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A novel separate chanceconstrained programming model to design a sustainable medical ventilator supply chain network during the Covid19 pandemic
1.  Department of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran 
2.  Department of Industrial Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran 
Providing new models or designing sustainable networks in recent studies represents a growing trend. However, there is still a gap in the simultaneous modeling of the three dimensions of sustainability in the electronic medical device supply chain (SC). In this paper, a novel hybrid chanceconstrained programming and cost function model is presented for a green and sustainable closedloop medical ventilator SC network design. To bring the problem closer to reality, a wide range of parameters including all cost parameters, demands, the upper bound of the released $ co_2 $, and the minimum percentage of the units of product to be disposed and collected from a customer and to be dismantled and shipped from DCs are modeled as uncertain along with the normal probability distribution. The problem was first formulated into the framework of a biobjective stochastic mixedinteger linear programming (MILP) model; then, it was reformulated into a triobjective deterministic mixedinteger nonlinear programming (MINLP) one. In order to model the environmental sustainability dimension, in addition to handling the total greenhouse gas emissions, the total waste products were also controlled. The efficiency and applicability of the proposed model were tested in an Iranian medical ventilator production and distribution network. For sensitivity analyses, the effect of some critical parameters on the values of the objective functions was carefully examined. Finally, valuable managerial insights into the challenges of companies during the COVID19 pandemic were presented. Numerical results showed that with the increase in the number of customers in the COVID19 crisis, social responsibility could improve cost mean by up to 8%.
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A. M. FathollahiFard and M. HajiaghaeiKeshteli, A stochastic multiobjective model for a closedloop supply chain with environmental considerations, Applied Soft Computing, 69 (2018), 232249. doi: 10.1016/j.asoc.2018.04.055. 
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M. FazliKhalaf, A. Mirzazadeh and M. S. Pishvaee, A robust fuzzy stochastic programming model for the design of a reliable green closedloop supply chain network, Human and Ecological Risk Assessment: An International Journal, 23 (2017), 21192149. doi: 10.1080/10807039.2017.1367644. 
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R. Lotfi, N. Mardani and G. W. Weber, Robust bilevel programming for renewable energy location, International Journal of Energy Research, 45 (2021), 75217534. doi: 10.1002/er.6332. 
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R. Lotfi, Y. Z. Mehrjerdi, M. S. Pishvaee, A. Sadeghieh and G. W. Weber, A robust optimization model for sustainable and resilient closedloop supply chain network design considering conditional value at risk, Numer. Algebra Control Optim., 11 (2021), 221253. doi: 10.3934/naco.2020023. 
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[24] 
A. S. Mohammadi, A. Alemtabriz, M. S. Pishvaee and M. Zandieh, A multistage stochastic programming model for sustainable closedloop supply chain network design with financial decisions: A case study of plastic production and recycling supply chain, Scientia Iranica, 27 (2020), 377395. doi: 10.24200/sci.2019.21531. 
[25] 
Z. Mohtashami, A. BozorgiAmiri and R. TavakkoliMoghaddam, A twostage multiobjective second generation biodiesel supply chain design considering social sustainability: A case study, Energy, 233 (2021), 121020. doi: 10.1016/j.energy.2021.121020. 
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L. A. MoncayoMartínez and D. Z. Zhang, Multiobjective ant colony optimisation: A metaheuristic approach to supply chain design, International Journal of Production Economics, 131 (2011), 407420. 
[27] 
S. Nayeri, S. A. Torabi, M. Tavakoli and Z. Sazvar, A multiobjective fuzzy robust stochastic model for designing a sustainableresilientresponsive supply chain network, Journal of Cleaner Production, 311 (2021), 127691. doi: 10.1016/j.jclepro.2021.127691. 
[28] 
M. Nicola, Z. Alsafi, C. Sohrabi, A. Kerwan, A. AlJabir, C. Iosifidis, M. Agha and R. Agha, The socioeconomic implications of the coronavirus pandemic (COVID19): A review, International Journal of Surgery, 78 (2020), 185193. doi: 10.1016/j.ijsu.2020.04.018. 
[29] 
K. P. Nurjanni, M. S. Carvalho and L. Costa, Green supply chain design: A mathematical modeling approach based on a multiobjective optimization model, International Journal of Production Economics, 183 (2017), 421432. doi: 10.1016/j.ijpe.2016.08.028. 
[30] 
E. Özceylan, N. Demirel, C. Cetinkaya and E. Demirel, A closedloop supply chain network design for automotive industry in Turkey, Computer and Industrial Engineering, 113 (2016), 727745. 
[31] 
S. M. Pahlevan, S. M. S. Hosseini and A. Goli, Sustainable supply chain network design using products' life cycle in the aluminum industry, Environmental Science and Pollution Research, (2021), 1–25. 
[32] 
S. H. R. Pasandideh, S. T. A. Niaki and K. Asadi, Biobjective optimization of a multiproduct multiperiod threeechelon supply chain problem under uncertain environments: NSGAII and NRGA, Inform. Sci., 292 (2015), 5774. doi: 10.1016/j.ins.2014.08.068. 
[33] 
M. M. Paydar, V. Babaveisi and A. S. Safaei, An engine oil closedloop supply chain design considering collection risk, Computers & Chemical Engineering, 104 (2017), 3855. doi: 10.1016/j.compchemeng.2017.04.005. 
[34] 
M. S. Pishvaee and J. Razmi, Environmental supply chain network design using multiobjective fuzzy mathematical programming, Appl. Math. Model., 36 (2012), 34333446. doi: 10.1016/j.apm.2011.10.007. 
[35] 
M. S. Pishvaee, J. 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), 1438. 
[36] 
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[37] 
A. Sadrnia, A. P. Sani and N. R. Langarudi, Sustainable closedloop supply chain network optimization for construction machinery recovering, J. Ind. Manag. Optim., 17 (2021), 23892414. doi: 10.3934/jimo.2020074. 
[38] 
T. Santoso, S. Ahmed, M. Goetschalckx and A. Shapiro, A stochastic programming approach for supply chain network design under uncertainty, European J. Oper. Res., 167 (2005), 96115. doi: 10.1016/j.ejor.2004.01.046. 
[39] 
S. Seuring and M. Müller, From a literature review to a conceptual framework for sustainable supply chain management, Journal of Cleaner Production, 16 (2008), 16991710. 
[40] 
H. Soleimani and G. Kannan, A hybrid particle swarm optimization and genetic algorithm for closedloop supply chain network design in largescale networks, Appl. Math. Model., 39 (2015), 39904012. doi: 10.1016/j.apm.2014.12.016. 
[41] 
M. Talaei, B. F. Moghaddam, M. S. Pishvaee, A. BozorgiAmiri and S. Gholamnejad, A robust fuzzy optimization model for carbonefficient closedloop supply chain network design problem: A numerical illustration in electronics industry, Journal of Cleaner Production, 113 (2015), 662673. 
[42] 
A. B. Tavana, M. Rabieh, M. S. Phishvaee and M. Esmaeili, A stochastic Mathematical Programming Approach to Resilient Supplier Selection and Order Allocation Problem: A Case Study of Iran Khodro Supply Chain, Scientia Iranica, 2021. 
[43] 
E. B. Tirkolaee, P. Abbasian and G. W. Weber, Sustainable fuzzy multitrip locationrouting problem for medical waste management during the COVID19 outbreak, Science of the Total Environment, 726 (2021), 143607. doi: 10.1016/j.scitotenv.2020.143607. 
[44] 
E. B. Tirkolaee, I. Mahdavi, M. M. S. Esfahani and G. W. Weber, A robust green locationallocationinventory problem to design an urban waste management system under uncertainty, Waste Management, 102 (2020), 340350. doi: 10.1016/j.wasman.2019.10.038. 
[45] 
Y.C. Tsao, V.V. Thanh, J.C. Lu and V. Yu, Designing sustainable supply chain networks under uncertain environments: Fuzzy multiobjective programming, Journal of Cleaner Production, 174 (2018), 15501565. doi: 10.1016/j.jclepro.2017.10.272. 
[46] 
M. Varsei and S. Polyakovskiy, Sustainable supply chain network design: A case of the wine industry in Australia, Omega, 66 (2017), 236247. doi: 10.1016/j.omega.2015.11.009. 
[47] 
P. Yang, H. Wee, S. Chung and P. Ho, Sequential and global optimization for a closedloop deteriorating inventory supply chain, Math. Comput. Modelling, 52 (2010), 161176. doi: 10.1016/j.mcm.2010.02.005. 
[48] 
V. Yakavenka, I. Mallidis, D. Vlachos, E. Iakovou and Z. Eleni, Development of a multiobjective model for the design of sustainable supply chains: The case of perishable food products, Ann. Oper. Res., 294 (2020), 593621. doi: 10.1007/s10479019034345. 
[49] 
G. Zhang, J. Shang and W. Li, Collaborative production planning of supply chain under price and demand uncertainty, European J. Oper. Res., 215 (2011), 590603. doi: 10.1016/j.ejor.2011.07.007. 
[50] 
ISO, Final Draft International Standard ISO/FDIS 26000: 2010(E), Guidance on social responsibility (2010). 
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SAI. Social Accountability 8000 International Standards, SAI, New York (2001). 
[52] 
ISEA. Account Ability 1000. (AA1000) Framework, Standard, Guidelines and Professional Qualification, ISEA, London (1999). 
[53] 
ISO/TMB/WG/SR. Participating in the Future International Standard ISO 26000 on Social Responsibility, International Organization for Standardization, Geneva (2006). 
show all references
References:
[1] 
A. R. K. K. Abad and S. H. R. Pasandideh, Green closedloop supply chain network design: A novel biobjective chanceconstraint approach, RAIRO Oper. Res., 55 (2021), 811840. doi: 10.1051/ro/2021035. 
[2] 
A. Alshamsi and A. Diabat, A reverse logistics network design, Journal of Manufacturing Systems, 37 (2015), 589598. doi: 10.1016/j.jmsy.2015.02.006. 
[3] 
G. H. Brundtland, Our common futurecall for action, Environmental Conservation, 14 (1987), 291294. 
[4] 
M. K. Chalmardi and J.F. CamachoVallejo, A bilevel programming model for sustainable supply chain network design that considers incentives for using cleaner technologies, Journal of Cleaner Production, 213 (2019), 10351050. doi: 10.1016/j.jclepro.2018.12.197. 
[5] 
K. Devika, A. Jafarian and V. Nourbakhsh, Designing a sustainable closedloop supply chain network based on triple bottom line approach: A comparison of metaheuristics hybridization techniques, European J. Oper. Res., 235 (2014), 594615. doi: 10.1016/j.ejor.2013.12.032. 
[6] 
S. Elhedhli and R. Merrick, Green supply chain network design to reduce carbon emissions, Transportation Research Part D: Transport and Environment, 17 (2012), 370379. doi: 10.1016/j.trd.2012.02.002. 
[7] 
A. M. FathollahiFard and M. HajiaghaeiKeshteli, A stochastic multiobjective model for a closedloop supply chain with environmental considerations, Applied Soft Computing, 69 (2018), 232249. doi: 10.1016/j.asoc.2018.04.055. 
[8] 
M. FazliKhalaf, A. Mirzazadeh and M. S. Pishvaee, A robust fuzzy stochastic programming model for the design of a reliable green closedloop supply chain network, Human and Ecological Risk Assessment: An International Journal, 23 (2017), 21192149. doi: 10.1080/10807039.2017.1367644. 
[9] 
P. Ghadimi, C. Wang and M. K. Lim, Sustainable supply chain modeling and analysis: Past debate, present problems and future challenges, Resources, Conservation and Recycling, 140 (2019), 7284. doi: 10.1016/j.resconrec.2018.09.005. 
[10] 
A. Goli, E. B. Tirkolaee and N. S. Aydin, Fuzzy integrated cell formation and production scheduling considering automated guided vehicles and human factors, IEEE Transactions on Fuzzy Systems, 29 (2021), 36863695. doi: 10.1109/TFUZZ.2021.3053838. 
[11] 
A. Goli, H. K. Zare, R. TavakkoliMoghaddam and A. Sadeghieh, Application of robust optimization for a product portfolio problem using an invasive weed optimization algorithm, Numer. Algebra Control Optim., 92 (2019), 187209. doi: 10.3934/naco.2019014. 
[12] 
V. Gonela, D. Salazar, J. Zhang, A. Osmani, I. Awudu and B. Altman, Designing a sustainable stochastic electricity generation network with hybrid production strategies, International Journal of Production Research, 57 (2018), 23042326. 
[13] 
K. Govindan, H. Soleimani and D. Kannan, Reverse logistics and closedloop supply chain: A comprehensive review to explore the future, European J. Oper. Res., 240 (2015), 603626. doi: 10.1016/j.ejor.2014.07.012. 
[14] 
V. D. R. Guide Jr and L. N. Van Wassenhove, OR FORUMThe evolution of closedloop supply chain research, Operations Research, 57 (2009), 1018. 
[15] 
H. HeidariFathian and S. H. R. Pasandideh, Greenblood supply chain network design: Robust optimization, bounded objective function & Lagrangian relaxation, Computer & Industrial Engineering, 122 (2018), 95105. doi: 10.1016/j.cie.2018.05.051. 
[16] 
C. L. Hwang and A. S. M. Masud, Multiple Objective Decision Making, Methods and Applications: A StateofTheArt Survey, SpringerVerlag, BerlinNew York, 1979. 
[17] 
A. R. KalantariKhalilAbad and S. H. R. Pasandideh, Green closedloop supply chain network design with stochastic demand: A new accelerated benders decomposition method, Scientia Iranica, 2020. doi: 10.24200/sci.2020.53412.3249. 
[18] 
E. Keyvanshokooh, S. M. Ryan and E. Kabir, Hybrid robust and stochastic optimization for closed loop supply chain network design using accelerated benders decomposition, European J. Oper. Res., 249 (2016), 7692. doi: 10.1016/j.ejor.2015.08.028. 
[19] 
S. Liu and L. G. Papageorgiou, Multi objective optimization of production, distribution and capacity planning of global supply chains in the process industry, OmegaPart of Special Issue: Management Science and Environmental Issues, 41 (2013), 369382. 
[20] 
R. Lotfi, B. Kargar, S. H. Hoseini, S. Nazari, S. Safavi and G. W. Weber, Resilience and sustainable supply chain network design by considering renewable energy, International Journal of Energy Research, 45 (2021), 1774917766. doi: 10.1002/er.6943. 
[21] 
R. Lotfi, N. Mardani and G. W. Weber, Robust bilevel programming for renewable energy location, International Journal of Energy Research, 45 (2021), 75217534. doi: 10.1002/er.6332. 
[22] 
R. Lotfi, Y. Z. Mehrjerdi, M. S. Pishvaee, A. Sadeghieh and G. W. Weber, A robust optimization model for sustainable and resilient closedloop supply chain network design considering conditional value at risk, Numer. Algebra Control Optim., 11 (2021), 221253. doi: 10.3934/naco.2020023. 
[23] 
A. Mitra, T. Ray Chadhuri, A. Mitra, P. Pramanick and S. Zaman, Impact of COVID19 related shutdown on atmospheric carbon dioxide level in the city of Kolkata, Parana Journal of Science and Education, 6 (2020), 8492. 
[24] 
A. S. Mohammadi, A. Alemtabriz, M. S. Pishvaee and M. Zandieh, A multistage stochastic programming model for sustainable closedloop supply chain network design with financial decisions: A case study of plastic production and recycling supply chain, Scientia Iranica, 27 (2020), 377395. doi: 10.24200/sci.2019.21531. 
[25] 
Z. Mohtashami, A. BozorgiAmiri and R. TavakkoliMoghaddam, A twostage multiobjective second generation biodiesel supply chain design considering social sustainability: A case study, Energy, 233 (2021), 121020. doi: 10.1016/j.energy.2021.121020. 
[26] 
L. A. MoncayoMartínez and D. Z. Zhang, Multiobjective ant colony optimisation: A metaheuristic approach to supply chain design, International Journal of Production Economics, 131 (2011), 407420. 
[27] 
S. Nayeri, S. A. Torabi, M. Tavakoli and Z. Sazvar, A multiobjective fuzzy robust stochastic model for designing a sustainableresilientresponsive supply chain network, Journal of Cleaner Production, 311 (2021), 127691. doi: 10.1016/j.jclepro.2021.127691. 
[28] 
M. Nicola, Z. Alsafi, C. Sohrabi, A. Kerwan, A. AlJabir, C. Iosifidis, M. Agha and R. Agha, The socioeconomic implications of the coronavirus pandemic (COVID19): A review, International Journal of Surgery, 78 (2020), 185193. doi: 10.1016/j.ijsu.2020.04.018. 
[29] 
K. P. Nurjanni, M. S. Carvalho and L. Costa, Green supply chain design: A mathematical modeling approach based on a multiobjective optimization model, International Journal of Production Economics, 183 (2017), 421432. doi: 10.1016/j.ijpe.2016.08.028. 
[30] 
E. Özceylan, N. Demirel, C. Cetinkaya and E. Demirel, A closedloop supply chain network design for automotive industry in Turkey, Computer and Industrial Engineering, 113 (2016), 727745. 
[31] 
S. M. Pahlevan, S. M. S. Hosseini and A. Goli, Sustainable supply chain network design using products' life cycle in the aluminum industry, Environmental Science and Pollution Research, (2021), 1–25. 
[32] 
S. H. R. Pasandideh, S. T. A. Niaki and K. Asadi, Biobjective optimization of a multiproduct multiperiod threeechelon supply chain problem under uncertain environments: NSGAII and NRGA, Inform. Sci., 292 (2015), 5774. doi: 10.1016/j.ins.2014.08.068. 
[33] 
M. M. Paydar, V. Babaveisi and A. S. Safaei, An engine oil closedloop supply chain design considering collection risk, Computers & Chemical Engineering, 104 (2017), 3855. doi: 10.1016/j.compchemeng.2017.04.005. 
[34] 
M. S. Pishvaee and J. Razmi, Environmental supply chain network design using multiobjective fuzzy mathematical programming, Appl. Math. Model., 36 (2012), 34333446. doi: 10.1016/j.apm.2011.10.007. 
[35] 
M. S. Pishvaee, J. 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), 1438. 
[36] 
H. G. Resat and B. Unsal, A novel multiobjective optimization approach for sustainable supply chain: A case study in packaging industry, Sustainable Production and Consumption, 20 (2019), 2939. doi: 10.1016/j.spc.2019.04.008. 
[37] 
A. Sadrnia, A. P. Sani and N. R. Langarudi, Sustainable closedloop supply chain network optimization for construction machinery recovering, J. Ind. Manag. Optim., 17 (2021), 23892414. doi: 10.3934/jimo.2020074. 
[38] 
T. Santoso, S. Ahmed, M. Goetschalckx and A. Shapiro, A stochastic programming approach for supply chain network design under uncertainty, European J. Oper. Res., 167 (2005), 96115. doi: 10.1016/j.ejor.2004.01.046. 
[39] 
S. Seuring and M. Müller, From a literature review to a conceptual framework for sustainable supply chain management, Journal of Cleaner Production, 16 (2008), 16991710. 
[40] 
H. Soleimani and G. Kannan, A hybrid particle swarm optimization and genetic algorithm for closedloop supply chain network design in largescale networks, Appl. Math. Model., 39 (2015), 39904012. doi: 10.1016/j.apm.2014.12.016. 
[41] 
M. Talaei, B. F. Moghaddam, M. S. Pishvaee, A. BozorgiAmiri and S. Gholamnejad, A robust fuzzy optimization model for carbonefficient closedloop supply chain network design problem: A numerical illustration in electronics industry, Journal of Cleaner Production, 113 (2015), 662673. 
[42] 
A. B. Tavana, M. Rabieh, M. S. Phishvaee and M. Esmaeili, A stochastic Mathematical Programming Approach to Resilient Supplier Selection and Order Allocation Problem: A Case Study of Iran Khodro Supply Chain, Scientia Iranica, 2021. 
[43] 
E. B. Tirkolaee, P. Abbasian and G. W. Weber, Sustainable fuzzy multitrip locationrouting problem for medical waste management during the COVID19 outbreak, Science of the Total Environment, 726 (2021), 143607. doi: 10.1016/j.scitotenv.2020.143607. 
[44] 
E. B. Tirkolaee, I. Mahdavi, M. M. S. Esfahani and G. W. Weber, A robust green locationallocationinventory problem to design an urban waste management system under uncertainty, Waste Management, 102 (2020), 340350. doi: 10.1016/j.wasman.2019.10.038. 
[45] 
Y.C. Tsao, V.V. Thanh, J.C. Lu and V. Yu, Designing sustainable supply chain networks under uncertain environments: Fuzzy multiobjective programming, Journal of Cleaner Production, 174 (2018), 15501565. doi: 10.1016/j.jclepro.2017.10.272. 
[46] 
M. Varsei and S. Polyakovskiy, Sustainable supply chain network design: A case of the wine industry in Australia, Omega, 66 (2017), 236247. doi: 10.1016/j.omega.2015.11.009. 
[47] 
P. Yang, H. Wee, S. Chung and P. Ho, Sequential and global optimization for a closedloop deteriorating inventory supply chain, Math. Comput. Modelling, 52 (2010), 161176. doi: 10.1016/j.mcm.2010.02.005. 
[48] 
V. Yakavenka, I. Mallidis, D. Vlachos, E. Iakovou and Z. Eleni, Development of a multiobjective model for the design of sustainable supply chains: The case of perishable food products, Ann. Oper. Res., 294 (2020), 593621. doi: 10.1007/s10479019034345. 
[49] 
G. Zhang, J. Shang and W. Li, Collaborative production planning of supply chain under price and demand uncertainty, European J. Oper. Res., 215 (2011), 590603. doi: 10.1016/j.ejor.2011.07.007. 
[50] 
ISO, Final Draft International Standard ISO/FDIS 26000: 2010(E), Guidance on social responsibility (2010). 
[51] 
SAI. Social Accountability 8000 International Standards, SAI, New York (2001). 
[52] 
ISEA. Account Ability 1000. (AA1000) Framework, Standard, Guidelines and Professional Qualification, ISEA, London (1999). 
[53] 
ISO/TMB/WG/SR. Participating in the Future International Standard ISO 26000 on Social Responsibility, International Organization for Standardization, Geneva (2006). 
Year  Scholars  Flow  goals  Decision variables  Sustainability dimensions  Uncertainty modeling method  Uncertain parameters  Case study  
location/allocation  production technology  transportation mode  economical  Environmental  social  
2014  Pasandideh et al. [32]  Direct  M  √  √  Hybrid chanceconstraint and cost function  costs, demand, production and setup times  General  
2015  Alshamsi and Diabat [2]  Reverse  S  √  √  √  √  √      Washing machines and tumble dryers  
2016  Nurjanni et al. [29]  Directreverse  M  √  √  √  √      General  
2016  Keyvanshokooh et al. [18]  Directreverse  M  √  √  √  √  Robust stochastic programming approach  demand and returns based on market conditions  General  
2018  Fathollahi Fard and Hajiaghaei Keshteli [7]  Directreverse  M  √  √  √  twostage stochastic scenario based  production, manufacturing costs, assigning the cost of costumers to distribution centers, demands and return rates  General  
2018  Tsao et al. [45]  Direct  M  √  √  √  √  √  fuzzy programming  demand, costs, carbon emissions, job opportunities, and the detrimental effects  General  
2018  Gonela et al. [12]  Direct  M  √  √  √  √  multiobjective stochastic MILP programming  electricity conversion rate, biomass yield rate, and coal excavation rate  Electricity generation  
2019  Resat and unusal [36]  Directreverse  M  √  √  √  √  √      Packaging  
2019  Chalmardi and Vallejo [4]  Direct  M  √  √  √  √      General  
2020  Yakavenka et al. [48]  Direct  M  √  √  √  √  √      Perishable food  
2020  Kalantari Khalil Abad and Pasandideh [17]  Directreverse  S  √  √  √  √  twostage stochastic scenario based  demand and carbon cap  General  
2020  Mohammadi et al. [24]  Directreverse  M  √  √  √  √  multistage stochastic programming  demand and return products  plastic  
2021  Lotfi et al. [20]  Direct  S  √  √  √  twostage robust stochastic programming  Costs, 
General  
2021  Mohtashami et al. [25]  Direct  M  √  √  √  √      Biodiesel  
2021  Sadrnia et al. [37]  Directreverse  M  √  √  √  √      General  
2021  Pahlevan et al. [31]  Directreverse  M  √  √  √  √      Aluminum  
2021  Nayeri et al. [27]  Direct  M  √  √  √  √  √  fuzzy robust stochastic approach  The demand, costs, the capacity of facilities, environmental impacts, job opportunities, and the rates of remained capacity at disrupted facilities  Water heater  
  Current research  Directreverse  M  √  √  √  √  √  √  hybrid chanceconstraint programming and cost function  production, reproduction, holding, disassembly, collecting and transportation costs, demands, upper bound of 
Medical ventilator (ICU and portable) 
Year  Scholars  Flow  goals  Decision variables  Sustainability dimensions  Uncertainty modeling method  Uncertain parameters  Case study  
location/allocation  production technology  transportation mode  economical  Environmental  social  
2014  Pasandideh et al. [32]  Direct  M  √  √  Hybrid chanceconstraint and cost function  costs, demand, production and setup times  General  
2015  Alshamsi and Diabat [2]  Reverse  S  √  √  √  √  √      Washing machines and tumble dryers  
2016  Nurjanni et al. [29]  Directreverse  M  √  √  √  √      General  
2016  Keyvanshokooh et al. [18]  Directreverse  M  √  √  √  √  Robust stochastic programming approach  demand and returns based on market conditions  General  
2018  Fathollahi Fard and Hajiaghaei Keshteli [7]  Directreverse  M  √  √  √  twostage stochastic scenario based  production, manufacturing costs, assigning the cost of costumers to distribution centers, demands and return rates  General  
2018  Tsao et al. [45]  Direct  M  √  √  √  √  √  fuzzy programming  demand, costs, carbon emissions, job opportunities, and the detrimental effects  General  
2018  Gonela et al. [12]  Direct  M  √  √  √  √  multiobjective stochastic MILP programming  electricity conversion rate, biomass yield rate, and coal excavation rate  Electricity generation  
2019  Resat and unusal [36]  Directreverse  M  √  √  √  √  √      Packaging  
2019  Chalmardi and Vallejo [4]  Direct  M  √  √  √  √      General  
2020  Yakavenka et al. [48]  Direct  M  √  √  √  √  √      Perishable food  
2020  Kalantari Khalil Abad and Pasandideh [17]  Directreverse  S  √  √  √  √  twostage stochastic scenario based  demand and carbon cap  General  
2020  Mohammadi et al. [24]  Directreverse  M  √  √  √  √  multistage stochastic programming  demand and return products  plastic  
2021  Lotfi et al. [20]  Direct  S  √  √  √  twostage robust stochastic programming  Costs, 
General  
2021  Mohtashami et al. [25]  Direct  M  √  √  √  √      Biodiesel  
2021  Sadrnia et al. [37]  Directreverse  M  √  √  √  √      General  
2021  Pahlevan et al. [31]  Directreverse  M  √  √  √  √      Aluminum  
2021  Nayeri et al. [27]  Direct  M  √  √  √  √  √  fuzzy robust stochastic approach  The demand, costs, the capacity of facilities, environmental impacts, job opportunities, and the rates of remained capacity at disrupted facilities  Water heater  
  Current research  Directreverse  M  √  √  √  √  √  √  hybrid chanceconstraint programming and cost function  production, reproduction, holding, disassembly, collecting and transportation costs, demands, upper bound of 
Medical ventilator (ICU and portable) 
Indices  Statement  
:  Set of manufacturing plants, 

:  Set of warehouses 

:  Set of customers (university of medical S sciences) 

:  Set of DCs 

:  Set of transportation modes from manufacturing plants 

:  Set of transportation modes from warehouses 

:  Set of transportation modes from customers 

:  Set of transportation modes from DCs 

:  Set of production technologies 
Indices  Statement  
:  Set of manufacturing plants, 

:  Set of warehouses 

:  Set of customers (university of medical S sciences) 

:  Set of DCs 

:  Set of transportation modes from manufacturing plants 

:  Set of transportation modes from warehouses 

:  Set of transportation modes from customers 

:  Set of transportation modes from DCs 

:  Set of production technologies 
Parameters  Explanation  
:  Fixed cost for establishing the manufacturing plant 

:  Fixed cost for establishing the warehouse 

:  Fixed cost for establishing DC 

:  Unit variable cost for producing a unit product with the technology 

:  Unit variable cost for handling a unit of product with the technology 

:  Unit variable cost for collecting a unit of product with the technology 

:  Unit variable cost for disassembling a unit of product with the technology 

:  Unit variable cost for reproducing a unit product with the technology 

:  Unit transportation cost for products with the technology 

:  Unit transportation cost for products with the technology 

:  Unit transportation cost for products with the technology 

:  Unit transportation cost for products with the technology 

:  The rate of the released 

:  The rate of the released 

:  The rate of the released 

:  The rate of the released 

:  
:  
:  
:  
:  Maximum production capacity of the manufacturing plant 

:  Maximum storage and handling, and the processing capacity of the warehouse 

:  Maximum disassembly capacity of DC 

:  Maximum reproduction capacity of the manufacturing plant 

:  Transportation rate from the manufacturing plant 

:  Transportation rate from the warehouse 

:  Transportation rate cost for collecting the unit of product from the customer 

:  Transportation rate from the DC 

:  Distance between the manufacturing plant 

:  Distance between the warehouse 

:  Distance between the customer 

:  Distance between the DC 

:  Minimum percentage of the units of product to be disposed to be collected from a customer with the mean 

:  Minimum percentage of the units of product to be dismantled to be shipped from a DC with the mean 

:  Demand of the customer 

:  The upper bound of the emission capacity of 

:  The upper bound of the number of products to be disposed  
:  The chance of rejecting a solution that does not satisfy the constraint  
:  The lower critical point of the standard normal distribution used for a 

:  The number of fixed job opportunities (i.e., job opportunities which are independent of the production capacity like managerial positions) created by the manufacturing plant 

:  The number of fixed job opportunities (i.e., job opportunities which are independent of the production capacity like managerial positions) created by the warehouse 

:  The number of fixed job opportunities (i.e., job opportunities which are independent of the production capacity like managerial positions) created by the DC 

:  The number of variable job opportunities (i.e., job opportunities which vary by production capacity like manufacturing line workers) created through producing at the manufacturing plant 

:  The number of variable job opportunities created through handling at the warehouse 

:  The number of variable job opportunities created through disassembling at the DC 

:  The number of variable job opportunities created through remanufacturing at the manufacturing plant 

:  Average fraction of the potentially hazardous products when the technology 

:  The lost days caused from work's damages during the establishment of the technology 

:  The lost days caused from the work's damages during the establishment of the warehouse 

:  The lost days caused from the work's damages during the establishment of the DC 

:  The lost days caused from the work's damages during production at the manufacturing plant 

:  The lost days caused from the work's damages during handling at the warehouse 

:  The lost days caused from the work's damages during disassembling at the DC 

:  The lost days caused from the work's damages during remanufacturing at the manufacturing plant 

:  Weighting the factor of the total number of the produced job opportunities  
:  Weighting the factor of the total number of the potentially hazardous products  
:  Weighting the factor of the total number of lost days caused from the work's damages 
Parameters  Explanation  
:  Fixed cost for establishing the manufacturing plant 

:  Fixed cost for establishing the warehouse 

:  Fixed cost for establishing DC 

:  Unit variable cost for producing a unit product with the technology 

:  Unit variable cost for handling a unit of product with the technology 

:  Unit variable cost for collecting a unit of product with the technology 

:  Unit variable cost for disassembling a unit of product with the technology 

:  Unit variable cost for reproducing a unit product with the technology 

:  Unit transportation cost for products with the technology 

:  Unit transportation cost for products with the technology 

:  Unit transportation cost for products with the technology 

:  Unit transportation cost for products with the technology 

:  The rate of the released 

:  The rate of the released 

:  The rate of the released 

:  The rate of the released 

:  
:  
:  
:  
:  Maximum production capacity of the manufacturing plant 

:  Maximum storage and handling, and the processing capacity of the warehouse 

:  Maximum disassembly capacity of DC 

:  Maximum reproduction capacity of the manufacturing plant 

:  Transportation rate from the manufacturing plant 

:  Transportation rate from the warehouse 

:  Transportation rate cost for collecting the unit of product from the customer 

:  Transportation rate from the DC 

:  Distance between the manufacturing plant 

:  Distance between the warehouse 

:  Distance between the customer 

:  Distance between the DC 

:  Minimum percentage of the units of product to be disposed to be collected from a customer with the mean 

:  Minimum percentage of the units of product to be dismantled to be shipped from a DC with the mean 

:  Demand of the customer 

:  The upper bound of the emission capacity of 

:  The upper bound of the number of products to be disposed  
:  The chance of rejecting a solution that does not satisfy the constraint  
:  The lower critical point of the standard normal distribution used for a 

:  The number of fixed job opportunities (i.e., job opportunities which are independent of the production capacity like managerial positions) created by the manufacturing plant 

:  The number of fixed job opportunities (i.e., job opportunities which are independent of the production capacity like managerial positions) created by the warehouse 

:  The number of fixed job opportunities (i.e., job opportunities which are independent of the production capacity like managerial positions) created by the DC 

:  The number of variable job opportunities (i.e., job opportunities which vary by production capacity like manufacturing line workers) created through producing at the manufacturing plant 

:  The number of variable job opportunities created through handling at the warehouse 

:  The number of variable job opportunities created through disassembling at the DC 

:  The number of variable job opportunities created through remanufacturing at the manufacturing plant 

:  Average fraction of the potentially hazardous products when the technology 

:  The lost days caused from work's damages during the establishment of the technology 

:  The lost days caused from the work's damages during the establishment of the warehouse 

:  The lost days caused from the work's damages during the establishment of the DC 

:  The lost days caused from the work's damages during production at the manufacturing plant 

:  The lost days caused from the work's damages during handling at the warehouse 

:  The lost days caused from the work's damages during disassembling at the DC 

:  The lost days caused from the work's damages during remanufacturing at the manufacturing plant 

:  Weighting the factor of the total number of the produced job opportunities  
:  Weighting the factor of the total number of the potentially hazardous products  
:  Weighting the factor of the total number of lost days caused from the work's damages 
Decision variables  Description  
:  1 if the manufacturing plant 

:  1 if the warehouse 

:  1 if DC 

:  The number of the unit product shipped from the manufacturing plant 

:  The number of the unit product shipped from the warehouse 

:  he number of the unit product to be disposed and collected from the customer 

:  The number of the unit product to be dismantled and shipped from the DC 
Decision variables  Description  
:  1 if the manufacturing plant 

:  1 if the warehouse 

:  1 if DC 

:  The number of the unit product shipped from the manufacturing plant 

:  The number of the unit product shipped from the warehouse 

:  he number of the unit product to be disposed and collected from the customer 

:  The number of the unit product to be dismantled and shipped from the DC 
University of Medical Sciences(customer zones)  Mean of the stochastic demand (unit per month)  Variance of the stochastic demand 
500  400  
260  90  
150  40  
210  160  
160  40  
200  90  
180  250  
170  250 
University of Medical Sciences(customer zones)  Mean of the stochastic demand (unit per month)  Variance of the stochastic demand 
500  400  
260  90  
150  40  
210  160  
160  40  
200  90  
180  250  
170  250 
Factories(i)  Production technology(m)  Mean of the Stochastic fixed cost (million Rials)  Variance of the Stochastic fixed cost (million Rials) 
Number of fixed job opportunities  Number of variable job opportunities created through manufacturing  Number of variable job opportunities created through remanufacturing 
ICU  120000  169000  70  15  10  
MRI  123000  144000  60  17  9  
ICU  143000  121000  78  17  9  
MRI  143000  100000  73  16  12  
ICU  132000  100000  78  16  10  
MRI  170000  121000  79  18  9 
Factories(i)  Production technology(m)  Mean of the Stochastic fixed cost (million Rials)  Variance of the Stochastic fixed cost (million Rials) 
Number of fixed job opportunities  Number of variable job opportunities created through manufacturing  Number of variable job opportunities created through remanufacturing 
ICU  120000  169000  70  15  10  
MRI  123000  144000  60  17  9  
ICU  143000  121000  78  17  9  
MRI  143000  100000  73  16  12  
ICU  132000  100000  78  16  10  
MRI  170000  121000  79  18  9 
Medical equipment storage centers (j)  Mean of the Stochastic fixed cost (million Rials)  Variance of the Stochastic fixed cost(million Rials) 
Number of fixed job opportunities  Number of variable job opportunities created through handling 
112000  121000  50  13  
140000  144000  55  14  
112000  100000  58  12 
Medical equipment storage centers (j)  Mean of the Stochastic fixed cost (million Rials)  Variance of the Stochastic fixed cost(million Rials) 
Number of fixed job opportunities  Number of variable job opportunities created through handling 
112000  121000  50  13  
140000  144000  55  14  
112000  100000  58  12 
Disassembly centers (l)  Mean of the Stochastic fixed cost (million Rials)  Variance of the Stochastic fixed cost(million Rials) 
Number of fixed job opportunities  Number of variable job opportunities created through disassembling 
70000  49000  39  15  
75000  36000  32  13  
72000  36000  42  15 
Disassembly centers (l)  Mean of the Stochastic fixed cost (million Rials)  Variance of the Stochastic fixed cost(million Rials) 
Number of fixed job opportunities  Number of variable job opportunities created through disassembling 
70000  49000  39  15  
75000  36000  32  13  
72000  36000  42  15 
Environmental constraints ( 
Customer demands constraints ( 
Return flow establishing constraints ( 

Coefficient confidence  0.95  0.99  0.95 
the lower critical point of the standard normal distribution  1.645  1.96  1.645 
Environmental constraints ( 
Customer demands constraints ( 
Return flow establishing constraints ( 

Coefficient confidence  0.95  0.99  0.95 
the lower critical point of the standard normal distribution  1.645  1.96  1.645 
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