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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

Yi Jing 1,, and  Wenchuan Li 2,

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
VariablesGeneration intervalVariablesGeneration 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}]$
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VariablesGeneration intervalVariablesGeneration 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}]$
Table 2.  The bill of each kind of core component to each type of product
AB-1B-2C-1C-2D
Ⅰ110401
Ⅱ101041
Ⅲ101041
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AB-1B-2C-1C-2D
Ⅰ110401
Ⅱ101041
Ⅲ101041
Table 3.  The demand data for new products in market of each distributor
$j=$12345
$p=$123123123123123
$t=1$378384400394395396365367389370391405398408423
$t=2$387407402380387394376395399368378393409416416
$t=3$380397393376391409384389384374397393365367389
$t=4$393395390381388391370395383393395390376395399
$t=5$398408423370391405381387394394395396374389384
$t=6$409416416368378393385386397380387394370395383
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$j=$12345
$p=$123123123123123
$t=1$378384400394395396365367389370391405398408423
$t=2$387407402380387394376395399368378393409416416
$t=3$380397393376391409384389384374397393365367389
$t=4$393395390381388391370395383393395390376395399
$t=5$398408423370391405381387394394395396374389384
$t=6$409416416368378393385386397380387394370395383
Table 4.  The demand data for remanufactured products in market of each distributor
$j=$12345
$p=$123123123123123
$t=1$157163165158166170168172172158160162158167171
$t=2$160162169160162173162163165163169171167170172
$t=3$155156160162168175158167171162168175152159166
$t=4$162163165156159168167170172156159168158163170
$t=5$158160162152159166167174174157163165155156160
$t=6$163169171158163170151163166160162169162163165
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$j=$12345
$p=$123123123123123
$t=1$157163165158166170168172172158160162158167171
$t=2$160162169160162173162163165163169171167170172
$t=3$155156160162168175158167171162168175152159166
$t=4$162163165156159168167170172156159168158163170
$t=5$158160162152159166167174174157163165155156160
$t=6$163169171158163170151163166160162169162163165
Table 5.  The quantity of EOL products available in market of each distributor
$j=$12345
$p=$123123123123123
$t=1$186188189186191197191192187184184190187198202
$t=2$190198199184195198198193195192195198199207205
$t=3$184184190181195195187198202181195195196198205
$t=4$192195198197190199199204204197190199182190191
$t=5$174198204187179195189184198186191197198193195
$t=6$182190191188189191180193194184195198187179195
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$j=$12345
$p=$123123123123123
$t=1$186188189186191197191192187184184190187198202
$t=2$190198199184195198198193195192195198199207205
$t=3$184184190181195195187198202181195195196198205
$t=4$192195198197190199199204204197190199182190191
$t=5$174198204187179195189184198186191197198193195
$t=6$182190191188189191180193194184195198187179195
Table 6.  The parameters data about joint recycling center
$c$ $p$
123456123
$UDC_{ct} $353030252530 $SDT_{pt} $100012001200
$ICQC_{ct}^{a} $101010555 $UDTC_{pt} $100100100
$\theta_{ct} $0.950.920.920.900.900.85 $ICRP_{pt}^{a} $101010
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$c$ $p$
123456123
$UDC_{ct} $353030252530 $SDT_{pt} $100012001200
$ICQC_{ct}^{a} $101010555 $UDTC_{pt} $100100100
$\theta_{ct} $0.950.920.920.900.900.85 $ICRP_{pt}^{a} $101010
Table 7.  The parameters data about products in manufacturing/remanufacturing factories
$i=$123
$p=$123123123
$SA_{pit} $250003000035000250003000035000250003000035000
$SRA_{pit} $250003000035000250003000035000250003000035000
$UAC_{pit} $590074007900600075008000605075508050
$URAC_{pit} $590074007900600075008000605075508050
$ICNP_{pit}^{f} $202020202020202020
$ICRMP_{pit}^{f} $202020202020202020
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$i=$123
$p=$123123123
$SA_{pit} $250003000035000250003000035000250003000035000
$SRA_{pit} $250003000035000250003000035000250003000035000
$UAC_{pit} $590074007900600075008000605075508050
$URAC_{pit} $590074007900600075008000605075508050
$ICNP_{pit}^{f} $202020202020202020
$ICRMP_{pit}^{f} $202020202020202020
Table 8.  The parameters data about components in manufacturing/remanufacturing factories
i=123
c=123456123456123456
SPcit250002000024000150001800018000250002000024000150001800018000250002000024000150001800018000
SRPcit100006000700050006000500010000600070005000600050001000060007000500060005000
UPCcit3900240027007095950400025002800751001000410026002900801051050
URPCcit95055065022283251000600700253035010506507502832375
ICQCcitf101010555101010555101010555
ICNCcitf151515101010151515101010151515101010
ICRCcitf151515101010151515101010151515101010
UTCacitf403030151525453535151530403030151525
PPCcit820520540135135355820520540135135355800500520120120345
MPci240080016003200640024002400800160032006400240024008001600320064002400
MRPci105035070014002800105010503507001400280010501050350700140028001050
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i=123
c=123456123456123456
SPcit250002000024000150001800018000250002000024000150001800018000250002000024000150001800018000
SRPcit100006000700050006000500010000600070005000600050001000060007000500060005000
UPCcit3900240027007095950400025002800751001000410026002900801051050
URPCcit95055065022283251000600700253035010506507502832375
ICQCcitf101010555101010555101010555
ICNCcitf151515101010151515101010151515101010
ICRCcitf151515101010151515101010151515101010
UTCacitf403030151525453535151530403030151525
PPCcit820520540135135355820520540135135355800500520120120345
MPci240080016003200640024002400800160032006400240024008001600320064002400
MRPci105035070014002800105010503507001400280010501050350700140028001050
Table 9.  The parameters data about distributors
j=12345
p=123123123123123
URCCpjt100011501150100011501150105012001200105012001200110012501250
URCDpjt90010501050900105010509501100110095011001100100011501150
SPNpjt181602067021340181602066521340181502068021345181502068021345181702069021365
SPRpjt125701474015400125701474015400125801474015410125801474015410125901476015430
USNPpjt412046904840412046904840411046904840411046904840412046904850
USRPpjt285033403490285033403490285033403500285033403500286033503500
UTCpjtda303030353535303030353535303030
ICNPpjtd202020202020202020202020202020
ICRMPpjtd202020202020202020202020202020
ICRPpjtd101010101010101010101010101010
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j=12345
p=123123123123123
URCCpjt100011501150100011501150105012001200105012001200110012501250
URCDpjt90010501050900105010509501100110095011001100100011501150
SPNpjt181602067021340181602066521340181502068021345181502068021345181702069021365
SPRpjt125701474015400125701474015400125801474015410125801474015410125901476015430
USNPpjt412046904840412046904840411046904840411046904840412046904850
USRPpjt285033403490285033403490285033403500285033403500286033503500
UTCpjtda303030353535303030353535303030
ICNPpjtd202020202020202020202020202020
ICRMPpjtd202020202020202020202020202020
ICRPpjtd101010101010101010101010101010
Table 10.  The unit transportation cost of products from factories to distributors
i123
j123451234512345
MPN1ijt154401544015460154601550015840158701578015780158401610016070161001610016070
MPN2ijt176401764017670176701772017990180001798017980179901829018270182901829018270
MPN3ijt182201822018260182601830018580186001856018560185801886018850188601886018850
MPR1ijt107301073010770107701081010970109901095010950108701109011070110901109011070
MPR2ijt126301263012650126501269012860128801284012840128601297012950129701297012950
MPR3ijt132001320013240132401329013430134501341013410134301355013530135501355013530
UTCpijtfd404050506060504050606050504040
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i123
j123451234512345
MPN1ijt154401544015460154601550015840158701578015780158401610016070161001610016070
MPN2ijt176401764017670176701772017990180001798017980179901829018270182901829018270
MPN3ijt182201822018260182601830018580186001856018560185801886018850188601886018850
MPR1ijt107301073010770107701081010970109901095010950108701109011070110901109011070
MPR2ijt126301263012650126501269012860128801284012840128601297012950129701297012950
MPR3ijt132001320013240132401329013430134501341013410134301355013530135501355013530
UTCpijtfd404050506060504050606050504040
Table 11.  The comparison results among SGA, AGA and SAGA
AlgorithmRunning resultConvergence generation
BestMeanWorstProportion of Best ResultStandard DeviationBestMeanWorst
SGA(Pcr = 0:6, Pmu = 0:005)10301400210248836510201769436%453083712736754
SGA(Pcr = 0:6, Pmu = 0:02)10489119010390498010330972820%672762616658682
SGA(Pcr = 0:8, Pmu = 0:005)10349936010314128010244155246%432193658688712
SGA(Pcr = 0:8, Pmu = 0:02)10451489410386140910330972842%566313724742766
AGA10657088410636021210591170654%262057458489511
SAGA10730207810721756210698445262%124847489527557
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AlgorithmRunning resultConvergence generation
BestMeanWorstProportion of Best ResultStandard DeviationBestMeanWorst
SGA(Pcr = 0:6, Pmu = 0:005)10301400210248836510201769436%453083712736754
SGA(Pcr = 0:6, Pmu = 0:02)10489119010390498010330972820%672762616658682
SGA(Pcr = 0:8, Pmu = 0:005)10349936010314128010244155246%432193658688712
SGA(Pcr = 0:8, Pmu = 0:02)10451489410386140910330972842%566313724742766
AGA10657088410636021210591170654%262057458489511
SAGA10730207810721756210698445262%124847489527557
Table 12.  Definition of the subscripts
NotationDescription
$t$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
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NotationDescription
$t$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
Table 13.  Definition of the variables occurred in the first level model
NotationDescription
$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
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NotationDescription
$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
Table 14.  Definition of the variables occurred in the second level model
NotationDescription
$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
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NotationDescription
$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
Table 15.  Definition of the variables occurred in the third level model
NotationDescription
$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
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NotationDescription
$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
Table 16.  Definition of the parameters occurred in the first level model
NotationDescription
$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
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NotationDescription
$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
Table 17.  Definition of the parameters occurred in the second level model
NotationDescription
$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
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NotationDescription
$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
Table 18.  Definition of the parameters occurred in the third level model
NotationDescription
$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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NotationDescription
$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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