	1050	950	1100	1100	950	1100	1100	1000	1150	1150
SPN_pjt	18160	20670	21340	18160	20665	21340	18150	20680	21345	18150	20680	21345	18170	20690	21365
SPR_pjt	12570	14740	15400	12570	14740	15400	12580	14740	15410	12580	14740	15410	12590	14760	15430
USNP_pjt	4120	4690	4840	4120	4690	4840	4110	4690	4840	4110	4690	4840	4120	4690	4850
USRP_pjt	2850	3340	3490	2850	3340	3490	2850	3340	3500	2850	3340	3500	2860	3350	3500
UTC_pjt^da	30	30	30	35	35	35	30	30	30	35	35	35	30	30	30
ICNP_pjt^d	20	20	20	20	20	20	20	20	20	20	20	20	20	20	20
ICRMP_pjt^d	20	20	20	20	20	20	20	20	20	20	20	20	20	20	20
ICRP_pjt^d	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
MPN_1ijt	15440	15440	15460	15460	15500	15840	15870	15780	15780	15840	16100	16070	16100	16100	16070
MPN_2ijt	17640	17640	17670	17670	17720	17990	18000	17980	17980	17990	18290	18270	18290	18290	18270
MPN_3ijt	18220	18220	18260	18260	18300	18580	18600	18560	18560	18580	18860	18850	18860	18860	18850
MPR_1ijt	10730	10730	10770	10770	10810	10970	10990	10950	10950	10870	11090	11070	11090	11090	11070
MPR_2ijt	12630	12630	12650	12650	12690	12860	12880	12840	12840	12860	12970	12950	12970	12970	12950
MPR_3ijt	13200	13200	13240	13240	13290	13430	13450	13410	13410	13430	13550	13530	13550	13550	13530
UTC_pijt^fd	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(P_cr = 0:6, P_mu = 0:005)	103014002	102488365	102017694	36%	453083	712	736	754
SGA(P_cr = 0:6, P_mu = 0:02)	104891190	103904980	103309728	20%	672762	616	658	682
SGA(P_cr = 0:8, P_mu = 0:005)	103499360	103141280	102441552	46%	432193	658	688	712
SGA(P_cr = 0:8, P_mu = 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
$t$	the index set of periods, $\{1, 2, \cdots, T\}$
$p$	the index set of product type, $\{1, 2, \cdots, P\}$
$c$	the index set of component kind, $\{1, 2, \cdots, C\}$
$i$	the index set of manufacturing/remanufacturing factory, $\{1,$ $ 2,$ $ \cdots,$ $ I\}$
$j$	the index set of distributor, $\{1, 2, \cdots, J\}$
$lt_{1},lt_{2},lt_{3} $	the accumulative leading time of the joint recycling center, manufacturing/remanufacturing factories and distribution centers, respectively

Notation	Description
$af_{cit} $	the quantity of batches of qualified component $c$ to be transported from the recycling center to factory $i$ in period $t$
$da_{pjt} $	the quantity of batches of return product $p$ to be transported from distributor $j$ to the recycling center in period $t$
$\sigma_{pt} $	the binary variable indicating whether return product $p$ is disassembled & tested in batches in period $t$
$dt_{pt} $	the quantity of batches of return product $p$ to be disassembled & tested in period $t$
$d_{ct} $	the quantity of component $c$ to be disposed in period $t$
$\alpha_{pt}^{a},\beta_{ct}^{a} $	the inventory of return product $p$ and qualified component $c$ at the recycling center at the end of period $t$, respectively

Notation	Description
$fdn_{pijt},fdr_{pijt} $	the quantity of batches of new and remanufacturing product $p$ to be transported from factory $i$ to distributor $j$ in period $t$, respectively
$\eta_{pit},\delta_{pit} $	the binary variable indicating whether new and remanufacturing product $p$ is assembled by factory $i$ in batches in period $t$, respectively
$x_{pit},y_{pit} $	the quantity of batches of new and remanufactured product $p$ to be assembled at factory $i$ in period $t$, respectively
$\pi_{cit},\tau_{cit} $	the binary variable indicating whether component $c$ is newly processed and reprocessed by factory $i$ in batches in period $t$, respectively
$v_{cit},z_{cit} $	the quantity of batches of component $c$ to be processed and reprocessed at factory $i$ in period $t$, respectively
$\lambda_{pit}^{f},\chi_{pit}^{f} $	the inventory of new and remanufactured product $p$ at factory $i$ at the end of period $t$, respectively
$\beta_{cit}^{f},\zeta_{cit}^{f},\xi_{cit}^{f} $	the inventory of qualified, new and remanufactured component $c$ at factory $i$ at the end of period $t$, respectively
$subc_{cit} $	the quantity of one-way substitution for component $c$ at factory $i$ in period $t$
$af_{cit} $	this notation has occurred in the first level model

	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

$j=$	1			2			3			4			5
$p=$	1	2	3	1	2	3	1	2	3	1	2	3	1	2	3
$t=1$	157	163	165	158	166	170	168	172	172	158	160	162	158	167	171
$t=2$	160	162	169	160	162	173	162	163	165	163	169	171	167	170	172
$t=3$	155	156	160	162	168	175	158	167	171	162	168	175	152	159	166
$t=4$	162	163	165	156	159	168	167	170	172	156	159	168	158	163	170
$t=5$	158	160	162	152	159	166	167	174	174	157	163	165	155	156	160
$t=6$	163	169	171	158	163	170	151	163	166	160	162	169	162	163	165

$j=$	1			2			3			4			5
$p=$	1	2	3	1	2	3	1	2	3	1	2	3	1	2	3
$t=1$	157	163	165	158	166	170	168	172	172	158	160	162	158	167	171
$t=2$	160	162	169	160	162	173	162	163	165	163	169	171	167	170	172
$t=3$	155	156	160	162	168	175	158	167	171	162	168	175	152	159	166
$t=4$	162	163	165	156	159	168	167	170	172	156	159	168	158	163	170
$t=5$	158	160	162	152	159	166	167	174	174	157	163	165	155	156	160
$t=6$	163	169	171	158	163	170	151	163	166	160	162	169	162	163	165

Notation	Description
$nss_{pjt},rss_{pjt} $	the quantity of new and remanufactured product $p$ in short supply at distributor $j$ in period $t$, respectively
$\gamma_{pjt} $	the quantity of EOL product $p$ to be recycled by distributor $j$ from downstream markets in period $t$
$\lambda_{pjt}^{d},\chi_{pjt}^{d},\alpha_{pjt}^{d} $	the inventory of new, remanufactured and return product $p$ at distributor $j$ at the end of period $t$, respectively
$da_{pjt} $	this natation has occurred in the first level model
$fdn_{pijt},fdr_{pijt} $	these notations have occurred in second level model

Notation	Description
$tcb_{c} $	the quantity of qualified component $c$ transported per batch from the recycling center to factories
$trb_{p} $	the quantity of return product $p$ transported per batch from distributors to the recycling center
$dtb_{p} $	the quantity of return product $p$ disassembled & tested per batch
$PPC_{cit} $	the unit purchase cost of qualified component $c$ paid to the recycling center by factory $i$ in period $t$
$URCC_{pjt} $	the unit recycling cost of return product $p$ paid to distributor $j$ by the recycling center in period $t$
$SDT_{pt} $	the set-up cost incurred if return product $p$ is disassembled & tested in batches in period $t$
$UDTC_{pt} $	the unit disassembly & tested cost of return product $p$ in period $t$
$UDC_{ct} $	the unit disposing cost of component $c$ in period $t$
$ICQC_{ct}^{a},ICRP_{pt}^{a} $	the unit inventory cost of qualified component $c$ and return product $p$ at the recycling center in period $t$, respectively
$UTC_{cit}^{af} $	the unit transportation cost of qualified component $c$ from the recycling center to factory $i$ in period $t$
$BOC_{pc} $	the bill of component $c$ to product $p$
$\theta_{ct} $	the remanufacturable rate of component $c$ in period $t$
$\overline \alpha_{p}^{a},\overline \beta_{c}^{a} $	the maximum inventory level of return products and qualified components at the recycling center, respectively
$MDT_{p} $	the maximum quantity of return product $p$ can be disassembled & tested in every periods
$MT^{a}$	the maximum quantity of qualified components can be transported from the recycling center to factories in every periods

Notation	Description
$MPN_{pijt},MPR_{pijt} $	the middle price of new and remanufactured product $p$ paid to factory $i$ by distributor $j$ in period $t$, respectively
$tpb_{p} $	the quantity of new or remanufactured product $p$ transported per batch from factories todistributors
$ab_{pi},rab_{pi} $	the quantity of new and remanufactured product $p$ assembled per batch at factory $i$, respectively
$pb_{ci},rpb_{ci} $	the quantity of component $c$ processed and reprocessed per batch at factory $i$, respectively
$SA_{pit},SRA_{pit} $	the set-up cost incurred if new and remanufactured product $p$ is assembled in batches at factory $i$ in period $t$, respectively
$UAC_{pit},URAC_{pit} $	the unit assembly cost of new and remanufactured product $p$ at factory $i$ in period $t$, respectively
$SP_{cit},SRP_{cit} $	the set-up cost incurred if component $c$ is newly processed and reprocessed in batches at factory $i$ in period $t$, respectively
$UPC_{cit},URPC_{cit} $	the unit processing and reprocessing cost of component $c$ at factory $i$ in period $t$, respectively
$ICNP_{pit}^{f},ICRMP_{pit}^{f} $	the unit inventory cost of new and remanufactured product $p$ at factory $i$ in period $t$, respectively
$ICQC_{cit}^{f},ICNC_{cit}^{f},ICRC_{cit}^{f} $	the unit inventory cost of qualified, new and remanufactured component $c$ at factory $i$ in period $t$, respectively
$UTC_{pijt}^{fd} $	the unit transportation cost of product $p$ from factory $i$ to distributor $j$ in period $t$
$\overline \beta_{ci}^{f},\overline \zeta_{ci}^{f},\overline \xi_{ci}^{f},\overline \lambda_{pi}^{f},\overline \chi_{pi}^{f} $	the maximum inventory level of qualified components, new components, remanufactured components, new products andremanufactured products at factory $i$, respectively
$MA_{pi},MRA_{pi} $	the maximum quantity of new and remanufactured product $p$ can be assembled in factory $i$ in every periods, respectively
$MP_{ci},MRP_{ci} $	the maximum quantity of component $c$ can be processed and reprocessed in factory $i$ in every periods, respectively
$MT_{i}^{f} $	the maximum quantity of products can be transported from factory $i$ to distributors in every periods
$PPC_{cit},tcb_{c},BOC_{pc} $	these notations have occurred in the first level model

Notation	Description
$SPN_{pjt},SPR_{pjt} $	the selling price of new and remanufactured product $p$ at distributor $j$ in period $t$, respectively
$DNM_{pjt},DRM_{pjt} $	the demands of new and remanufactured product $p$ in the market of distributor $j$ in period $t$, respectively
$URCD_{pjt} $	the unit recycling cost of EOL product $p$ paid to retailers or customers by distributor $j$ in period $t$
$USNP_{pjt},USRP_{pjt} $	the unit shortage cost of new and remanufactured product $p$ paid by distributor $j$ in period $t$, respectively
$ICNP_{pjt}^{d},ICRMP_{pjt}^{d},ICRP_{pjt}^{d} $	the unit inventory cost of new, remanufactured and return product $p$ at distributor $j$ in period $t$, respectively
$UTC_{pjt}^{da} $	the unit transportation cost of return product $p$ from distributor $j$ to the recycling center in period $t$
$EPA_{pjt} $	the quantity of EOL product $p$ available in the market of distributor $j$ in period $t$
$\overline \lambda_{pj}^{d},\overline \chi_{pj}^{d},\overline \alpha_{pj}^{d} $	the maximum inventory level of new, remanufactured and return products at distributor $j$, respectively
$MT_{j}^{d} $	the maximum quantity of return products can be transported from distributor $j$ to the recycling center in every periods
$URCC_{pjt},trb_{p} $	these notations have occurred in the first level model
$MPN_{pijt},tpb_{p},MPR_{pijt} $	these notations have occurred in the second level model

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