
-
Previous Article
Numerical solution to optimal control problems of oscillatory processes
- JIMO Home
- This Issue
-
Next Article
Open-loop equilibrium mean-variance reinsurance, new business and investment strategies with constraints
Online First articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Online First publication benefits the research community by making new scientific discoveries known as quickly as possible.
Readers can access Online First articles via the “Online First” tab for the selected journal.
Green cross-dock based supply chain network design under demand uncertainty using new metaheuristic algorithms
1. | Department of management, Firoozkooh branch, Islamic Azad University, Firoozkooh, Iran |
2. | Department of Industrial Engineering and Future Studies, Faculty of Engineering, University of Isfahan, Iran |
3. | Department of Industrial Engineering, Qaemshahr branch, Islamic Azad University, Qaemshahr, Iran |
This study concerns the optimization of green supply chain network design under demand uncertainty. The issue of demand uncertainty has been addressed using a scenario-based analysis approach. The main contribution of this research is to investigate the optimization of cross-dock based supply chain under uncertainty using scenario-based formulation and metaheuristic algorithms. The problem has been formulated as a two-objective mathematical model with the objectives of minimizing the costs and minimizing the environmental impact of the supply chain. Two metaheuristic algorithms, namely non-dominated sorting genetic algorithm II (NSGA-II) and multi-objective invasive weed optimization (MOIWO), have been developed to optimize this mathematical model. This paper focuses on the use of new metaheuristic algorithms such as MOIWO in green supply chain network design, which has received less attention in previous studies. The performance of the two solution methods has been evaluated in terms of three indices, which measure the quality, spacing, and diversification of solutions. Evaluations indicate that the developed MOIWO algorithm produces more Pareto solutions and solutions of higher quality than NSGA-II. A performance test carried out with 31 problem instances of different sizes shows that the two methods perform similarly in terms of the spread of solutions on the Pareto front, but MOIWO provides higher quality solutions than NSGA-II.
References:
[1] |
A. Abdi, N. Akbarpour, A. S. Amiri and M. Hajiaghaei-Keshteli, Innovative approaches to design and address green supply chain network with simultaneous pick-up and split delivery, Journal of Cleaner Production, 250 (2020), 119437.
doi: 10.1016/j.jclepro.2019.119437. |
[2] |
S. H. Amin, G. Zhang and M. Hajiaghaei-Keshteli,
An integrated model for closed-loop supply chain configuration and supplier selection: Multi-objective approach, Expert Systems with Applications, 39 (2012), 6782-6791.
doi: 10.1016/j.eswa.2011.12.056. |
[3] |
A. Baghalian, S. Rezapour and R. Z. Farahani,
Robust supply chain network design with service level against disruptions and demand uncertainties: A real-life case, European Journal of Operational Research, 227 (2013), 199-215.
doi: 10.1016/j.ejor.2012.12.017. |
[4] |
A. I. Barros, R. Dekker and V. Scholten,
A two-level network for recycling sand: A case study, European Journal of Operational Research, 110 (1998), 199-214.
doi: 10.1016/S0377-2217(98)00093-9. |
[5] |
T. F. Burgess, P. Grimshaw, L. H. Huatuco and N. E. Shaw, Mapping the operations and supply chain management field: A journal governance perspective, International Journal of Operations & Production Management, (2017).
doi: 10.1108/IJOPM-01-2016-0043. |
[6] |
K. Deb, A. Pratap, S. Agarwal and T. Meyarivan,
A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Transactions on Evolutionary Computation, 6 (2002), 182-197.
doi: 10.1109/4235.996017. |
[7] |
B. Fahimnia, J. Sarkis, F. Dehghanian, N. Banihashemi and S. Rahman,
The impact of carbon pricing on a closed-loop supply chain: An Australian case study, Journal of Cleaner Production, 59 (2013), 210-225.
doi: 10.1016/j.jclepro.2013.06.056. |
[8] |
R. Z. Farahani, S. Rezapour and L. Kardar, Supply Chain Sustainability and Raw Material Management: Concepts and Processes, (2012).
doi: 10.4018/978-1-61350-504-5. |
[9] |
Y.-H. Feng and G.-G. Wang,
Binary moth search algorithm for discounted 0-1 knapsack problem, IEEE Access, 6 (2018), 10708-10719.
doi: 10.1109/ACCESS.2018.2809445. |
[10] |
Y. Feng, S. Deb, G. G. Wang and A. H. Alavi, Monarch butterfly optimization: A comprehensive review, Expert Systems with Applications, (2020), 114418.
doi: 10.1016/j.eswa.2020.114418. |
[11] |
Y. Feng, G.-G. Wang, W. Li and N. Li,
Multi-strategy monarch butterfly optimization algorithm for discounted 0-1 knapsack problem, Neural Computing and Applications, 30 (2018), 3019-3036.
doi: 10.1007/s00521-017-2903-1. |
[12] |
Y. Feng, X. Yu and G.-G. Wang, A novel monarch butterfly optimization with global position updating operator for large-scale 0-1 Knapsack problems, Mathematics, 7 (2019), 1056.
doi: 10.3390/math7111056. |
[13] |
H. Garg,
A hybrid PSO-GA algorithm for constrained optimization problems, Applied Mathematics and Computation, 274 (2016), 292-305.
doi: 10.1016/j.amc.2015.11.001. |
[14] |
H. Garg,
A hybrid GSA-GA algorithm for constrained optimization problems, Information Sciences, 478 (2019), 499-523.
doi: 10.1016/j.ins.2018.11.041. |
[15] |
Z. Ghelichi, M. Saidi-Mehrabad and M. S. Pishvaee,
A stochastic programming approach toward optimal design and planning of an integrated green biodiesel supply chain network under uncertainty: A case study, Energy, 156 (2018), 661-687.
doi: 10.1016/j.energy.2018.05.103. |
[16] |
S. Gholipour, A. Ashoftehfard and H. Mina,
Green supply chain network design considering inventory-location-routing problem: A fuzzy solution approach, International Journal of Logistics Systems and Management, 35 (2020), 436-452.
doi: 10.1504/IJLSM.2020.106272. |
[17] |
H. Gholizadeh and H. Fazlollahtabar, Robust optimization and modified genetic algorithm for a closed loop green supply chain under uncertainty: Case study in melting industry, Computers & Industrial Engineering, 147 (2020), 106653.
doi: 10.1016/j.cie.2020.106653. |
[18] |
A. Goli, H. K. Zare, R. Tavakkoli-Moghaddam and A. Sadegheih,
Multiobjective fuzzy mathematical model for a financially constrained closed-loop supply chain with labor employment, Computational Intelligence, 36 (2020), 4-34.
doi: 10.1111/coin.12228. |
[19] |
K. Govindan, H. Soleimani and D. Kannan,
Reverse logistics and closed-loop supply chain: A comprehensive review to explore the future, European Journal of Operational Research, 240 (2015), 603-626.
doi: 10.1016/j.ejor.2014.07.012. |
[20] |
V. D. R. Guide, T. P. Harrison and L. N. Van Wassenhove,
The challenge of closed-loop supply chains, Interfaces, 33 (2003), 3-6.
doi: 10.1287/inte.33.6.3.25182. |
[21] |
H. C. Jang, Y. N. Lien and T. C. Tsai, Rescue information system for earthquake disasters based on MANET emergency communication platform. In Proceedings of the 2009 International Conference on Wireless Communications and Mobile Computing: Connecting the World Wirelessly, ACM, (2009), 623–627.
doi: 10.1145/1582379.1582514. |
[22] |
V. Jayaraman, V. D. R. Guide Jr and R. Srivastava, A closed-loop logistics model for remanufacturing, Journal of the Operational Research Society, (1999), 497–508.
doi: 10.1057/palgrave.jors.2600716. |
[23] |
G. Kannan, P. Sasikumar and K. Devika,
A genetic algorithm approach for solving a closed loop supply chain model: A case of battery recycling, Applied Mathematical Modelling, 34 (2010), 655-670.
doi: 10.1016/j.apm.2009.06.021. |
[24] |
N. Lamba and P. Thareja, Developing the structural model based on analyzing the relationship between the barriers of green supply chain management using TOPSIS approach, Materials Today: Proceedings, (2020). |
[25] |
J. Li, H. Lei, A. H. Alavi and G.-G. Wang, Elephant herding optimization: variants, hybrids, and applications, Mathematics, 8 (2020), 1415.
doi: 10.3390/math8091415. |
[26] |
L. Liang and H. J. Quesada,
Green design of a cellulosic butanol supply chain network: A case study of sorghum stem bio-butanol in missouri, BioResources, 13 (2018), 5617-5642.
doi: 10.15376/biores.13.3.5617-5642. |
[27] |
R. Lotfi, Y. Z. Mehrjerdi, M. S. Pishvaee, A. Sadeghieh and G.-W. Weber, A robust optimization model for sustainable and resilient closed-loop supply chain network design considering conditional value at risk, Numerical Algebra, Control & Optimization, 11 (2021), 221-–253.
doi: 10.3934/naco.2020023. |
[28] |
D. Louwers, B. J. Kip, E. Peters, F. Souren, S. Douwe and P. Flapper,
A facility location allocation model for reusing carpet materials, Computers & Industrial Engineering, 36 (1919), 855-869.
doi: 10.1016/S0360-8352(99)00168-0. |
[29] |
A. R. Mehrabian and C. Lucas,
A novel numerical optimization algorithm inspired from weed colonization, Ecological Informatics, 1 (2006), 355-366.
doi: 10.1016/j.ecoinf.2006.07.003. |
[30] |
S. Niroomand, H. Garg and A. Mahmoodirad,
An intuitionistic fuzzy two stage supply chain network design problem with multi-mode demand and multi-mode transportation, ISA Transactions, 107 (2020), 117-133.
doi: 10.1016/j.isatra.2020.07.033. |
[31] |
R. S. Rad and N. Nahavandi, A novel multi-objective optimization model for integrated problem of green closed loop supply chain network design and quantity discount, Applied Mathematical Modelling, (2018). |
[32] |
A. Shabani, R. F. Saen and S. M. R. Torabipour,
A new benchmarking approach in Cold Chain, Appl. Math. Model., 36 (2012), 212-224.
doi: 10.1016/j.apm.2011.05.051. |
[33] |
T. Spengler, H. Püchert, T. Penkuhn and O. Rentz, Environmental integrated production and recycling management, In Produktion und Umwelt, Springer Berlin Heidelberg, (1997), 239–257. |
[34] |
M. Talaei, B. F. Moghaddam, M. S. Pishvaee, A. Bozorgi-Amiri and S. Gholamnejad,
A robust fuzzy optimization model for carbon-efficient closed-loop supply chain network design problem: A numerical illustration in electronics industry, Journal of Cleaner Production, 113 (2016), 662-673.
doi: 10.1016/j.jclepro.2015.10.074. |
[35] |
M.-L. Tseng, M. S. Islam, N. Karia and F. Ahmad, A literature review on green supply chain management: Trends and future challenges, Resources, Conservation and Recycling, 141, (2019), 145–162.
doi: 10.1016/j.resconrec.2018.10.009. |
[36] |
G. G. Wang, Moth search algorithm: A bio-inspired metaheuristic algorithm for global optimization problems, Memetic Computing, 10, (2018), 151–164. |
[37] |
G.-G. Wang, S. Deb and L. D. S. Coelho, Elephant herding optimization, In 2015 3rd International Symposium on Computational and Business Intelligence (ISCBI), (2015), 1–5.
doi: 10.1109/ISCBI.2015.8. |
[38] |
G.-G. Wang, S. Deb and L. D. S. Coelho, Earthworm optimization algorithm: A bio-inspired metaheuristic algorithm for global optimization problems, International Journal of Bio-Inspired Computation, 12, (2018), 1–22.
doi: 10.1504/IJBIC.2018.093328. |
[39] |
G.-G. Wang, S. Deb and Z. Cui, Monarch butterfly optimization, Neural computing and applications, 31, (2019), 1995–2014. |
[40] |
G.-G. Wang, S. Deb, X.-Z. Gao and L. D. S. Coelho, A new metaheuristic optimization algorithm motivated by elephant herding behavior, International Journal of Bio-Inspired Computation, 8, (2016), 394–409.
doi: 10.1504/IJBIC.2016.10002274. |
[41] |
W. Xing, S. Y. Wang, Q. H. Zhao and G. W. Hua, Impact of fairness on strategies in dual-channel supply chain, Systems Engineering-Theory & Practice, 31, (2011), 1249–1256. |
[42] |
Q. Zhu, J. Sarkis and K.-H. Lai, Green supply chain management implications for "closing the loop", Transportation Research Part E: Logistics and Transportation Review, 44, (2008), 1–18.
doi: 10.1016/j.tre.2006.06.003. |
[43] |
E. Zitzler and L. Thiele, Multiobjective evolutionary algorithms: A comparative case study and the strength Pareto approach, IEEE Transactions on Evolutionary Computation, 3, (1999), 257–271.
doi: 10.1109/4235.797969. |
show all references
References:
[1] |
A. Abdi, N. Akbarpour, A. S. Amiri and M. Hajiaghaei-Keshteli, Innovative approaches to design and address green supply chain network with simultaneous pick-up and split delivery, Journal of Cleaner Production, 250 (2020), 119437.
doi: 10.1016/j.jclepro.2019.119437. |
[2] |
S. H. Amin, G. Zhang and M. Hajiaghaei-Keshteli,
An integrated model for closed-loop supply chain configuration and supplier selection: Multi-objective approach, Expert Systems with Applications, 39 (2012), 6782-6791.
doi: 10.1016/j.eswa.2011.12.056. |
[3] |
A. Baghalian, S. Rezapour and R. Z. Farahani,
Robust supply chain network design with service level against disruptions and demand uncertainties: A real-life case, European Journal of Operational Research, 227 (2013), 199-215.
doi: 10.1016/j.ejor.2012.12.017. |
[4] |
A. I. Barros, R. Dekker and V. Scholten,
A two-level network for recycling sand: A case study, European Journal of Operational Research, 110 (1998), 199-214.
doi: 10.1016/S0377-2217(98)00093-9. |
[5] |
T. F. Burgess, P. Grimshaw, L. H. Huatuco and N. E. Shaw, Mapping the operations and supply chain management field: A journal governance perspective, International Journal of Operations & Production Management, (2017).
doi: 10.1108/IJOPM-01-2016-0043. |
[6] |
K. Deb, A. Pratap, S. Agarwal and T. Meyarivan,
A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Transactions on Evolutionary Computation, 6 (2002), 182-197.
doi: 10.1109/4235.996017. |
[7] |
B. Fahimnia, J. Sarkis, F. Dehghanian, N. Banihashemi and S. Rahman,
The impact of carbon pricing on a closed-loop supply chain: An Australian case study, Journal of Cleaner Production, 59 (2013), 210-225.
doi: 10.1016/j.jclepro.2013.06.056. |
[8] |
R. Z. Farahani, S. Rezapour and L. Kardar, Supply Chain Sustainability and Raw Material Management: Concepts and Processes, (2012).
doi: 10.4018/978-1-61350-504-5. |
[9] |
Y.-H. Feng and G.-G. Wang,
Binary moth search algorithm for discounted 0-1 knapsack problem, IEEE Access, 6 (2018), 10708-10719.
doi: 10.1109/ACCESS.2018.2809445. |
[10] |
Y. Feng, S. Deb, G. G. Wang and A. H. Alavi, Monarch butterfly optimization: A comprehensive review, Expert Systems with Applications, (2020), 114418.
doi: 10.1016/j.eswa.2020.114418. |
[11] |
Y. Feng, G.-G. Wang, W. Li and N. Li,
Multi-strategy monarch butterfly optimization algorithm for discounted 0-1 knapsack problem, Neural Computing and Applications, 30 (2018), 3019-3036.
doi: 10.1007/s00521-017-2903-1. |
[12] |
Y. Feng, X. Yu and G.-G. Wang, A novel monarch butterfly optimization with global position updating operator for large-scale 0-1 Knapsack problems, Mathematics, 7 (2019), 1056.
doi: 10.3390/math7111056. |
[13] |
H. Garg,
A hybrid PSO-GA algorithm for constrained optimization problems, Applied Mathematics and Computation, 274 (2016), 292-305.
doi: 10.1016/j.amc.2015.11.001. |
[14] |
H. Garg,
A hybrid GSA-GA algorithm for constrained optimization problems, Information Sciences, 478 (2019), 499-523.
doi: 10.1016/j.ins.2018.11.041. |
[15] |
Z. Ghelichi, M. Saidi-Mehrabad and M. S. Pishvaee,
A stochastic programming approach toward optimal design and planning of an integrated green biodiesel supply chain network under uncertainty: A case study, Energy, 156 (2018), 661-687.
doi: 10.1016/j.energy.2018.05.103. |
[16] |
S. Gholipour, A. Ashoftehfard and H. Mina,
Green supply chain network design considering inventory-location-routing problem: A fuzzy solution approach, International Journal of Logistics Systems and Management, 35 (2020), 436-452.
doi: 10.1504/IJLSM.2020.106272. |
[17] |
H. Gholizadeh and H. Fazlollahtabar, Robust optimization and modified genetic algorithm for a closed loop green supply chain under uncertainty: Case study in melting industry, Computers & Industrial Engineering, 147 (2020), 106653.
doi: 10.1016/j.cie.2020.106653. |
[18] |
A. Goli, H. K. Zare, R. Tavakkoli-Moghaddam and A. Sadegheih,
Multiobjective fuzzy mathematical model for a financially constrained closed-loop supply chain with labor employment, Computational Intelligence, 36 (2020), 4-34.
doi: 10.1111/coin.12228. |
[19] |
K. Govindan, H. Soleimani and D. Kannan,
Reverse logistics and closed-loop supply chain: A comprehensive review to explore the future, European Journal of Operational Research, 240 (2015), 603-626.
doi: 10.1016/j.ejor.2014.07.012. |
[20] |
V. D. R. Guide, T. P. Harrison and L. N. Van Wassenhove,
The challenge of closed-loop supply chains, Interfaces, 33 (2003), 3-6.
doi: 10.1287/inte.33.6.3.25182. |
[21] |
H. C. Jang, Y. N. Lien and T. C. Tsai, Rescue information system for earthquake disasters based on MANET emergency communication platform. In Proceedings of the 2009 International Conference on Wireless Communications and Mobile Computing: Connecting the World Wirelessly, ACM, (2009), 623–627.
doi: 10.1145/1582379.1582514. |
[22] |
V. Jayaraman, V. D. R. Guide Jr and R. Srivastava, A closed-loop logistics model for remanufacturing, Journal of the Operational Research Society, (1999), 497–508.
doi: 10.1057/palgrave.jors.2600716. |
[23] |
G. Kannan, P. Sasikumar and K. Devika,
A genetic algorithm approach for solving a closed loop supply chain model: A case of battery recycling, Applied Mathematical Modelling, 34 (2010), 655-670.
doi: 10.1016/j.apm.2009.06.021. |
[24] |
N. Lamba and P. Thareja, Developing the structural model based on analyzing the relationship between the barriers of green supply chain management using TOPSIS approach, Materials Today: Proceedings, (2020). |
[25] |
J. Li, H. Lei, A. H. Alavi and G.-G. Wang, Elephant herding optimization: variants, hybrids, and applications, Mathematics, 8 (2020), 1415.
doi: 10.3390/math8091415. |
[26] |
L. Liang and H. J. Quesada,
Green design of a cellulosic butanol supply chain network: A case study of sorghum stem bio-butanol in missouri, BioResources, 13 (2018), 5617-5642.
doi: 10.15376/biores.13.3.5617-5642. |
[27] |
R. Lotfi, Y. Z. Mehrjerdi, M. S. Pishvaee, A. Sadeghieh and G.-W. Weber, A robust optimization model for sustainable and resilient closed-loop supply chain network design considering conditional value at risk, Numerical Algebra, Control & Optimization, 11 (2021), 221-–253.
doi: 10.3934/naco.2020023. |
[28] |
D. Louwers, B. J. Kip, E. Peters, F. Souren, S. Douwe and P. Flapper,
A facility location allocation model for reusing carpet materials, Computers & Industrial Engineering, 36 (1919), 855-869.
doi: 10.1016/S0360-8352(99)00168-0. |
[29] |
A. R. Mehrabian and C. Lucas,
A novel numerical optimization algorithm inspired from weed colonization, Ecological Informatics, 1 (2006), 355-366.
doi: 10.1016/j.ecoinf.2006.07.003. |
[30] |
S. Niroomand, H. Garg and A. Mahmoodirad,
An intuitionistic fuzzy two stage supply chain network design problem with multi-mode demand and multi-mode transportation, ISA Transactions, 107 (2020), 117-133.
doi: 10.1016/j.isatra.2020.07.033. |
[31] |
R. S. Rad and N. Nahavandi, A novel multi-objective optimization model for integrated problem of green closed loop supply chain network design and quantity discount, Applied Mathematical Modelling, (2018). |
[32] |
A. Shabani, R. F. Saen and S. M. R. Torabipour,
A new benchmarking approach in Cold Chain, Appl. Math. Model., 36 (2012), 212-224.
doi: 10.1016/j.apm.2011.05.051. |
[33] |
T. Spengler, H. Püchert, T. Penkuhn and O. Rentz, Environmental integrated production and recycling management, In Produktion und Umwelt, Springer Berlin Heidelberg, (1997), 239–257. |
[34] |
M. Talaei, B. F. Moghaddam, M. S. Pishvaee, A. Bozorgi-Amiri and S. Gholamnejad,
A robust fuzzy optimization model for carbon-efficient closed-loop supply chain network design problem: A numerical illustration in electronics industry, Journal of Cleaner Production, 113 (2016), 662-673.
doi: 10.1016/j.jclepro.2015.10.074. |
[35] |
M.-L. Tseng, M. S. Islam, N. Karia and F. Ahmad, A literature review on green supply chain management: Trends and future challenges, Resources, Conservation and Recycling, 141, (2019), 145–162.
doi: 10.1016/j.resconrec.2018.10.009. |
[36] |
G. G. Wang, Moth search algorithm: A bio-inspired metaheuristic algorithm for global optimization problems, Memetic Computing, 10, (2018), 151–164. |
[37] |
G.-G. Wang, S. Deb and L. D. S. Coelho, Elephant herding optimization, In 2015 3rd International Symposium on Computational and Business Intelligence (ISCBI), (2015), 1–5.
doi: 10.1109/ISCBI.2015.8. |
[38] |
G.-G. Wang, S. Deb and L. D. S. Coelho, Earthworm optimization algorithm: A bio-inspired metaheuristic algorithm for global optimization problems, International Journal of Bio-Inspired Computation, 12, (2018), 1–22.
doi: 10.1504/IJBIC.2018.093328. |
[39] |
G.-G. Wang, S. Deb and Z. Cui, Monarch butterfly optimization, Neural computing and applications, 31, (2019), 1995–2014. |
[40] |
G.-G. Wang, S. Deb, X.-Z. Gao and L. D. S. Coelho, A new metaheuristic optimization algorithm motivated by elephant herding behavior, International Journal of Bio-Inspired Computation, 8, (2016), 394–409.
doi: 10.1504/IJBIC.2016.10002274. |
[41] |
W. Xing, S. Y. Wang, Q. H. Zhao and G. W. Hua, Impact of fairness on strategies in dual-channel supply chain, Systems Engineering-Theory & Practice, 31, (2011), 1249–1256. |
[42] |
Q. Zhu, J. Sarkis and K.-H. Lai, Green supply chain management implications for "closing the loop", Transportation Research Part E: Logistics and Transportation Review, 44, (2008), 1–18.
doi: 10.1016/j.tre.2006.06.003. |
[43] |
E. Zitzler and L. Thiele, Multiobjective evolutionary algorithms: A comparative case study and the strength Pareto approach, IEEE Transactions on Evolutionary Computation, 3, (1999), 257–271.
doi: 10.1109/4235.797969. |







Authors | Year of publication | Supply chain network design | Green supply chain | Reducing costs | Reducing environmental impacts | Qualitative analysis | Qualitative analysis | Uncertainty | Metaheuristic algorithms |
Barros et al. | 1998 | * | * | * | - | ||||
Louwers et al. | 1999 | * | * | * | - | ||||
Jayaraman et al. | 1999 | * | * | * | - | ||||
Guide et al. | 2003 | * | * | * | * | - | |||
Zhu et al. | 2008 | * | * | * | * | - | |||
Kannan et al. | 2010 | * | * | * | * | - | |||
Xing et al. | 2011 | * | * | * | - | ||||
Farahani et al. | 2011 | * | * | * | - | ||||
Shabani et al. | 2021 | * | * | * | - | ||||
Amin and Zhang | 2012 | * | * | * | * | * | - | ||
Fahimnia et al. | 2013 | * | * | * | - | ||||
Talaei et al. | 2016 | * | * | * | * | * | - | ||
Garb et al. | 2016 | * | * | PSO-GA | |||||
Burgess et al. | 2017 | * | * | * | * | - | |||
Rad & Nahavandi | 2018 | * | * | * | * | - | |||
Ghelichi et al. | 2018 | * | * | * | * | * | - | ||
Liang & Quesada | 2018 | * | * | - | |||||
Goli et al. | 2019 | * | * | * | IWO | ||||
Garb et al. | 2019 | * | * | GSA-GA | |||||
Lotfi et al. | 2019 | * | * | * | * | * | - | ||
Niroomand et al. | 2020 | * | * | * | * | - | |||
Lamba & therja | 2020 | * | * | - | |||||
Gholizadeh & Fazlollahtabar | 2020 | * | * | * | GA | ||||
Golipout et al. | 2020 | * | * | * | * | - | |||
Abdi et al. | 2020 | * | * | * | * | GA-PSO, RDA | |||
Present study | 2020 | * | * | * | * | * | * | MOIWO, NSGA-II |
Authors | Year of publication | Supply chain network design | Green supply chain | Reducing costs | Reducing environmental impacts | Qualitative analysis | Qualitative analysis | Uncertainty | Metaheuristic algorithms |
Barros et al. | 1998 | * | * | * | - | ||||
Louwers et al. | 1999 | * | * | * | - | ||||
Jayaraman et al. | 1999 | * | * | * | - | ||||
Guide et al. | 2003 | * | * | * | * | - | |||
Zhu et al. | 2008 | * | * | * | * | - | |||
Kannan et al. | 2010 | * | * | * | * | - | |||
Xing et al. | 2011 | * | * | * | - | ||||
Farahani et al. | 2011 | * | * | * | - | ||||
Shabani et al. | 2021 | * | * | * | - | ||||
Amin and Zhang | 2012 | * | * | * | * | * | - | ||
Fahimnia et al. | 2013 | * | * | * | - | ||||
Talaei et al. | 2016 | * | * | * | * | * | - | ||
Garb et al. | 2016 | * | * | PSO-GA | |||||
Burgess et al. | 2017 | * | * | * | * | - | |||
Rad & Nahavandi | 2018 | * | * | * | * | - | |||
Ghelichi et al. | 2018 | * | * | * | * | * | - | ||
Liang & Quesada | 2018 | * | * | - | |||||
Goli et al. | 2019 | * | * | * | IWO | ||||
Garb et al. | 2019 | * | * | GSA-GA | |||||
Lotfi et al. | 2019 | * | * | * | * | * | - | ||
Niroomand et al. | 2020 | * | * | * | * | - | |||
Lamba & therja | 2020 | * | * | - | |||||
Gholizadeh & Fazlollahtabar | 2020 | * | * | * | GA | ||||
Golipout et al. | 2020 | * | * | * | * | - | |||
Abdi et al. | 2020 | * | * | * | * | GA-PSO, RDA | |||
Present study | 2020 | * | * | * | * | * | * | MOIWO, NSGA-II |
Indices | Symbol | Value |
Total number of potential suppliers | 15 | |
Number of potential manufacturing plants | 10 | |
Number of potential distribution centers | 20 | |
Number of potential cross-docking warehouses | 35 | |
Number of retailers | 50 | |
Number of manufacturing technologies | 3 | |
Number of demand scenarios | 3 |
Indices | Symbol | Value |
Total number of potential suppliers | 15 | |
Number of potential manufacturing plants | 10 | |
Number of potential distribution centers | 20 | |
Number of potential cross-docking warehouses | 35 | |
Number of retailers | 50 | |
Number of manufacturing technologies | 3 | |
Number of demand scenarios | 3 |
Parameter | Description | Value |
The cost of using the technology |
15000 | |
The cost of opening the plant |
60000 | |
The cost of opening the distribution center |
20000 | |
The cost of opening the cross-docking warehouse |
7000 | |
The fixed cost of a long-term relationship with the supplier |
1000 | |
The variable cost of moving the product in the distribution center |
100 | |
The variable cost of moving the product in the cross-docking warehouse |
80 | |
The cost of transporting each unit of product from the supplier |
45 | |
The cost of transporting each unit of product from the plant |
50 | |
The cost of transporting each unit of product from the distribution center |
30 | |
The cost of transporting each unit of product from the cross-docking warehouse |
25 | |
The cost of transporting each unit of product from the distribution center |
30 | |
The cost of manufacturing each unit of product in the plant |
190 | |
The greenhouse gas emission cost due to the manufacturing of each unit of product in the plant |
230 | |
The environmental impact of transporting each unit of product from the supplier |
70 | |
The environmental impact of transporting each unit of product from the plant |
60 | |
The environmental impact of transporting each unit of product from the distribution center |
60 | |
The environmental impact of transporting each unit of product from the cross-docking warehouse |
60 | |
The environmental impact of transporting each unit of product from the distribution center |
40 | |
The environmental impact of the supplier |
130 | |
The environmental impact of opening the plant |
230 | |
The environmental impact of opening the distribution center |
160 | |
The environmental impact of opening the cross-docking warehouse |
150 | |
Capacity of the supplier |
25000 | |
Production capacity of the plant |
20000 | |
Product transfer capacity at the distribution center |
15000 | |
Product transfer capacity at in the cross-docking warehouse |
10000 | |
The maximum number of suppliers required | 6 | |
The maximum number of plants required | 5 | |
The maximum number of distribution centers required | 10 | |
The maximum number of cross-docking warehouses required | 30 | |
The probability of occurrence of each scenario | 0.1-0.3-0.6 |
Parameter | Description | Value |
The cost of using the technology |
15000 | |
The cost of opening the plant |
60000 | |
The cost of opening the distribution center |
20000 | |
The cost of opening the cross-docking warehouse |
7000 | |
The fixed cost of a long-term relationship with the supplier |
1000 | |
The variable cost of moving the product in the distribution center |
100 | |
The variable cost of moving the product in the cross-docking warehouse |
80 | |
The cost of transporting each unit of product from the supplier |
45 | |
The cost of transporting each unit of product from the plant |
50 | |
The cost of transporting each unit of product from the distribution center |
30 | |
The cost of transporting each unit of product from the cross-docking warehouse |
25 | |
The cost of transporting each unit of product from the distribution center |
30 | |
The cost of manufacturing each unit of product in the plant |
190 | |
The greenhouse gas emission cost due to the manufacturing of each unit of product in the plant |
230 | |
The environmental impact of transporting each unit of product from the supplier |
70 | |
The environmental impact of transporting each unit of product from the plant |
60 | |
The environmental impact of transporting each unit of product from the distribution center |
60 | |
The environmental impact of transporting each unit of product from the cross-docking warehouse |
60 | |
The environmental impact of transporting each unit of product from the distribution center |
40 | |
The environmental impact of the supplier |
130 | |
The environmental impact of opening the plant |
230 | |
The environmental impact of opening the distribution center |
160 | |
The environmental impact of opening the cross-docking warehouse |
150 | |
Capacity of the supplier |
25000 | |
Production capacity of the plant |
20000 | |
Product transfer capacity at the distribution center |
15000 | |
Product transfer capacity at in the cross-docking warehouse |
10000 | |
The maximum number of suppliers required | 6 | |
The maximum number of plants required | 5 | |
The maximum number of distribution centers required | 10 | |
The maximum number of cross-docking warehouses required | 30 | |
The probability of occurrence of each scenario | 0.1-0.3-0.6 |
Scenario No. | 1 | 2 | 3 |
Probability of senario | 0.1 | 0.6 | 0.3 |
Retailer demand | 100 | 250 | 320 |
Scenario No. | 1 | 2 | 3 |
Probability of senario | 0.1 | 0.6 | 0.3 |
Retailer demand | 100 | 250 | 320 |
Plant No. | 1 | 5 | 6 | 7 | 9 |
Technology ID | 1 | 1 | 2 | 3 | 2 |
Plant No. | 1 | 5 | 6 | 7 | 9 |
Technology ID | 1 | 1 | 2 | 3 | 2 |
Distribution center No. | 7 | 9 | 14 | 15 | 18 | 19 | 20 |
Distribution center No. | 7 | 9 | 14 | 15 | 18 | 19 | 20 |
Cross-docking warehouse No. | 2 | 4 | 9 | 10 | 11 | 14 | 18 | 19 | 26 | 28 | 29 | 30 |
Cross-docking warehouse No. | 2 | 4 | 9 | 10 | 11 | 14 | 18 | 19 | 26 | 28 | 29 | 30 |
Items | Cost | Environmental impact |
Selecting suppliers | 4000 | 520 |
Establishing manufacturing plants | 300000 | 75000 |
Establishing distribution centers | 160000 | 1280 |
Establishing warehouses | 84000 | 1800 |
Manufacturing the productb | 37000 | 960 |
Transportation | 34000 | 1620 |
Total | 619000 | 81180 |
Items | Cost | Environmental impact |
Selecting suppliers | 4000 | 520 |
Establishing manufacturing plants | 300000 | 75000 |
Establishing distribution centers | 160000 | 1280 |
Establishing warehouses | 84000 | 1800 |
Manufacturing the productb | 37000 | 960 |
Transportation | 34000 | 1620 |
Total | 619000 | 81180 |
Instance No. | |||||||
Instance No. | |||||||
1 | 6 | 4 | 2 | 1 | 1 | 1 | 2 |
2 | 8 | 5 | 2 | 1 | 2 | 1 | 2 |
3 | 10 | 5 | 2 | 1 | 2 | 1 | 3 |
4 | 12 | 7 | 2 | 1 | 3 | 2 | 3 |
5 | 14 | 8 | 3 | 1 | 3 | 2 | 4 |
6 | 16 | 8 | 3 | 1 | 4 | 2 | 4 |
7 | 18 | 10 | 3 | 2 | 4 | 3 | 5 |
8 | 20 | 12 | 3 | 2 | 5 | 3 | 5 |
9 | 22 | 12 | 4 | 2 | 5 | 3 | 6 |
10 | 24 | 15 | 4 | 2 | 6 | 4 | 6 |
11 | 26 | 16 | 4 | 2 | 6 | 4 | 7 |
12 | 28 | 18 | 5 | 2 | 7 | 4 | 7 |
13 | 30 | 20 | 6 | 3 | 7 | 5 | 8 |
14 | 35 | 24 | 7 | 3 | 8 | 5 | 8 |
15 | 40 | 25 | 8 | 3 | 8 | 5 | 9 |
16 | 45 | 25 | 9 | 3 | 9 | 6 | 9 |
17 | 50 | 30 | 10 | 4 | 9 | 6 | 10 |
18 | 55 | 30 | 11 | 4 | 10 | 6 | 10 |
19 | 60 | 40 | 12 | 4 | 10 | 7 | 11 |
20 | 65 | 40 | 13 | 5 | 11 | 7 | 11 |
21 | 70 | 50 | 14 | 5 | 11 | 7 | 12 |
22 | 75 | 50 | 15 | 5 | 12 | 8 | 12 |
23 | 80 | 60 | 16 | 6 | 12 | 8 | 13 |
24 | 85 | 60 | 17 | 6 | 13 | 8 | 13 |
25 | 90 | 70 | 18 | 6 | 13 | 9 | 14 |
26 | 95 | 70 | 19 | 7 | 14 | 9 | 14 |
27 | 100 | 80 | 20 | 7 | 14 | 9 | 15 |
28 | 105 | 80 | 21 | 7 | 15 | 10 | 15 |
29 | 110 | 90 | 22 | 8 | 15 | 10 | 16 |
30 | 115 | 90 | 23 | 8 | 16 | 10 | 16 |
31 | 120 | 100 | 24 | 8 | 16 | 11 | 17 |
Instance No. | |||||||
Instance No. | |||||||
1 | 6 | 4 | 2 | 1 | 1 | 1 | 2 |
2 | 8 | 5 | 2 | 1 | 2 | 1 | 2 |
3 | 10 | 5 | 2 | 1 | 2 | 1 | 3 |
4 | 12 | 7 | 2 | 1 | 3 | 2 | 3 |
5 | 14 | 8 | 3 | 1 | 3 | 2 | 4 |
6 | 16 | 8 | 3 | 1 | 4 | 2 | 4 |
7 | 18 | 10 | 3 | 2 | 4 | 3 | 5 |
8 | 20 | 12 | 3 | 2 | 5 | 3 | 5 |
9 | 22 | 12 | 4 | 2 | 5 | 3 | 6 |
10 | 24 | 15 | 4 | 2 | 6 | 4 | 6 |
11 | 26 | 16 | 4 | 2 | 6 | 4 | 7 |
12 | 28 | 18 | 5 | 2 | 7 | 4 | 7 |
13 | 30 | 20 | 6 | 3 | 7 | 5 | 8 |
14 | 35 | 24 | 7 | 3 | 8 | 5 | 8 |
15 | 40 | 25 | 8 | 3 | 8 | 5 | 9 |
16 | 45 | 25 | 9 | 3 | 9 | 6 | 9 |
17 | 50 | 30 | 10 | 4 | 9 | 6 | 10 |
18 | 55 | 30 | 11 | 4 | 10 | 6 | 10 |
19 | 60 | 40 | 12 | 4 | 10 | 7 | 11 |
20 | 65 | 40 | 13 | 5 | 11 | 7 | 11 |
21 | 70 | 50 | 14 | 5 | 11 | 7 | 12 |
22 | 75 | 50 | 15 | 5 | 12 | 8 | 12 |
23 | 80 | 60 | 16 | 6 | 12 | 8 | 13 |
24 | 85 | 60 | 17 | 6 | 13 | 8 | 13 |
25 | 90 | 70 | 18 | 6 | 13 | 9 | 14 |
26 | 95 | 70 | 19 | 7 | 14 | 9 | 14 |
27 | 100 | 80 | 20 | 7 | 14 | 9 | 15 |
28 | 105 | 80 | 21 | 7 | 15 | 10 | 15 |
29 | 110 | 90 | 22 | 8 | 15 | 10 | 16 |
30 | 115 | 90 | 23 | 8 | 16 | 10 | 16 |
31 | 120 | 100 | 24 | 8 | 16 | 11 | 17 |
NSGA II | MOIWO | |||||||
Test problem | MID | DM | SNS | Solution time | MID | DM | SNS | Solution time |
1 | 2128.402 | 388.3026 | 337.138 | 19.6 | 2392.871 | 387.0695 | 62.36729 | 21.9 |
2 | 9901.841 | 947.1654 | 1327.495 | 24.8 | 10025.83 | 2126.98 | 811.6118 | 22.2 |
3 | 14960.24 | 1626.795 | 1424.479 | 26.9 | 17064.71 | 1115.375 | 630.3547 | 23.5 |
4 | 26614.19 | 656.5366 | 2013.4 | 34.8 | 29887.93 | 71.44966 | 36.73556 | 34.4 |
5 | 43885.55 | 3292.813 | 2982.944 | 39.7 | 43253.99 | 1438.363 | 1676.061 | 38.6 |
6 | 65925.99 | 1670.296 | 3692.972 | 45.6 | 65007.11 | 3411.264 | 2778.861 | 42.3 |
7 | 170150.2 | 7986.59 | 6394.361 | 51.7 | 172745.8 | 3498.732 | 2442.37 | 55.3 |
8 | 252032.8 | 5583.598 | 4870.001 | 62.7 | 256509.7 | 5928.794 | 4474.071 | 57.5 |
9 | 284951.5 | 16779.53 | 9177.958 | 63.8 | 273177.9 | 6887.26 | 4848.212 | 65.1 |
10 | 381924 | 15844.87 | 4170.522 | 67.4 | 367442.1 | 8144.148 | 10614.28 | 74.2 |
11 | 407187.7 | 13023.62 | 5017.187 | 73.5 | 396215.3 | 3333.181 | 2116.804 | 76.5 |
12 | 511353.5 | 14114.78 | 6296.453 | 78.9 | 500211 | 5713.979 | 7539.665 | 79.9 |
13 | 564882.1 | 15743.56 | 5480.24 | 84.9 | 535189.2 | 10652.97 | 5908.288 | 87.8 |
14 | 1018173 | 16063.69 | 4831.171 | 95.1 | 537751 | 11154.74 | 6256.459 | 93.8 |
15 | 666245.3 | 19694.52 | 6667.181 | 102.1 | 565154 | 12045.07 | 7077.878 | 109.7 |
16 | 633000.8 | 12577.59 | 7022.577 | 116.3 | 590704.9 | 13867.63 | 8038.837 | 121.4 |
17 | 746779.6 | 12953.08 | 5979.238 | 121.9 | 636111.9 | 14579.36 | 8050.933 | 133.2 |
18 | 843457.6 | 13023.62 | 6144.048 | 127.3 | 711607.4 | 15010.54 | 9184.642 | 146.1 |
19 | 795303.2 | 14352.39 | 6745.26 | 138.6 | 715590.4 | 16567.74 | 10596.68 | 150.5 |
20 | 948178.2 | 17867.75 | 7016.65 | 144.8 | 840491.9 | 18883.24 | 11367.66 | 150.9 |
21 | 889252.7 | 18674.4 | 5709.634 | 152.6 | 843119.3 | 19923.22 | 11808.66 | 153.6 |
22 | 979589.8 | 18340.73 | 6096.018 | 172.8 | 964187.6 | 22824.67 | 12901.56 | 162.4 |
23 | 1252267 | 22662.02 | 5907.127 | 189.6 | 1124600 | 25030.35 | 13380.75 | 184.6 |
24 | 1399254 | 24910.39 | 6013.365 | 205.4 | 1346977 | 25886.89 | 14847.5 | 209.6 |
25 | 1626187 | 26719.46 | 5702.392 | 232.2 | 1431072 | 27008.7 | 15218.09 | 218.6 |
26 | 1808562 | 27314.07 | 6976.036 | 237.2 | 1551875 | 32284.12 | 16639.52 | 233.6 |
27 | 2165170 | 26285.52 | 6046.077 | 249.8 | 1835831 | 32571.71 | 17894.87 | 262.8 |
28 | 2115911 | 34620.55 | 6021.699 | 278.2 | 2071615 | 37901.51 | 20138.68 | 289.8 |
29 | 2601260 | 31453.13 | 5924.462 | 286.4 | 2418931 | 41658.63 | 23395.58 | 290.2 |
30 | 3037899 | 40728.54 | 6957.946 | 328.4 | 2731168 | 47049.29 | 27300.69 | 303.6 |
31 | 3450494 | 34538.37 | 7073.724 | 359.8 | 2986884 | 47585.72 | 31641.19 | 336.2 |
Average | 958480.1 | 16465.75 | 5355.476 | 135.9 | 857186.9 | 16598.15 | 9989.673 | 136.4 |
NSGA II | MOIWO | |||||||
Test problem | MID | DM | SNS | Solution time | MID | DM | SNS | Solution time |
1 | 2128.402 | 388.3026 | 337.138 | 19.6 | 2392.871 | 387.0695 | 62.36729 | 21.9 |
2 | 9901.841 | 947.1654 | 1327.495 | 24.8 | 10025.83 | 2126.98 | 811.6118 | 22.2 |
3 | 14960.24 | 1626.795 | 1424.479 | 26.9 | 17064.71 | 1115.375 | 630.3547 | 23.5 |
4 | 26614.19 | 656.5366 | 2013.4 | 34.8 | 29887.93 | 71.44966 | 36.73556 | 34.4 |
5 | 43885.55 | 3292.813 | 2982.944 | 39.7 | 43253.99 | 1438.363 | 1676.061 | 38.6 |
6 | 65925.99 | 1670.296 | 3692.972 | 45.6 | 65007.11 | 3411.264 | 2778.861 | 42.3 |
7 | 170150.2 | 7986.59 | 6394.361 | 51.7 | 172745.8 | 3498.732 | 2442.37 | 55.3 |
8 | 252032.8 | 5583.598 | 4870.001 | 62.7 | 256509.7 | 5928.794 | 4474.071 | 57.5 |
9 | 284951.5 | 16779.53 | 9177.958 | 63.8 | 273177.9 | 6887.26 | 4848.212 | 65.1 |
10 | 381924 | 15844.87 | 4170.522 | 67.4 | 367442.1 | 8144.148 | 10614.28 | 74.2 |
11 | 407187.7 | 13023.62 | 5017.187 | 73.5 | 396215.3 | 3333.181 | 2116.804 | 76.5 |
12 | 511353.5 | 14114.78 | 6296.453 | 78.9 | 500211 | 5713.979 | 7539.665 | 79.9 |
13 | 564882.1 | 15743.56 | 5480.24 | 84.9 | 535189.2 | 10652.97 | 5908.288 | 87.8 |
14 | 1018173 | 16063.69 | 4831.171 | 95.1 | 537751 | 11154.74 | 6256.459 | 93.8 |
15 | 666245.3 | 19694.52 | 6667.181 | 102.1 | 565154 | 12045.07 | 7077.878 | 109.7 |
16 | 633000.8 | 12577.59 | 7022.577 | 116.3 | 590704.9 | 13867.63 | 8038.837 | 121.4 |
17 | 746779.6 | 12953.08 | 5979.238 | 121.9 | 636111.9 | 14579.36 | 8050.933 | 133.2 |
18 | 843457.6 | 13023.62 | 6144.048 | 127.3 | 711607.4 | 15010.54 | 9184.642 | 146.1 |
19 | 795303.2 | 14352.39 | 6745.26 | 138.6 | 715590.4 | 16567.74 | 10596.68 | 150.5 |
20 | 948178.2 | 17867.75 | 7016.65 | 144.8 | 840491.9 | 18883.24 | 11367.66 | 150.9 |
21 | 889252.7 | 18674.4 | 5709.634 | 152.6 | 843119.3 | 19923.22 | 11808.66 | 153.6 |
22 | 979589.8 | 18340.73 | 6096.018 | 172.8 | 964187.6 | 22824.67 | 12901.56 | 162.4 |
23 | 1252267 | 22662.02 | 5907.127 | 189.6 | 1124600 | 25030.35 | 13380.75 | 184.6 |
24 | 1399254 | 24910.39 | 6013.365 | 205.4 | 1346977 | 25886.89 | 14847.5 | 209.6 |
25 | 1626187 | 26719.46 | 5702.392 | 232.2 | 1431072 | 27008.7 | 15218.09 | 218.6 |
26 | 1808562 | 27314.07 | 6976.036 | 237.2 | 1551875 | 32284.12 | 16639.52 | 233.6 |
27 | 2165170 | 26285.52 | 6046.077 | 249.8 | 1835831 | 32571.71 | 17894.87 | 262.8 |
28 | 2115911 | 34620.55 | 6021.699 | 278.2 | 2071615 | 37901.51 | 20138.68 | 289.8 |
29 | 2601260 | 31453.13 | 5924.462 | 286.4 | 2418931 | 41658.63 | 23395.58 | 290.2 |
30 | 3037899 | 40728.54 | 6957.946 | 328.4 | 2731168 | 47049.29 | 27300.69 | 303.6 |
31 | 3450494 | 34538.37 | 7073.724 | 359.8 | 2986884 | 47585.72 | 31641.19 | 336.2 |
Average | 958480.1 | 16465.75 | 5355.476 | 135.9 | 857186.9 | 16598.15 | 9989.673 | 136.4 |
Iteration | MID | DM | SNS | |
Random simulation | 100 | 1347512 | 17541.19 | 3421.96 |
Random simulation | 500 | 1296475 | 20047.48 | 4343.55 |
Random simulation | 1000 | 1253954 | 22096.37 | 5736.47 |
MOIWO | 200 | 1124600 | 25030.35 | 13380.75 |
NSGA-II | 200 | 1252267 | 22662.02 | 5907.12 |
Best method | - | MOIWO | MOIWO | MOIWO |
Iteration | MID | DM | SNS | |
Random simulation | 100 | 1347512 | 17541.19 | 3421.96 |
Random simulation | 500 | 1296475 | 20047.48 | 4343.55 |
Random simulation | 1000 | 1253954 | 22096.37 | 5736.47 |
MOIWO | 200 | 1124600 | 25030.35 | 13380.75 |
NSGA-II | 200 | 1252267 | 22662.02 | 5907.12 |
Best method | - | MOIWO | MOIWO | MOIWO |
Mean | Std. Deviation | Std. Error Mean | 95% Confidence Interval of the Difference | t | df | Sig. (2-tailed) | ||
Lower | Upper | |||||||
NSGAII-MID MOIWO-MID | 101293.165 | 135632.934 | 24360.394 | 51542.603 | 151043.727 | 4.158 | 30 | .000 |
Mean | Std. Deviation | Std. Error Mean | 95% Confidence Interval of the Difference | t | df | Sig. (2-tailed) | ||
Lower | Upper | |||||||
NSGAII-MID MOIWO-MID | 101293.165 | 135632.934 | 24360.394 | 51542.603 | 151043.727 | 4.158 | 30 | .000 |
Mean | Std. Deviation | Std. Error Mean | 95% Confidence Interval of the Difference | t | df | Sig. (2-tailed) | ||
Lower | Upper | |||||||
NSGAII-SNS MOIWO-SNS | -4634.19 | 7169.486 | 1287.677 | -7263.98 | -2004.40 | -3.599 | 30 | .001 |
Mean | Std. Deviation | Std. Error Mean | 95% Confidence Interval of the Difference | t | df | Sig. (2-tailed) | ||
Lower | Upper | |||||||
NSGAII-SNS MOIWO-SNS | -4634.19 | 7169.486 | 1287.677 | -7263.98 | -2004.40 | -3.599 | 30 | .001 |
Mean | Std. Deviation | Std. Error Mean | 95% Confidence Interval of the Difference | t | df | Sig. (2-tailed) | ||
Lower | Upper | |||||||
NSGAII-DM MOIWI-DM | -132.401 | 5447.236 | 978.352 | -2130.46 | 1865.66 | -.135 | 30 | .893 |
Mean | Std. Deviation | Std. Error Mean | 95% Confidence Interval of the Difference | t | df | Sig. (2-tailed) | ||
Lower | Upper | |||||||
NSGAII-DM MOIWI-DM | -132.401 | 5447.236 | 978.352 | -2130.46 | 1865.66 | -.135 | 30 | .893 |
OB1 | OB2 | OB1 | OB2 | OB1 | OB2 | OB1 | OB2 | OB1 | OB2 |
575413 | 73608 | 606912 | 78914 | 619000 | 81180 | 621994 | 84252 | 630881 | 87539 |
596470 | 70029 | 619944 | 74532 | 627820 | 75855 | 655736 | 78734 | 699668 | 86211 |
605106 | 66585 | 661924 | 69282 | 690996 | 72564 | 703981 | 77182 | 795615 | 83357 |
616235 | 66387 | 759706 | 65312 | 730679 | 70027 | 728719 | 70189 | 819769 | 76894 |
639479 | 66268 | 797345 | 61378 | 751322 | 67136 | 880525 | 63570 | 876866 | 71727 |
702385 | 60188 | 826948 | 57410 | 809028 | 64373 | 896155 | 59665 | 972932 | 66554 |
775653 | 56490 | 948546 | 54882 | 879333 | 60945 | 934413 | 56740 | 983940 | 60876 |
OB1 | OB2 | OB1 | OB2 | OB1 | OB2 | OB1 | OB2 | OB1 | OB2 |
575413 | 73608 | 606912 | 78914 | 619000 | 81180 | 621994 | 84252 | 630881 | 87539 |
596470 | 70029 | 619944 | 74532 | 627820 | 75855 | 655736 | 78734 | 699668 | 86211 |
605106 | 66585 | 661924 | 69282 | 690996 | 72564 | 703981 | 77182 | 795615 | 83357 |
616235 | 66387 | 759706 | 65312 | 730679 | 70027 | 728719 | 70189 | 819769 | 76894 |
639479 | 66268 | 797345 | 61378 | 751322 | 67136 | 880525 | 63570 | 876866 | 71727 |
702385 | 60188 | 826948 | 57410 | 809028 | 64373 | 896155 | 59665 | 972932 | 66554 |
775653 | 56490 | 948546 | 54882 | 879333 | 60945 | 934413 | 56740 | 983940 | 60876 |
[1] |
Ashkan Mohsenzadeh Ledari, Alireza Arshadi Khamseh, Mohammad Mohammadi. A three echelon revenue oriented green supply chain network design. Numerical Algebra, Control and Optimization, 2018, 8 (2) : 157-168. doi: 10.3934/naco.2018009 |
[2] |
Helmut Mausser, Oleksandr Romanko. CVaR proxies for minimizing scenario-based Value-at-Risk. Journal of Industrial and Management Optimization, 2014, 10 (4) : 1109-1127. doi: 10.3934/jimo.2014.10.1109 |
[3] |
Binghai Zhou, Yuanrui Lei, Shi Zong. Lagrangian relaxation algorithm for the truck scheduling problem with products time window constraint in multi-door cross-dock. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021151 |
[4] |
Behrad Erfani, Sadoullah Ebrahimnejad, Amirhossein Moosavi. An integrated dynamic facility layout and job shop scheduling problem: A hybrid NSGA-II and local search algorithm. Journal of Industrial and Management Optimization, 2020, 16 (4) : 1801-1834. doi: 10.3934/jimo.2019030 |
[5] |
Masoud Rabbani, Nastaran Oladzad-Abbasabady, Niloofar Akbarian-Saravi. Ambulance routing in disaster response considering variable patient condition: NSGA-II and MOPSO algorithms. Journal of Industrial and Management Optimization, 2022, 18 (2) : 1035-1062. doi: 10.3934/jimo.2021007 |
[6] |
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 |
[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] |
Feimin Zhong, Wei Zeng, Zhongbao Zhou. Mechanism design in a supply chain with ambiguity in private information. Journal of Industrial and Management Optimization, 2020, 16 (1) : 261-287. doi: 10.3934/jimo.2018151 |
[9] |
Azam Moradi, Jafar Razmi, Reza Babazadeh, Ali Sabbaghnia. An integrated Principal Component Analysis and multi-objective mathematical programming approach to agile supply chain network design under uncertainty. Journal of Industrial and Management Optimization, 2019, 15 (2) : 855-879. doi: 10.3934/jimo.2018074 |
[10] |
Amin Reza Kalantari Khalil Abad, Farnaz Barzinpour, Seyed Hamid Reza Pasandideh. A novel separate chance-constrained programming model to design a sustainable medical ventilator supply chain network during the Covid-19 pandemic. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2021234 |
[11] |
Gang Xie, Wuyi Yue, Shouyang Wang. Optimal selection of cleaner products in a green supply chain with risk aversion. Journal of Industrial and Management Optimization, 2015, 11 (2) : 515-528. doi: 10.3934/jimo.2015.11.515 |
[12] |
Liping Zhang. A nonlinear complementarity model for supply chain network equilibrium. Journal of Industrial and Management Optimization, 2007, 3 (4) : 727-737. doi: 10.3934/jimo.2007.3.727 |
[13] |
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 |
[14] |
Zuo-Jun max Shen. Integrated supply chain design models: a survey and future research directions. Journal of Industrial and Management Optimization, 2007, 3 (1) : 1-27. doi: 10.3934/jimo.2007.3.1 |
[15] |
Robert Ebihart Msigwa, Yue Lu, Xiantao Xiao, Liwei Zhang. A perturbation-based approach for continuous network design problem with emissions. Numerical Algebra, Control and Optimization, 2015, 5 (2) : 135-149. doi: 10.3934/naco.2015.5.135 |
[16] |
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 |
[17] |
Chirantan Mondal, Bibhas C. Giri. Investigating a green supply chain with product recycling under retailer's fairness behavior. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021129 |
[18] |
Xiaoxi Zhu, Kai Liu, Miaomiao Wang, Rui Zhang, Minglun Ren. Product line extension with a green added product: Impacts of segmented consumer preference on supply chain improvement and consumer surplus. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022021 |
[19] |
Jian Liu, Xin Wu, Jiang-Ling Lei. The combined impacts of consumer green preference and fairness concern on the decision of three-party supply chain. Journal of Industrial and Management Optimization, 2022, 18 (4) : 2749-2782. doi: 10.3934/jimo.2021090 |
[20] |
Tinggui Chen, Yanhui Jiang. Research on operating mechanism for creative products supply chain based on game theory. Discrete and Continuous Dynamical Systems - S, 2015, 8 (6) : 1103-1112. doi: 10.3934/dcdss.2015.8.1103 |
2021 Impact Factor: 1.411
Tools
Metrics
Other articles
by authors
[Back to Top]