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doi: 10.3934/naco.2020023

A robust optimization model for sustainable and resilient closed-loop supply chain network design considering conditional value at risk

1. 

Department of Industrial Engineering, Yazd University, Yazd, Iran

2. 

School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran

3. 

Poznan University of Technology Faculty of Engineering, Management, Poznan, Poland, IAM, METU, Ankara, Turkey

* Corresponding author: Yahia Zare Mehrjerdi

Received  October 2019 Revised  November 2019 Published  August 2020

One of the challenges facing supply chain designers is designing a sustainable and resilient supply chain network. The present study considers a closed-loop supply chain by taking into account sustainability, resilience, robustness, and risk aversion for the first time. The study suggests a two-stage mixed-integer linear programming model for the problem. Further, the robust counterpart model is used to handle uncertainties. Furthermore, conditional value at risk criterion in the model is considered in order to create real-life conditions. The sustainability goals addressed in the present study include minimizing the costs, $ \text{CO}_2 $ emission, and energy, along with maximizing employment. In addition, effective environmental and social life-cycle evaluations are provided to assess the associated effects of the model on society, environment, and energy consumption. The model aims to answer the questions regarding the establishment of facilities and amount of transported goods between facilities. The model is implemented in a car assembler company in Iran. Based on the results, several managerial insights are offered to the decision-makers. Due to the complexity of the problem, a constraint relaxation is applied to produce quality upper and lower bounds in medium and large-scale models. Moreover, the LP-Metric method is used to merge the objectives to attain an optimal solution. The results revealed that the robust counterpart provides a better estimation of the total cost, pollution, energy consumption, and employment level compared to the basic model.

Citation: 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 & Optimization, doi: 10.3934/naco.2020023
References:
[1]

S. H. Amin and F. Baki, A facility location model for global closed-loop supply chain network design, Applied Mathematical Modelling, 41 (2017), 316-330.  doi: 10.1016/j.apm.2016.08.030.  Google Scholar

[2]

S. H. AminG. Zhang and P. Akhtar, Effects of uncertainty on a tire closed-loop supply chain network, Expert Systems with Applications, 73 (2017), 82-91.   Google Scholar

[3]

G. BehzadiM. O. SullivanT. Olsen and A. Zhang, Allocation flexibility for agribusiness supply chains under market demand disruption, International Journal of Production Research, 56 (2018), 3524-3546.   Google Scholar

[4]

C. BenoîtG. A. NorrisS. ValdiviaA. CirothA. MobergU. BosS. PrakashC. Ugaya and T. Beck, The guidelines for social life cycle assessment of products: just in time!, The International Journal of Life Cycle Assessment, 15 (2010), 156-163.   Google Scholar

[5]

M. Brandenburg, Low carbon supply chain configuration for a new product–a goal programming approach, International Journal of Production Research, 53 (2015), 6588-6610.   Google Scholar

[6]

M. Brandenburg, A hybrid approach to configure eco-efficient supply chains under consideration of performance and risk aspects, Omega, 70 (2017), 58-76.   Google Scholar

[7]

S. R. CardosoA. P. Barbosa-Póvoa and S. Relvas, Integrating financial risk measures into the design and planning of closed-loop supply chains, Computers & Chemical Engineering, 85 (2016), 105-123.   Google Scholar

[8]

J. CzyzykM. P. Mesnier and J. J. Moré, The neos server, IEEE Computational Science and Engineering, 5 (1998), 68-75.   Google Scholar

[9]

E. D. Dolan, Neos server 4.0 administrative guide, arXiv preprint cs/0107034. Google Scholar

[10]

M. EskandarpourP. DejaxJ. Miemczyk and O. Péton, Sustainable supply chain network design: An optimization-oriented review, Omega, 54 (2015), 11-32.   Google Scholar

[11]

H. Fang and R. Xiao, Resilient closed–loop supply chain network design based on patent protection, International Journal of Computer Applications in Technology, 48 (2013), 49-57.   Google Scholar

[12]

M. Goedkoop, R. Heijungs, M. Huijbregts, A. De Schryver, J. Struijs, R. Van Zelm et al., A life cycle impact assessment method which comprises harmonised category indicators at the midpoint and the endpoint level, The Hague, Ministry of VROM. ReCiPe., . Google Scholar

[13]

A. GoliH. K. ZareR. Tavakkoli-Moghaddam and A. Sadeghieh, Application of robust optimization for a product portfolio problem using an invasive weed optimization algorithm, Numerical Algebra, Control & Optimization, 9 (2019), 187-209.  doi: 10.3934/naco.2019014.  Google Scholar

[14]

W. Gropp and J. Moré, Optimization environments and the neos server. Approximation Theory and Optimization (eds. md buhmann and a. iserles), 1997.  Google Scholar

[15]

T. W. Hill and A. Ravindran, On programming with absolute-value functions, Journal of Optimization Theory and Applications, 17 (1975), 181-183.  doi: 10.1007/BF00933924.  Google Scholar

[16]

M. A. HuijbregtsS. HellwegR. FrischknechtH. W. HendriksK. Hungerbuhler and A. J. Hendriks, Cumulative energy demand as predictor for the environmental burden of commodity production, Environmental Science & Technology, 44 (2010), 2189-2196.   Google Scholar

[17]

G. JalaliR. Tavakkoli-MoghaddamM. Ghomi-Avili and A. Jabbarzadeh, A network design model for a resilient closed-loop supply chain with lateral transshipment, International Journal of Engineering, 30 (2017), 374-383.   Google Scholar

[18]

D. K. KadambalaN. SubramanianM. K. TiwariM. Abdulrahman and C. Liu, Closed loop supply chain networks: Designs for energy and time value efficiency, International Journal of Production Economics, 183 (2017), 382-393.   Google Scholar

[19]

G. KaraA. Özmen and G.-W. Weber, Stability advances in robust portfolio optimization under parallelepiped uncertainty, Central European Journal of Operations Research, 27 (2019), 241-261.  doi: 10.1007/s10100-017-0508-5.  Google Scholar

[20]

S. Khalilpourazari and M. Mohammadi, Optimization of closed-loop supply chain network design: a water cycle algorithm approach, in 2016 12th International Conference on Industrial Engineering (ICIE), IEEE, (2016), 41–45. Google Scholar

[21]

P. R. Kleindorfer and G. H. Saad, Managing disruption risks in supply chains, Production and Operations Management, 14 (2005), 53-68.   Google Scholar

[22]

W. KlibiA. Martel and A. Guitouni, The design of robust value-creating supply chain networks: a critical review, European Journal of Operational Research, 203 (2010), 283-293.   Google Scholar

[23]

R. Lotfi and N. M. AMIN, Multi-objective capacitated facility location with hybrid fuzzy simplex and genetic algorithm approach, Google Scholar

[24]

R. LotfiY. Z. Mehrjerdi and N. Mardani, A multi-objective and multi-product advertising billboard location model with attraction factor mathematical modeling and solutions, International Journal of Applied Logistics (IJAL), 7 (2017), 64-86.   Google Scholar

[25]

R. Lotfi, Y. Z. Mehrjerdi, M. S. Pishvaee, Razmi and A. Sadeghieh, A robust optimization approach to resilience and sustainable closed-loop supply chain network design under risk averse Presented at the 15th Iran International Industrial Engineering Conference, 2019. Google Scholar

[26]

R. Lotfi, G.-W. Weber, S. M. Sajadifar and N. Mardani, Interdependent demand in the two-period newsvendor problem, Journal of Industrial & Management Optimization, 777–792. doi: 10.3934/jimo.2018143.  Google Scholar

[27]

M. Mahmud, N. Huda, S. Farjana and C. Lang, Environmental impacts of solar-photovoltaic and solar-thermal systems with life-cycle assessment, Energies, 11 (2018), 2346. Google Scholar

[28]

S. MariY. Lee and M. Memon, Sustainable and resilient supply chain network design under disruption risks, Sustainability, 6 (2014), 6666-6686.   Google Scholar

[29]

S. Mari, Y. Lee and M. Memon, Sustainable and resilient garment supply chain network design with fuzzy multi-objectives under uncertainty, Sustainability, 8 (2016), 1038. Google Scholar

[30]

M. J. Meixell and V. B. Gargeya, Global supply chain design: A literature review and critique, Transportation Research Part E: Logistics and Transportation Review, 41 (2005), 531-550.   Google Scholar

[31]

M. T. MeloS. Nickel and F. Saldanha-Da-Gama, Facility location and supply chain management–a review, European Journal of Operational Research, 196 (2009), 401-412.  doi: 10.1016/j.ejor.2008.05.007.  Google Scholar

[32]

J. M. MulveyR. J. Vanderbei and S. A. Zenios, Robust optimization of large-scale systems, Operations Research, 43 (1995), 264-281.  doi: 10.1287/opre.43.2.264.  Google Scholar

[33]

J. Q. F. NetoG. WaltherJ. BloemhofJ. Van Nunen and T. Spengler, A methodology for assessing eco-efficiency in logistics networks, European Journal of Operational Research, 193 (2009), 670-682.   Google Scholar

[34]

A. R. Nour and A. M. Kamali, A weighted metric method to optimize multi-response robust problems, Google Scholar

[35]

N. Noyan, Risk-averse two-stage stochastic programming with an application to disaster management, Computers & Operations Research, 39 (2012), 541-559.  doi: 10.1016/j.cor.2011.03.017.  Google Scholar

[36]

M. S. PishvaeeJ. Razmi and S. A. Torabi, An accelerated benders decomposition algorithm for sustainable supply chain network design under uncertainty: A case study of medical needle and syringe supply chain, Transportation Research Part E: Logistics and Transportation Review, 67 (2014), 14-38.  doi: 10.1016/j.fss.2012.04.010.  Google Scholar

[37]

S. Prakash, S. Kumar, G. Soni, V. Jain and A. P. S. Rathore, Closed-loop supply chain network design and modelling under risks and demand uncertainty: an integrated robust optimization approach, Annals of Operations Research, 1–28. Google Scholar

[38]

S. PrakashG. Soni and A. P. S. Rathore, Embedding risk in closed-loop supply chain network design: Case of a hospital furniture manufacturer, Journal of Modelling in Management, 12 (2017), 551-574.   Google Scholar

[39]

J. Quariguasi Frota NetoG. WaltherJ. BloemhofJ. Van Nunen and T. Spengler, From closed-loop to sustainable supply chains: the weee case, International Journal of Production Research, 48 (2010), 4463-4481.   Google Scholar

[40]

N. SahebjamniaA. M. Fathollahi-Fard and M. Hajiaghaei-Keshteli, Sustainable tire closed-loop supply chain network design: Hybrid metaheuristic algorithms for large-scale networks, Journal of cleaner production, 196 (2018), 273-296.   Google Scholar

[41]

Y. ShiL. C. AlwanC. Tang and X. Yue, A newsvendor model with autocorrelated demand under a time-consistent dynamic cvar measure, IISE Transactions, 51 (2019), 653-671.   Google Scholar

[42]

H. Soleimani and K. Govindan, Reverse logistics network design and planning utilizing conditional value at risk, European Journal of Operational Research, 237 (2014), 487-497.  doi: 10.1016/j.ejor.2014.02.030.  Google Scholar

[43]

A. SorokinV. BoginskiA. Nahapetyan and P. M. Pardalos, Computational risk management techniques for fixed charge network flow problems with uncertain arc failures, Journal of Combinatorial Optimization, 25 (2013), 99-122.  doi: 10.1007/s10878-011-9422-2.  Google Scholar

[44]

K. SubulanA. BaykasoğluF. B. ÖzsoydanA. S. Taşan and H. Selim, A case-oriented approach to a lead/acid battery closed-loop supply chain network design under risk and uncertainty, Journal of Manufacturing Systems, 37 (2015), 340-361.   Google Scholar

[45]

H. A. Taha, Operations Research: An Introduction, Vol. 790, Pearson/Prentice Hall, 2011. Google Scholar

[46]

M. TalaeiB. F. MoghaddamM. S. PishvaeeA. 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.   Google Scholar

[47]

R. Tavakkoli-MoghaddamS. SadriN. Pourmohammad-Zia and M. Mohammadi, A hybrid fuzzy approach for the closed-loop supply chain network design under uncertainty, Journal of Intelligent & Fuzzy Systems, 28 (2015), 2811-2826.   Google Scholar

[48]

S. TorabiJ. NamdarS. Hatefi and F. Jolai, An enhanced possibilistic programming approach for reliable closed-loop supply chain network design, International Journal of Production Research, 54 (2016), 1358-1387.   Google Scholar

show all references

References:
[1]

S. H. Amin and F. Baki, A facility location model for global closed-loop supply chain network design, Applied Mathematical Modelling, 41 (2017), 316-330.  doi: 10.1016/j.apm.2016.08.030.  Google Scholar

[2]

S. H. AminG. Zhang and P. Akhtar, Effects of uncertainty on a tire closed-loop supply chain network, Expert Systems with Applications, 73 (2017), 82-91.   Google Scholar

[3]

G. BehzadiM. O. SullivanT. Olsen and A. Zhang, Allocation flexibility for agribusiness supply chains under market demand disruption, International Journal of Production Research, 56 (2018), 3524-3546.   Google Scholar

[4]

C. BenoîtG. A. NorrisS. ValdiviaA. CirothA. MobergU. BosS. PrakashC. Ugaya and T. Beck, The guidelines for social life cycle assessment of products: just in time!, The International Journal of Life Cycle Assessment, 15 (2010), 156-163.   Google Scholar

[5]

M. Brandenburg, Low carbon supply chain configuration for a new product–a goal programming approach, International Journal of Production Research, 53 (2015), 6588-6610.   Google Scholar

[6]

M. Brandenburg, A hybrid approach to configure eco-efficient supply chains under consideration of performance and risk aspects, Omega, 70 (2017), 58-76.   Google Scholar

[7]

S. R. CardosoA. P. Barbosa-Póvoa and S. Relvas, Integrating financial risk measures into the design and planning of closed-loop supply chains, Computers & Chemical Engineering, 85 (2016), 105-123.   Google Scholar

[8]

J. CzyzykM. P. Mesnier and J. J. Moré, The neos server, IEEE Computational Science and Engineering, 5 (1998), 68-75.   Google Scholar

[9]

E. D. Dolan, Neos server 4.0 administrative guide, arXiv preprint cs/0107034. Google Scholar

[10]

M. EskandarpourP. DejaxJ. Miemczyk and O. Péton, Sustainable supply chain network design: An optimization-oriented review, Omega, 54 (2015), 11-32.   Google Scholar

[11]

H. Fang and R. Xiao, Resilient closed–loop supply chain network design based on patent protection, International Journal of Computer Applications in Technology, 48 (2013), 49-57.   Google Scholar

[12]

M. Goedkoop, R. Heijungs, M. Huijbregts, A. De Schryver, J. Struijs, R. Van Zelm et al., A life cycle impact assessment method which comprises harmonised category indicators at the midpoint and the endpoint level, The Hague, Ministry of VROM. ReCiPe., . Google Scholar

[13]

A. GoliH. K. ZareR. Tavakkoli-Moghaddam and A. Sadeghieh, Application of robust optimization for a product portfolio problem using an invasive weed optimization algorithm, Numerical Algebra, Control & Optimization, 9 (2019), 187-209.  doi: 10.3934/naco.2019014.  Google Scholar

[14]

W. Gropp and J. Moré, Optimization environments and the neos server. Approximation Theory and Optimization (eds. md buhmann and a. iserles), 1997.  Google Scholar

[15]

T. W. Hill and A. Ravindran, On programming with absolute-value functions, Journal of Optimization Theory and Applications, 17 (1975), 181-183.  doi: 10.1007/BF00933924.  Google Scholar

[16]

M. A. HuijbregtsS. HellwegR. FrischknechtH. W. HendriksK. Hungerbuhler and A. J. Hendriks, Cumulative energy demand as predictor for the environmental burden of commodity production, Environmental Science & Technology, 44 (2010), 2189-2196.   Google Scholar

[17]

G. JalaliR. Tavakkoli-MoghaddamM. Ghomi-Avili and A. Jabbarzadeh, A network design model for a resilient closed-loop supply chain with lateral transshipment, International Journal of Engineering, 30 (2017), 374-383.   Google Scholar

[18]

D. K. KadambalaN. SubramanianM. K. TiwariM. Abdulrahman and C. Liu, Closed loop supply chain networks: Designs for energy and time value efficiency, International Journal of Production Economics, 183 (2017), 382-393.   Google Scholar

[19]

G. KaraA. Özmen and G.-W. Weber, Stability advances in robust portfolio optimization under parallelepiped uncertainty, Central European Journal of Operations Research, 27 (2019), 241-261.  doi: 10.1007/s10100-017-0508-5.  Google Scholar

[20]

S. Khalilpourazari and M. Mohammadi, Optimization of closed-loop supply chain network design: a water cycle algorithm approach, in 2016 12th International Conference on Industrial Engineering (ICIE), IEEE, (2016), 41–45. Google Scholar

[21]

P. R. Kleindorfer and G. H. Saad, Managing disruption risks in supply chains, Production and Operations Management, 14 (2005), 53-68.   Google Scholar

[22]

W. KlibiA. Martel and A. Guitouni, The design of robust value-creating supply chain networks: a critical review, European Journal of Operational Research, 203 (2010), 283-293.   Google Scholar

[23]

R. Lotfi and N. M. AMIN, Multi-objective capacitated facility location with hybrid fuzzy simplex and genetic algorithm approach, Google Scholar

[24]

R. LotfiY. Z. Mehrjerdi and N. Mardani, A multi-objective and multi-product advertising billboard location model with attraction factor mathematical modeling and solutions, International Journal of Applied Logistics (IJAL), 7 (2017), 64-86.   Google Scholar

[25]

R. Lotfi, Y. Z. Mehrjerdi, M. S. Pishvaee, Razmi and A. Sadeghieh, A robust optimization approach to resilience and sustainable closed-loop supply chain network design under risk averse Presented at the 15th Iran International Industrial Engineering Conference, 2019. Google Scholar

[26]

R. Lotfi, G.-W. Weber, S. M. Sajadifar and N. Mardani, Interdependent demand in the two-period newsvendor problem, Journal of Industrial & Management Optimization, 777–792. doi: 10.3934/jimo.2018143.  Google Scholar

[27]

M. Mahmud, N. Huda, S. Farjana and C. Lang, Environmental impacts of solar-photovoltaic and solar-thermal systems with life-cycle assessment, Energies, 11 (2018), 2346. Google Scholar

[28]

S. MariY. Lee and M. Memon, Sustainable and resilient supply chain network design under disruption risks, Sustainability, 6 (2014), 6666-6686.   Google Scholar

[29]

S. Mari, Y. Lee and M. Memon, Sustainable and resilient garment supply chain network design with fuzzy multi-objectives under uncertainty, Sustainability, 8 (2016), 1038. Google Scholar

[30]

M. J. Meixell and V. B. Gargeya, Global supply chain design: A literature review and critique, Transportation Research Part E: Logistics and Transportation Review, 41 (2005), 531-550.   Google Scholar

[31]

M. T. MeloS. Nickel and F. Saldanha-Da-Gama, Facility location and supply chain management–a review, European Journal of Operational Research, 196 (2009), 401-412.  doi: 10.1016/j.ejor.2008.05.007.  Google Scholar

[32]

J. M. MulveyR. J. Vanderbei and S. A. Zenios, Robust optimization of large-scale systems, Operations Research, 43 (1995), 264-281.  doi: 10.1287/opre.43.2.264.  Google Scholar

[33]

J. Q. F. NetoG. WaltherJ. BloemhofJ. Van Nunen and T. Spengler, A methodology for assessing eco-efficiency in logistics networks, European Journal of Operational Research, 193 (2009), 670-682.   Google Scholar

[34]

A. R. Nour and A. M. Kamali, A weighted metric method to optimize multi-response robust problems, Google Scholar

[35]

N. Noyan, Risk-averse two-stage stochastic programming with an application to disaster management, Computers & Operations Research, 39 (2012), 541-559.  doi: 10.1016/j.cor.2011.03.017.  Google Scholar

[36]

M. S. PishvaeeJ. Razmi and S. A. Torabi, An accelerated benders decomposition algorithm for sustainable supply chain network design under uncertainty: A case study of medical needle and syringe supply chain, Transportation Research Part E: Logistics and Transportation Review, 67 (2014), 14-38.  doi: 10.1016/j.fss.2012.04.010.  Google Scholar

[37]

S. Prakash, S. Kumar, G. Soni, V. Jain and A. P. S. Rathore, Closed-loop supply chain network design and modelling under risks and demand uncertainty: an integrated robust optimization approach, Annals of Operations Research, 1–28. Google Scholar

[38]

S. PrakashG. Soni and A. P. S. Rathore, Embedding risk in closed-loop supply chain network design: Case of a hospital furniture manufacturer, Journal of Modelling in Management, 12 (2017), 551-574.   Google Scholar

[39]

J. Quariguasi Frota NetoG. WaltherJ. BloemhofJ. Van Nunen and T. Spengler, From closed-loop to sustainable supply chains: the weee case, International Journal of Production Research, 48 (2010), 4463-4481.   Google Scholar

[40]

N. SahebjamniaA. M. Fathollahi-Fard and M. Hajiaghaei-Keshteli, Sustainable tire closed-loop supply chain network design: Hybrid metaheuristic algorithms for large-scale networks, Journal of cleaner production, 196 (2018), 273-296.   Google Scholar

[41]

Y. ShiL. C. AlwanC. Tang and X. Yue, A newsvendor model with autocorrelated demand under a time-consistent dynamic cvar measure, IISE Transactions, 51 (2019), 653-671.   Google Scholar

[42]

H. Soleimani and K. Govindan, Reverse logistics network design and planning utilizing conditional value at risk, European Journal of Operational Research, 237 (2014), 487-497.  doi: 10.1016/j.ejor.2014.02.030.  Google Scholar

[43]

A. SorokinV. BoginskiA. Nahapetyan and P. M. Pardalos, Computational risk management techniques for fixed charge network flow problems with uncertain arc failures, Journal of Combinatorial Optimization, 25 (2013), 99-122.  doi: 10.1007/s10878-011-9422-2.  Google Scholar

[44]

K. SubulanA. BaykasoğluF. B. ÖzsoydanA. S. Taşan and H. Selim, A case-oriented approach to a lead/acid battery closed-loop supply chain network design under risk and uncertainty, Journal of Manufacturing Systems, 37 (2015), 340-361.   Google Scholar

[45]

H. A. Taha, Operations Research: An Introduction, Vol. 790, Pearson/Prentice Hall, 2011. Google Scholar

[46]

M. TalaeiB. F. MoghaddamM. S. PishvaeeA. 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.   Google Scholar

[47]

R. Tavakkoli-MoghaddamS. SadriN. Pourmohammad-Zia and M. Mohammadi, A hybrid fuzzy approach for the closed-loop supply chain network design under uncertainty, Journal of Intelligent & Fuzzy Systems, 28 (2015), 2811-2826.   Google Scholar

[48]

S. TorabiJ. NamdarS. Hatefi and F. Jolai, An enhanced possibilistic programming approach for reliable closed-loop supply chain network design, International Journal of Production Research, 54 (2016), 1358-1387.   Google Scholar

Figure 2.  Life cycle stages and corresponding inventories
Table 1.  Survey on CLSC
Reference Kind of CLSC Resilience Disruption Uncertainty Risk Objectives Industry Method
Talaei et al.[46] Reliable Both partial, complete disruption Probabilistic mixed programming P-robust Economic Numerical example Epsilon-constraint
Ghomi Avili et al. [17] Reliable and resilient Extra inventory Lateral transshipment Reliable and unreliable suppliers Complete disruption Two-stage probabilistic mixed programming Supply risk Economic Numerical example *CS
Tavakkoli Moghaddam et al. [47] Possibilistic fuzzy approach Economic Numerical example CS
Mari et al. [28] Sustainable and resilient Probabilistic disruption Probabilistic Economic and emissions of Carbon footprints Disruption costs Textile industry CS
Amin and Baki [1] Fuzzy programming Economic Electronics industry CS
Amin et al. [2] Scenario Scenario tree Economic Tire marketing CS
Soleimani and Govindan [42] Two-stage scenario CVaR Economic Numerical example CS
Cardoso et al. [7] Stochastic Variance, *VI, *DR, and CVaR Economic (ENPV) Numerical example *AEC
Subulan et al. [44] Stochastic-fuzzy and possibilistic VaR, CVaR, and downside risk Economic and the average of the collected volume of the used products Lead-acid battery CS
Prakash et al. [38] Robust and reliable Scenario Stochastic Worst risk case Economic Electronics trade industry CS
Prakash et al. [37] Waiting times Economic Hospital beds CS
Sahebjamnia et al. [40] Sustainable and resilient Economic, environmental, and social Tire industry *MH
Behzadi et al. [3] Resilient Diversified demand market, backup demand market, and flexible rerouting Scenario Robust optimization Two-stage stochastic Economic Kiwifruit CS
Brandenburg [5] Scenario Stochastic Economic and environmental FMCG manufacturer *WGP
Brandenburg [6] Green Simulation VaR Economic and environmental Numerical example CS
The present study Robust, sustainable resilient, and reliable Capacity Partial disruption Stochastic CVaR Economic, Environmental, social and energy Car manufacturing industry CS NEOS
*CS: Commercial Solver, AEC: Augmented epsilon constraint, MH: RDA and SA algorithm, GA and WWO algorithm, WGP: Weighted goal programming, VI: Variability index, DR: Downside risk, NA: Not Applicable.
Reference Kind of CLSC Resilience Disruption Uncertainty Risk Objectives Industry Method
Talaei et al.[46] Reliable Both partial, complete disruption Probabilistic mixed programming P-robust Economic Numerical example Epsilon-constraint
Ghomi Avili et al. [17] Reliable and resilient Extra inventory Lateral transshipment Reliable and unreliable suppliers Complete disruption Two-stage probabilistic mixed programming Supply risk Economic Numerical example *CS
Tavakkoli Moghaddam et al. [47] Possibilistic fuzzy approach Economic Numerical example CS
Mari et al. [28] Sustainable and resilient Probabilistic disruption Probabilistic Economic and emissions of Carbon footprints Disruption costs Textile industry CS
Amin and Baki [1] Fuzzy programming Economic Electronics industry CS
Amin et al. [2] Scenario Scenario tree Economic Tire marketing CS
Soleimani and Govindan [42] Two-stage scenario CVaR Economic Numerical example CS
Cardoso et al. [7] Stochastic Variance, *VI, *DR, and CVaR Economic (ENPV) Numerical example *AEC
Subulan et al. [44] Stochastic-fuzzy and possibilistic VaR, CVaR, and downside risk Economic and the average of the collected volume of the used products Lead-acid battery CS
Prakash et al. [38] Robust and reliable Scenario Stochastic Worst risk case Economic Electronics trade industry CS
Prakash et al. [37] Waiting times Economic Hospital beds CS
Sahebjamnia et al. [40] Sustainable and resilient Economic, environmental, and social Tire industry *MH
Behzadi et al. [3] Resilient Diversified demand market, backup demand market, and flexible rerouting Scenario Robust optimization Two-stage stochastic Economic Kiwifruit CS
Brandenburg [5] Scenario Stochastic Economic and environmental FMCG manufacturer *WGP
Brandenburg [6] Green Simulation VaR Economic and environmental Numerical example CS
The present study Robust, sustainable resilient, and reliable Capacity Partial disruption Stochastic CVaR Economic, Environmental, social and energy Car manufacturing industry CS NEOS
*CS: Commercial Solver, AEC: Augmented epsilon constraint, MH: RDA and SA algorithm, GA and WWO algorithm, WGP: Weighted goal programming, VI: Variability index, DR: Downside risk, NA: Not Applicable.
Table 2.  Optimal value of the robust objective function and the value of the global criterion objective function
Objective The optimal value of proposed objective function The optimal value of base model objective function *Avg. Gap
Cost Pollutant (CO2) Energy Employ Cost Pollutant (CO2) Energy Employ.
Min Z1(Cost) 71470.14 1989597.20 2274555.62 1749 71357.80 1901777.18 2181635.25 1788 1.7%
Min Z2(CO2) 174731.64 1250941.04 1953758.20 4399 171286.39 1217249.59 1882470.29 4499 1.6%
Min Z3(Energy) 78459.12 1317174.17 1591575.21 2100 76899.32 1258753.29 1556561.01 2150 1.6%
Max Z4(Employ) 176760.32 1734074.55 2358201.83 4505 173265.9 1650207.07 2263490.75 4520 2.7%
Min Lp 76688.59 1285769.68 1594682.21 2141 76589.90 1251038.15 1559701.11 2151 1.2%
GAP 0.1% 2.8% 2.2% -0.45% 1.2%
* Avg. GAP = Average ((Proposed model objective- base model objective)/ base model objective)
Objective The optimal value of proposed objective function The optimal value of base model objective function *Avg. Gap
Cost Pollutant (CO2) Energy Employ Cost Pollutant (CO2) Energy Employ.
Min Z1(Cost) 71470.14 1989597.20 2274555.62 1749 71357.80 1901777.18 2181635.25 1788 1.7%
Min Z2(CO2) 174731.64 1250941.04 1953758.20 4399 171286.39 1217249.59 1882470.29 4499 1.6%
Min Z3(Energy) 78459.12 1317174.17 1591575.21 2100 76899.32 1258753.29 1556561.01 2150 1.6%
Max Z4(Employ) 176760.32 1734074.55 2358201.83 4505 173265.9 1650207.07 2263490.75 4520 2.7%
Min Lp 76688.59 1285769.68 1594682.21 2141 76589.90 1251038.15 1559701.11 2151 1.2%
GAP 0.1% 2.8% 2.2% -0.45% 1.2%
* Avg. GAP = Average ((Proposed model objective- base model objective)/ base model objective)
Table 3.  Weight variations versus objectives
$ X_1 $ $ X_2 $ $ X_3 $ $ X_4 $ Cost Pollutant $ (\text{CO}_2) $ Energy Employment
0 0.33 0.33 0.33 78143.63 1285793 1594659 2141.56
0.5 0.16 0.16 0.16 76688.59 1285770 1594682 2141.56
1 0 0 0 71470.15 1989597 2274556 1749.06
0.33 0 0.33 0.33 76689.36 1316802 1591633 2141.56
0.16 0.5 0.16 0.16 79603.18 1274957 1612078 2214.48
0 1 0 0 174731.6 1250941 1953758 4399.22
0.33 0.33 0 0.33 81873.39 1270004 1672336 2340.66
0.16 0.16 0.5 0.16 76688.97 1289052 1592359 2141.56
0 0 1 0 78459.12 1317174 1591575 2100.21
0.33 0.33 0.33 0 76688.59 1285770 1594682 2100.75
0.16 0.16 0.16 0.5 76688.59 1285770 1594682 2141.56
0 0 0 1 176760.3 1734075 2358202 4505.85
0.25 0.25 0.25 0.25 76688.59 1285769.68 1594682.21 2141.55
$ X_1 $ $ X_2 $ $ X_3 $ $ X_4 $ Cost Pollutant $ (\text{CO}_2) $ Energy Employment
0 0.33 0.33 0.33 78143.63 1285793 1594659 2141.56
0.5 0.16 0.16 0.16 76688.59 1285770 1594682 2141.56
1 0 0 0 71470.15 1989597 2274556 1749.06
0.33 0 0.33 0.33 76689.36 1316802 1591633 2141.56
0.16 0.5 0.16 0.16 79603.18 1274957 1612078 2214.48
0 1 0 0 174731.6 1250941 1953758 4399.22
0.33 0.33 0 0.33 81873.39 1270004 1672336 2340.66
0.16 0.16 0.5 0.16 76688.97 1289052 1592359 2141.56
0 0 1 0 78459.12 1317174 1591575 2100.21
0.33 0.33 0.33 0 76688.59 1285770 1594682 2100.75
0.16 0.16 0.16 0.5 76688.59 1285770 1594682 2141.56
0 0 0 1 176760.3 1734075 2358202 4505.85
0.25 0.25 0.25 0.25 76688.59 1285769.68 1594682.21 2141.55
Table 4.  Medium and large scale problems
Table 5.  Comparison of the main model with the lower bound and worst possible case
Problem Lower bound Main model Worst-case GAP1 GAP2
LP-Relax $ 0\le X\le 1 $ (A) Time GAMS Main model $ X\in\{0,1\} $(B) Time Relaxation $ X=1 $(C) Time GAMS
P1 10862.19 2.00 76688.59 8.40 173172.68 2.41 -86% 126%
P2 15720.97 3.83 90009.11 93.68 239036.43 3.41 -83% 166%
P3 21307.43 11.33 111813.32 1082.85 301446.39 8.33 -81% 170%
P4 44956.51 843.11 *127011.40 *3705.6 457454.73 521.33 -65% 260%
P5 74585.42 2967.01 *165745.37 *28810 668562.73 1530.36 -55% 303%
P6-P8 No solution was found
* Solved by NEOS-Server, GAP1= (B-A)/A, GAP2=(C-B)/B.
Problem Lower bound Main model Worst-case GAP1 GAP2
LP-Relax $ 0\le X\le 1 $ (A) Time GAMS Main model $ X\in\{0,1\} $(B) Time Relaxation $ X=1 $(C) Time GAMS
P1 10862.19 2.00 76688.59 8.40 173172.68 2.41 -86% 126%
P2 15720.97 3.83 90009.11 93.68 239036.43 3.41 -83% 166%
P3 21307.43 11.33 111813.32 1082.85 301446.39 8.33 -81% 170%
P4 44956.51 843.11 *127011.40 *3705.6 457454.73 521.33 -65% 260%
P5 74585.42 2967.01 *165745.37 *28810 668562.73 1530.36 -55% 303%
P6-P8 No solution was found
* Solved by NEOS-Server, GAP1= (B-A)/A, GAP2=(C-B)/B.
Table A2-1.  Model parameters for medium and large scale problems
Parameters Value Description
$ de{{m}_{rpt{s}'}} $ ($ \left| {{s}'} \right| $-1)*1000 + uniform(1000, 2000) Demand for various scenarios
$ f{{s}_{s}} $ uniform (1000, 2000)
$ f{{m}_{m}} $ uniform(40000, 50000)
$ f{{d}_{d}} $ uniform(3000, 4000
$ f{{r}_{r}} $ uniform(1000, 2000) Fixed costs (opening) (Thousand dollar)
$ f{{m}_{m}} $ uniform(2000, 3000)
$ f{{k}_{k}} $ uniform(2000, 3000)
$ f{{e}_{e}} $ uniform(1000, 2000)
$ Vsm_{smpts'} $ uniform(3, 4)
$ Vsm_{mdpts'} $ uniform(3, 4)
$ Vdr_{drpts'} $ uniform(3, 4)
$ Vrc_{rcpts'} $ uniform(3, 4) Variable costs (Dollar)
$ Vck_{ckpts'} $ uniform(3, 4)
$ Vke_{kepts'} $ uniform(3, 4)
$ Vksc_{kscpts'} $ uniform(3, 4)
$ Vkm_{kmpts'} $ uniform(3, 4)
$ Ems_{sts'} $ uniform(100,200)
$ Emm_{mts'} $ uniform(1000, 2000)
$ Emd_{dts'} $ uniform(100,200)
$ Emr_{rts'} $ uniform(100,200) Fixed pollution (opening) (carbon dioxide) (Centiton)
$ Emc_{cts'} $ uniform(100,200)
$ Emk_{kts'} $ uniform(100,200)
$ Eme_{ets'} $ uniform(100,200)
$ Emsm_{smpts'} $ uniform(4, 5) Variable pollution (carbon dioxide) (Centiton)
$ Emmd_{mdpts'} $ uniform(4, 5)
$ Emdr_{drpts'} $ uniform(4, 5)
$ Emrc_{rcpts'} $ uniform(4, 5)
$ Emck_{ckpts'} $ uniform(4, 5)
$ Emke_{kepts'} $ uniform(4, 5)
$ Emksc_{kscpts'} $ uniform(4, 5)
$ Emkm_{kmpts'} $ uniform(4, 5)
$ Es_{sts'} $ uniform(4000, 5000)
$ Em_{mts'} $ uniform(40000, 50000)
$ Ed_{dts'} $ uniform(4000, 5000)
$ Er_{rts'} $ uniform(4000, 5000) Fixed consumed energy (opening) (MJ)
$ Ec_{mts'} $ uniform(4000, 5000)
$ Ek_{kts'} $ uniform(4000, 5000)
$ Ee_{ets'} $ uniform(4000, 5000)
$ Esm_{smpts'} $ uniform(4, 5) Variable pollution (MJ)
$ Eemd_{mdpts'} $ uniform(4, 5)
$ Edr_{drpts'} $ uniform(4, 5)
$ Erc_{rcpts'} $ uniform(4, 5)
$ Eck_{ckpts'} $ uniform(4, 5)
$ Eke_{kepts'} $ uniform(4, 5)
$ Eksc_{kscpts'} $ uniform(4, 5)
$ Ekm_{kmpts'} $ uniform(4, 5)
$ Os_{sts'} $ uniform(40, 50)
$ Om_{mts'} $ uniform(300,400)
$ Od_{dts'} $ uniform(40, 50)
$ Or_{rts'} $ uniform(5, 10) Fixed employment (person)
$ Om_{mts'} $ uniform(20, 30)
$ Ok_{kts'} $ uniform(10, 15)
$ Oe_{ets'} $ uniform(5, 10)
$ VOs_{st'} $ uniform(1000, 1100)
$ VOm_{mt'} $ uniform(1000, 1100)
$ VOd_{dt'} $ uniform(1000, 1100)
$ VOr_{rt'} $ uniform(1000, 1100) Salary Cost (Dollars)
$ VOc_{ct'} $ uniform(1000, 1100)
$ VOk_{kt'} $ uniform(1000, 1100)
$ VOe_{et'} $ uniform(1000, 1100)
$ prs_{s'} $ uniform(0.95, 0.98);
$ prm_{m'} $ uniform(0.95, 0.98);
$ prd_{d'} $ uniform(0.95, 0.98);
$ prr_{r'} $ uniform(0.95, 0.98); Availability probability (percent)
$ prm_{m'} $ uniform(0.95, 0.98);
$ prk_{k'} $ uniform(0.95, 0.98);
$ pre_{e'} $ uniform(0.95, 0.98);
$ CapS_{spts'} $ uniform(50000, 60000)*(($ s' $-1)*0.5+1)
$ CapM_{mpts'} $ uniform(100000, 110000)*(($ s' $-1)*0.5+1)
$ CapD_{dpts'} $ uniform(20000, 22000)*(($ s' $-1)*0.5+1)
$ CapR_{rpts'} $ uniform(3000, 3300)*(($ s' $-1)*0.5+1) Capacity (facility)
$ CapC_{cpts'} $ uniform(20000, 22000)*(($ s' $-1)*0.5+1)
$ CapK_{kpts'} $ uniform(5000, 5500)*(($ s' $-1)*0.5+1)
$ CapE_{epts'} $ uniform(3000, 3300)*(($ s' $-1)*0.5+1)
$ p^{s'} $ 0.33 Scenario occurrence probability
$ \beta $ uniform(0, 0.2) Expectation value weight
$ \omega $ uniform(0, 0.1) Fine associated with demand dissatisfaction
$ \lambda $ uniform(0, 0.1) CVaR index importance
$ \alpha $ uniform(0, 0.05) 95% Confidence level in CVaR
$ k_{s'1} $ 0.05 Fine coefficient of demand dissatisfaction for quadruple objective
$ k_{s'2} $ 0.05
$ k_{s'3} $ 0.05
$ k_{s'4} $ 0.05
$ \rho_{rpts'} $ uniform(0, 1) Return percentage
$ \rho_{1pts'} $ uniform(0.7, 0.71)
$ \rho_{2pts'} $ uniform(0.2, 0.21)
$ \rho_{3pts'} $ uniform(0.1, 0.11)
$ W_i $ 0.25 Objective weight
Parameters Value Description
$ de{{m}_{rpt{s}'}} $ ($ \left| {{s}'} \right| $-1)*1000 + uniform(1000, 2000) Demand for various scenarios
$ f{{s}_{s}} $ uniform (1000, 2000)
$ f{{m}_{m}} $ uniform(40000, 50000)
$ f{{d}_{d}} $ uniform(3000, 4000
$ f{{r}_{r}} $ uniform(1000, 2000) Fixed costs (opening) (Thousand dollar)
$ f{{m}_{m}} $ uniform(2000, 3000)
$ f{{k}_{k}} $ uniform(2000, 3000)
$ f{{e}_{e}} $ uniform(1000, 2000)
$ Vsm_{smpts'} $ uniform(3, 4)
$ Vsm_{mdpts'} $ uniform(3, 4)
$ Vdr_{drpts'} $ uniform(3, 4)
$ Vrc_{rcpts'} $ uniform(3, 4) Variable costs (Dollar)
$ Vck_{ckpts'} $ uniform(3, 4)
$ Vke_{kepts'} $ uniform(3, 4)
$ Vksc_{kscpts'} $ uniform(3, 4)
$ Vkm_{kmpts'} $ uniform(3, 4)
$ Ems_{sts'} $ uniform(100,200)
$ Emm_{mts'} $ uniform(1000, 2000)
$ Emd_{dts'} $ uniform(100,200)
$ Emr_{rts'} $ uniform(100,200) Fixed pollution (opening) (carbon dioxide) (Centiton)
$ Emc_{cts'} $ uniform(100,200)
$ Emk_{kts'} $ uniform(100,200)
$ Eme_{ets'} $ uniform(100,200)
$ Emsm_{smpts'} $ uniform(4, 5) Variable pollution (carbon dioxide) (Centiton)
$ Emmd_{mdpts'} $ uniform(4, 5)
$ Emdr_{drpts'} $ uniform(4, 5)
$ Emrc_{rcpts'} $ uniform(4, 5)
$ Emck_{ckpts'} $ uniform(4, 5)
$ Emke_{kepts'} $ uniform(4, 5)
$ Emksc_{kscpts'} $ uniform(4, 5)
$ Emkm_{kmpts'} $ uniform(4, 5)
$ Es_{sts'} $ uniform(4000, 5000)
$ Em_{mts'} $ uniform(40000, 50000)
$ Ed_{dts'} $ uniform(4000, 5000)
$ Er_{rts'} $ uniform(4000, 5000) Fixed consumed energy (opening) (MJ)
$ Ec_{mts'} $ uniform(4000, 5000)
$ Ek_{kts'} $ uniform(4000, 5000)
$ Ee_{ets'} $ uniform(4000, 5000)
$ Esm_{smpts'} $ uniform(4, 5) Variable pollution (MJ)
$ Eemd_{mdpts'} $ uniform(4, 5)
$ Edr_{drpts'} $ uniform(4, 5)
$ Erc_{rcpts'} $ uniform(4, 5)
$ Eck_{ckpts'} $ uniform(4, 5)
$ Eke_{kepts'} $ uniform(4, 5)
$ Eksc_{kscpts'} $ uniform(4, 5)
$ Ekm_{kmpts'} $ uniform(4, 5)
$ Os_{sts'} $ uniform(40, 50)
$ Om_{mts'} $ uniform(300,400)
$ Od_{dts'} $ uniform(40, 50)
$ Or_{rts'} $ uniform(5, 10) Fixed employment (person)
$ Om_{mts'} $ uniform(20, 30)
$ Ok_{kts'} $ uniform(10, 15)
$ Oe_{ets'} $ uniform(5, 10)
$ VOs_{st'} $ uniform(1000, 1100)
$ VOm_{mt'} $ uniform(1000, 1100)
$ VOd_{dt'} $ uniform(1000, 1100)
$ VOr_{rt'} $ uniform(1000, 1100) Salary Cost (Dollars)
$ VOc_{ct'} $ uniform(1000, 1100)
$ VOk_{kt'} $ uniform(1000, 1100)
$ VOe_{et'} $ uniform(1000, 1100)
$ prs_{s'} $ uniform(0.95, 0.98);
$ prm_{m'} $ uniform(0.95, 0.98);
$ prd_{d'} $ uniform(0.95, 0.98);
$ prr_{r'} $ uniform(0.95, 0.98); Availability probability (percent)
$ prm_{m'} $ uniform(0.95, 0.98);
$ prk_{k'} $ uniform(0.95, 0.98);
$ pre_{e'} $ uniform(0.95, 0.98);
$ CapS_{spts'} $ uniform(50000, 60000)*(($ s' $-1)*0.5+1)
$ CapM_{mpts'} $ uniform(100000, 110000)*(($ s' $-1)*0.5+1)
$ CapD_{dpts'} $ uniform(20000, 22000)*(($ s' $-1)*0.5+1)
$ CapR_{rpts'} $ uniform(3000, 3300)*(($ s' $-1)*0.5+1) Capacity (facility)
$ CapC_{cpts'} $ uniform(20000, 22000)*(($ s' $-1)*0.5+1)
$ CapK_{kpts'} $ uniform(5000, 5500)*(($ s' $-1)*0.5+1)
$ CapE_{epts'} $ uniform(3000, 3300)*(($ s' $-1)*0.5+1)
$ p^{s'} $ 0.33 Scenario occurrence probability
$ \beta $ uniform(0, 0.2) Expectation value weight
$ \omega $ uniform(0, 0.1) Fine associated with demand dissatisfaction
$ \lambda $ uniform(0, 0.1) CVaR index importance
$ \alpha $ uniform(0, 0.05) 95% Confidence level in CVaR
$ k_{s'1} $ 0.05 Fine coefficient of demand dissatisfaction for quadruple objective
$ k_{s'2} $ 0.05
$ k_{s'3} $ 0.05
$ k_{s'4} $ 0.05
$ \rho_{rpts'} $ uniform(0, 1) Return percentage
$ \rho_{1pts'} $ uniform(0.7, 0.71)
$ \rho_{2pts'} $ uniform(0.2, 0.21)
$ \rho_{3pts'} $ uniform(0.1, 0.11)
$ W_i $ 0.25 Objective weight
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