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doi: 10.3934/jimo.2021234
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A novel separate chance-constrained programming model to design a sustainable medical ventilator supply chain network during the Covid-19 pandemic

Amin Reza Kalantari Khalil Abad 1, , Farnaz Barzinpour 1, and  Seyed Hamid Reza Pasandideh 2,,

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

* Corresponding author: Seyed Hamid Reza Pasandideh

Received  July 2021 Revised  October 2021 Early access January 2022

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 chance-constrained programming and cost function model is presented for a green and sustainable closed-loop 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 bi-objective stochastic mixed-integer linear programming (MILP) model; then, it was reformulated into a tri-objective deterministic mixed-integer 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 COVID-19 pandemic were presented. Numerical results showed that with the increase in the number of customers in the COVID-19 crisis, social responsibility could improve cost mean by up to 8%.

Keywords: Healthcare system, sustainable supply chain design, closed-loop supply chain, ventilator, COVID-19 pandemic, MINLP optimization, chance-constrained programming, multi-objective optimization, goal attainment.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.
Citation: 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, doi: 10.3934/jimo.2021234
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show all references

References:
[1]

A. R. K. K. Abad and S. H. R. Pasandideh, Green closed-loop supply chain network design: A novel bi-objective chance-constraint approach, RAIRO Oper. Res., 55 (2021), 811-840.  doi: 10.1051/ro/2021035.

[2]

A. Alshamsi and A. Diabat, A reverse logistics network design, Journal of Manufacturing Systems, 37 (2015), 589-598.  doi: 10.1016/j.jmsy.2015.02.006.

[3]

G. H. Brundtland, Our common future-call for action, Environmental Conservation, 14 (1987), 291-294. 

[4]

M. K. Chalmardi and J.-F. Camacho-Vallejo, A bi-level programming model for sustainable supply chain network design that considers incentives for using cleaner technologies, Journal of Cleaner Production, 213 (2019), 1035-1050.  doi: 10.1016/j.jclepro.2018.12.197.

[5]

K. Devika, A. Jafarian and V. Nourbakhsh, Designing a sustainable closed-loop supply chain network based on triple bottom line approach: A comparison of metaheuristics hybridization techniques, European J. Oper. Res., 235 (2014), 594-615.  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), 370-379.  doi: 10.1016/j.trd.2012.02.002.

[7]

A. M. Fathollahi-Fard and M. Hajiaghaei-Keshteli, A stochastic multi-objective model for a closed-loop supply chain with environmental considerations, Applied Soft Computing, 69 (2018), 232-249.  doi: 10.1016/j.asoc.2018.04.055.

[8]

M. Fazli-Khalaf, A. Mirzazadeh and M. S. Pishvaee, A robust fuzzy stochastic programming model for the design of a reliable green closed-loop supply chain network, Human and Ecological Risk Assessment: An International Journal, 23 (2017), 2119-2149.  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), 72-84.  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), 3686-3695.  doi: 10.1109/TFUZZ.2021.3053838.

[11]

A. Goli, H. K. Zare, R. Tavakkoli-Moghaddam and A. Sadeghieh, Application of robust optimization for a product portfolio problem using an invasive weed optimization algorithm, Numer. Algebra Control Optim., 92 (2019), 187-209.  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), 2304-2326. 

[13]

K. Govindan, H. Soleimani and D. Kannan, Reverse logistics and closed-loop supply chain: A comprehensive review to explore the future, European J. Oper. Res., 240 (2015), 603-626.  doi: 10.1016/j.ejor.2014.07.012.

[14]

V. D. R. Guide Jr and L. N. Van Wassenhove, OR FORUM-The evolution of closed-loop supply chain research, Operations Research, 57 (2009), 10-18. 

[15]

H. Heidari-Fathian and S. H. R. Pasandideh, Green-blood supply chain network design: Robust optimization, bounded objective function & Lagrangian relaxation, Computer & Industrial Engineering, 122 (2018), 95-105.  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 State-of-The-Art Survey, Springer-Verlag, Berlin-New York, 1979.

[17]

A. R. Kalantari-Khalil-Abad and S. H. R. Pasandideh, Green closed-loop 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), 76-92.  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, Omega-Part of Special Issue: Management Science and Environmental Issues, 41 (2013), 369-382. 

[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), 17749-17766.  doi: 10.1002/er.6943.

[21]

R. Lotfi, N. Mardani and G. W. Weber, Robust bi-level programming for renewable energy location, International Journal of Energy Research, 45 (2021), 7521-7534.  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 closed-loop supply chain network design considering conditional value at risk, Numer. Algebra Control Optim., 11 (2021), 221-253.  doi: 10.3934/naco.2020023.

[23]

A. Mitra, T. Ray Chadhuri, A. Mitra, P. Pramanick and S. Zaman, Impact of COVID-19 related shutdown on atmospheric carbon dioxide level in the city of Kolkata, Parana Journal of Science and Education, 6 (2020), 84-92. 

[24]

A. S. Mohammadi, A. Alemtabriz, M. S. Pishvaee and M. Zandieh, A multi-stage stochastic programming model for sustainable closed-loop supply chain network design with financial decisions: A case study of plastic production and recycling supply chain, Scientia Iranica, 27 (2020), 377-395.  doi: 10.24200/sci.2019.21531.

[25]

Z. Mohtashami, A. Bozorgi-Amiri and R. Tavakkoli-Moghaddam, A two-stage multi-objective 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. Moncayo-Martínez and D. Z. Zhang, Multi-objective ant colony optimisation: A meta-heuristic approach to supply chain design, International Journal of Production Economics, 131 (2011), 407-420. 

[27]

S. Nayeri, S. A. Torabi, M. Tavakoli and Z. Sazvar, A multi-objective fuzzy robust stochastic model for designing a sustainable-resilient-responsive 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. Al-Jabir, C. Iosifidis, M. Agha and R. Agha, The socio-economic implications of the coronavirus pandemic (COVID-19): A review, International Journal of Surgery, 78 (2020), 185-193.  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 multi-objective optimization model, International Journal of Production Economics, 183 (2017), 421-432.  doi: 10.1016/j.ijpe.2016.08.028.

[30]

E. Özceylan, N. Demirel, C. Cetinkaya and E. Demirel, A closed-loop supply chain network design for automotive industry in Turkey, Computer and Industrial Engineering, 113 (2016), 727-745. 

[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, Bi-objective optimization of a multi-product multi-period three-echelon supply chain problem under uncertain environments: NSGA-II and NRGA, Inform. Sci., 292 (2015), 57-74.  doi: 10.1016/j.ins.2014.08.068.

[33]

M. M. Paydar, V. Babaveisi and A. S. Safaei, An engine oil closed-loop supply chain design considering collection risk, Computers & Chemical Engineering, 104 (2017), 38-55.  doi: 10.1016/j.compchemeng.2017.04.005.

[34]

M. S. Pishvaee and J. Razmi, Environmental supply chain network design using multi-objective fuzzy mathematical programming, Appl. Math. Model., 36 (2012), 3433-3446.  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), 14-38. 

[36]

H. G. Resat and B. Unsal, A novel multi-objective optimization approach for sustainable supply chain: A case study in packaging industry, Sustainable Production and Consumption, 20 (2019), 29-39.  doi: 10.1016/j.spc.2019.04.008.

[37]

A. Sadrnia, A. P. Sani and N. R. Langarudi, Sustainable closed-loop supply chain network optimization for construction machinery recovering, J. Ind. Manag. Optim., 17 (2021), 2389-2414.  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), 96-115.  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), 1699-1710. 

[40]

H. Soleimani and G. Kannan, A hybrid particle swarm optimization and genetic algorithm for closed-loop supply chain network design in large-scale networks, Appl. Math. Model., 39 (2015), 3990-4012.  doi: 10.1016/j.apm.2014.12.016.

[41]

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 (2015), 662-673. 

[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]

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Figure 1.  Significant growth in the demand for ventilator in New York City in 2020.1
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Figure 2.  The underlying configuration of integrated closed-loop medical ventilator SC network
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Figure 3.  Research roadmap
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Figure 4.  The necessity of the simultaneous reduction of the mean and variance of the costs to increase the decision -making confidence
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Figure 5.  Geographical locations of the selected facilities for solution
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Figure 6.  Schematic view of the connection and transportation methods between facilities
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Figure 7.  The effect of increasing the demand of all customers on different objective functions and CPU time
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Figure 8.  The effect of the increasing the upper bound of $co_2$ released on different objective functions and CPU time
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Figure 9.  The effect of increasing the upper bound of waste product on different objective functions and CPU time
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Figure 10.  Comparison between the expected value of cost in the models with and without the SR indicator
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Figure 11.  Comparison between the variance of cost in the models with and without the SR
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Figure 12.  The growing trend of the expected value of costs with increasing the number of customers
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Figure 13.  The growing trend of the cost variance with increasing the number of customers
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Table 1.  The assumption of the hypotheses that have been considered in previous studies and the gaps covered by this research
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 chance-constraint and cost function costs, demand, production and set-up times General
2015 Alshamsi and Diabat [2] Reverse S √ √ √ √ √ - - Washing machines and tumble dryers
2016 Nurjanni et al. [29] Direct-reverse M √ √ √ √ - - General
2016 Keyvanshokooh et al. [18] Direct-reverse M √ √ √ √ Robust stochastic programming approach demand and returns based on market conditions General
2018 Fathollahi Fard and Hajiaghaei Keshteli [7] Direct-reverse M √ √ √ two-stage 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 √ √ √ √ multi-objective stochastic MILP programming electricity con-version rate, biomass yield rate, and coal excavation rate Electricity generation
2019 Resat and unusal [36] Direct-reverse 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] Direct-reverse S √ √ √ √ two-stage stochastic scenario based demand and carbon cap General
2020 Mohammadi et al. [24] Direct-reverse M √ √ √ √ multi-stage stochastic programming demand and return products plastic
2021 Lotfi et al. [20] Direct S √ √ √ two-stage robust stochastic programming Costs, $co_2$ emission, energy consumption General
2021 Mohtashami et al. [25] Direct M √ √ √ √ - - Biodiesel
2021 Sadrnia et al. [37] Direct-reverse M √ √ √ √ - - General
2021 Pahlevan et al. [31] Direct-reverse 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 Direct-reverse M √ √ √ √ √ √ hybrid chance-constraint programming and cost function production, reproduction, holding, disassembly, collecting and transportation costs, demands, upper bound of $co_2$ released, and the minimum percentage of the units of product to be disposed and collected from a customer and to be dismantled and shipped from a DC Medical ventilator (ICU and portable)
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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 chance-constraint and cost function costs, demand, production and set-up times General
2015 Alshamsi and Diabat [2] Reverse S √ √ √ √ √ - - Washing machines and tumble dryers
2016 Nurjanni et al. [29] Direct-reverse M √ √ √ √ - - General
2016 Keyvanshokooh et al. [18] Direct-reverse M √ √ √ √ Robust stochastic programming approach demand and returns based on market conditions General
2018 Fathollahi Fard and Hajiaghaei Keshteli [7] Direct-reverse M √ √ √ two-stage 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 √ √ √ √ multi-objective stochastic MILP programming electricity con-version rate, biomass yield rate, and coal excavation rate Electricity generation
2019 Resat and unusal [36] Direct-reverse 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] Direct-reverse S √ √ √ √ two-stage stochastic scenario based demand and carbon cap General
2020 Mohammadi et al. [24] Direct-reverse M √ √ √ √ multi-stage stochastic programming demand and return products plastic
2021 Lotfi et al. [20] Direct S √ √ √ two-stage robust stochastic programming Costs, $co_2$ emission, energy consumption General
2021 Mohtashami et al. [25] Direct M √ √ √ √ - - Biodiesel
2021 Sadrnia et al. [37] Direct-reverse M √ √ √ √ - - General
2021 Pahlevan et al. [31] Direct-reverse 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 Direct-reverse M √ √ √ √ √ √ hybrid chance-constraint programming and cost function production, reproduction, holding, disassembly, collecting and transportation costs, demands, upper bound of $co_2$ released, and the minimum percentage of the units of product to be disposed and collected from a customer and to be dismantled and shipped from a DC Medical ventilator (ICU and portable)
Table 2.  Sets and indexes of the model
Indices Statement
$ i $ : Set of manufacturing plants, $ i\in \{1,2,\dots,I\} $
$ j $ : Set of warehouses $ j\in \{1,2,\dots,J\} $
$ k $ : Set of customers (university of medical S sciences) $ k\in \{1,2,\dots,K\} $
$ l $ : Set of DCs $ l\in \{1,2,\dots,L\} $
$ m $ : Set of transportation modes from manufacturing plants $ m\in\{1,2,\dots,M\} $
$ n $ : Set of transportation modes from warehouses $ n\in \{1,2,…,N\} $
$ o $ : Set of transportation modes from customers $ o\in \{1,2,\dots,O\} $
$ q $ : Set of transportation modes from DCs $ q\in \{1,2,\dots,Q\} $
$ t $ : Set of production technologies $ t\in \{1,2,\dots,T\} $
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Indices Statement
$ i $ : Set of manufacturing plants, $ i\in \{1,2,\dots,I\} $
$ j $ : Set of warehouses $ j\in \{1,2,\dots,J\} $
$ k $ : Set of customers (university of medical S sciences) $ k\in \{1,2,\dots,K\} $
$ l $ : Set of DCs $ l\in \{1,2,\dots,L\} $
$ m $ : Set of transportation modes from manufacturing plants $ m\in\{1,2,\dots,M\} $
$ n $ : Set of transportation modes from warehouses $ n\in \{1,2,…,N\} $
$ o $ : Set of transportation modes from customers $ o\in \{1,2,\dots,O\} $
$ q $ : Set of transportation modes from DCs $ q\in \{1,2,\dots,Q\} $
$ t $ : Set of production technologies $ t\in \{1,2,\dots,T\} $
Table 3.  Parameters of the model
Parameters Explanation
$\widetilde{fp_{i,t}}$ : Fixed cost for establishing the manufacturing plant $i\in I$ with production technology $t\in T$ with the mean $\mu fp_{i,t}$ and the variance $\sigma^2 fp_{i,t}$
$\widetilde{fw_j }$ : Fixed cost for establishing the warehouse $j\in J$ with the mean $\mu fw_j$ and the variance $\sigma^2 fw_j$
$\widetilde{fd_l}$ : Fixed cost for establishing DC $l\in L$ with the mean $\mu fd_l$ and the variance $\sigma^2 fd_l$
$\widetilde{vp_{i,t} } $ : Unit variable cost for producing a unit product with the technology $t\in T$ in the manufacturing plant $i\in I$ with the mean $\mu vp_{i,t}$ and the variance $\sigma^2 vp_{i,t}$
$\widetilde{vh_{j,t}} $ : Unit variable cost for handling a unit of product with the technology $t\in T$ in the warehouse $j\in J$ with the mean $\mu vh_{j,t}$ and the variance $\sigma^2 vh_{j,t}$
$\widetilde{vc_{k,t}} $ : Unit variable cost for collecting a unit of product with the technology $t\in T$ to be disposed from the customer $k\in K$ with the mean $\mu vc_{k,t}$ and the variance $\sigma^2 vc_{k,t}$
$\widetilde{vd_{l,t}} $ : Unit variable cost for disassembling a unit of product with the technology $t\in T$ to be disposed in the DC $l\in L$ with the mean $\mu vd_{l,t}$ and the variance $\sigma^2 vd_{l,t}$
$\widetilde{vr_{i,t} } $ : Unit variable cost for reproducing a unit product with the technology $t\in T$ in the manufacturing plant $i\in I$ with the mean $\mu vr_{i,t}$ and the variance $\sigma^2 vr_{i,t}$
$\widetilde{tpw_{i,j,t}^m } $ : Unit transportation cost for products with the technology $t\in T$ from the manufacturing plant $i\in I$ to the warehouse $j\in J$ with the transportation mode $m\in M$, the mean $\mu tpw_{i,j,t}^m$ and the variance $\sigma^2 tpw_{i,j,t}^m$
$\widetilde{twc_{j,k,t}^n } $ : Unit transportation cost for products with the technology $t\in T$ from the warehouse $j\in J$ to the customer $k\in K$ with the transportation mode $n\in N$, the mean $\mu twc_{j,k,t}^n$ and the variance $\sigma^2 twc_{j,k,t}^n$
$\widetilde{tcd_{k,l,t}^o } $ : Unit transportation cost for products with the technology $t\in T$ from the customer $k\in K$ to DC $l\in L$ with the transportation mode $o\in O$, the mean $\mu tcd_{k,l,t}^o$ and the variance $\sigma^2 tcd_{k,l,t}^o$
$\widetilde{tdp_{l,i,t}^q } $ : Unit transportation cost for products with the technology $t\in T$ from the DC $l\in L$ to the manufacturing plant $i\in I$ with the transportation mode $v\in V$, the mean $\mu tdp_{l,i}^v$ and the variance $\sigma^2 tdp_{l,i}^v$
${ep_{i,t}} $ : The rate of the released $co_2$ to produce unit of product with the technology $t\in T$ in the manufacturing plant $i\in I$
$ew_{j,t}$ : The rate of the released $co_2$ to handle and storage unit of product with the technology $t\in T$ in the warehouse $j\in J$
$ed_{l,t}$ : The rate of the released $co_2$ to disassemble unit of product with the technology $t\in T$ to be disposed in the DC $l\in L$
$er_{i,t}$ : The rate of the released $co_2$ to remanufacture unit of product with the technology $t\in T$ to be dismantled in the manufacturing plant $i\in I$
$etp_m$ : $co_2$ released by the transportation mode $m\in M$ to forward a unit of product from a manufacturing plant to a warehouse for a unit distance
$etw_n$ : $co_2$ released by the transportation mode $n\in N$ to forward a unit of product from a warehouse to a customer for a unit distance
$etc_o $ : $co_2$ released by the transportation mode $o\in O$ to collect a unit disposal from a customer to a DC for a unit distance
$etd_q $ : $co_2$ released by the transportation mode $q\in Q$ to ship a unit of product to be dismantled from a DC to a manufacturing plant for a unit distance
$cp_{i,t} $ : Maximum production capacity of the manufacturing plant $i\in I$ for products with the technology $t\in T$
$cw_{j,t}$ : Maximum storage and handling, and the processing capacity of the warehouse $j\in J$ for products with the technology $t\in T$
$cd_{l,t}$ : Maximum disassembly capacity of DC $l\in L$ for products with the technology $t\in T$
$cr_{i,t}$ : Maximum reproduction capacity of the manufacturing plant $i\in I$ for products with the technology $t\in T$
$\xi p_{i,j}^m$ : Transportation rate from the manufacturing plant $i\in I$ to the warehouse $j\in J$ with the transportation mode $m\in M$
$\xi w_{j,k}^n$ : Transportation rate from the warehouse $j\in J$ to the customer $k\in K$ with the transportation mode $n\in N$
$\xi c_{k,l}^o$ : Transportation rate cost for collecting the unit of product from the customer $k\in K$ to the DC $l\in L$ with the transportation mode $o\in O$
$\xi d_{l,i}^q$ : Transportation rate from the DC $l\in L$ to the manufacturing plant $i\in I$ with the transportation mode $q\in Q$
$dpw_{i,j}$ : Distance between the manufacturing plant $i\in I$ and the warehouse $j\in J$
$dwc_{j,k}$ : Distance between the warehouse $j\in J$ and the customer $k\in K$
$dcd_{k,l}$ : Distance between the customer $k\in K$ and the DC $l\in L$
$ddp_{l,i}$ : Distance between the DC $l\in L$ and the manufacturing plant $i\in I$
$\tilde{\delta}$ : Minimum percentage of the units of product to be disposed to be collected from a customer with the mean $\mu \delta$ and the variance $\sigma \delta$
$\tilde{\delta'}$ : Minimum percentage of the units of product to be dismantled to be shipped from a DC with the mean $\mu \delta'$ and the variance $\sigma^2 \delta'$
$\widetilde{dem_{k,t}} $ : Demand of the customer $k\in K$ for products with technology $t\in T$ with the mean $\mu dem_{k,t}$ and the variance $\sigma^2 dem_{k,t}$
$ \widetilde{UBE}$ : The upper bound of the emission capacity of $co_2$ released, which is determined by the government and regulatory bodies with the mean $\mu UBE$ and the variance $\sigma UBE$
$UBD$ : The upper bound of the number of products to be disposed
$1-\sigma,1-\omega,1-\xi$ : The chance of rejecting a solution that does not satisfy the constraint
$Z_{1-\sigma},Z_{1-\omega},Z_{1- \xi}$ : The lower critical point of the standard normal distribution used for a $( 1-\sigma\%, 1-\omega\%, 1- \xi\%)$ chance constraint on the solution obtained
$fjp_{i,t}$ : 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 $i\in I$ with the technology $t\in T$
$fjw_j$ : The number of fixed job opportunities (i.e., job opportunities which are independent of the production capacity like managerial positions) created by the warehouse $j\in J$
$fjd_l$ : The number of fixed job opportunities (i.e., job opportunities which are independent of the production capacity like managerial positions) created by the DC $l\in L$
$vjp_{i,t}$ : 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 $i\in I$ with the technology $t\in T$
$vjh_j$ : The number of variable job opportunities created through handling at the warehouse $j\in J$
$vjd_l$ : The number of variable job opportunities created through disassembling at the DC $l\in L$
$vjr_{i,t}$ : The number of variable job opportunities created through remanufacturing at the manufacturing plant $i\in I$ with the technology $t\in T$
$ph_t$ : Average fraction of the potentially hazardous products when the technology $u\in U$ is used
$eldp_{i,t}$ : The lost days caused from work's damages during the establishment of the technology $u\in U$ at the manufacturing plant $i\in I$
$eldw_j$ : The lost days caused from the work's damages during the establishment of the warehouse $j\in J $
$eldd_l$ : The lost days caused from the work's damages during the establishment of the DC $l\in L$
$vldp_{i,t}$ : The lost days caused from the work's damages during production at the manufacturing plant $i\in I$ with the technology $u$
$vldh_j$ : The lost days caused from the work's damages during handling at the warehouse $j\in J$
$vldd_l$ : The lost days caused from the work's damages during disassembling at the DC $l\in L$
$vldr_{i,u}$ : The lost days caused from the work's damages during remanufacturing at the manufacturing plant $i\in I$ with the technology $u\in U$
$wj$ : Weighting the factor of the total number of the produced job opportunities
$wp$ : Weighting the factor of the total number of the potentially hazardous products
$wl$ : Weighting the factor of the total number of lost days caused from the work's damages
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Parameters Explanation
$\widetilde{fp_{i,t}}$ : Fixed cost for establishing the manufacturing plant $i\in I$ with production technology $t\in T$ with the mean $\mu fp_{i,t}$ and the variance $\sigma^2 fp_{i,t}$
$\widetilde{fw_j }$ : Fixed cost for establishing the warehouse $j\in J$ with the mean $\mu fw_j$ and the variance $\sigma^2 fw_j$
$\widetilde{fd_l}$ : Fixed cost for establishing DC $l\in L$ with the mean $\mu fd_l$ and the variance $\sigma^2 fd_l$
$\widetilde{vp_{i,t} } $ : Unit variable cost for producing a unit product with the technology $t\in T$ in the manufacturing plant $i\in I$ with the mean $\mu vp_{i,t}$ and the variance $\sigma^2 vp_{i,t}$
$\widetilde{vh_{j,t}} $ : Unit variable cost for handling a unit of product with the technology $t\in T$ in the warehouse $j\in J$ with the mean $\mu vh_{j,t}$ and the variance $\sigma^2 vh_{j,t}$
$\widetilde{vc_{k,t}} $ : Unit variable cost for collecting a unit of product with the technology $t\in T$ to be disposed from the customer $k\in K$ with the mean $\mu vc_{k,t}$ and the variance $\sigma^2 vc_{k,t}$
$\widetilde{vd_{l,t}} $ : Unit variable cost for disassembling a unit of product with the technology $t\in T$ to be disposed in the DC $l\in L$ with the mean $\mu vd_{l,t}$ and the variance $\sigma^2 vd_{l,t}$
$\widetilde{vr_{i,t} } $ : Unit variable cost for reproducing a unit product with the technology $t\in T$ in the manufacturing plant $i\in I$ with the mean $\mu vr_{i,t}$ and the variance $\sigma^2 vr_{i,t}$
$\widetilde{tpw_{i,j,t}^m } $ : Unit transportation cost for products with the technology $t\in T$ from the manufacturing plant $i\in I$ to the warehouse $j\in J$ with the transportation mode $m\in M$, the mean $\mu tpw_{i,j,t}^m$ and the variance $\sigma^2 tpw_{i,j,t}^m$
$\widetilde{twc_{j,k,t}^n } $ : Unit transportation cost for products with the technology $t\in T$ from the warehouse $j\in J$ to the customer $k\in K$ with the transportation mode $n\in N$, the mean $\mu twc_{j,k,t}^n$ and the variance $\sigma^2 twc_{j,k,t}^n$
$\widetilde{tcd_{k,l,t}^o } $ : Unit transportation cost for products with the technology $t\in T$ from the customer $k\in K$ to DC $l\in L$ with the transportation mode $o\in O$, the mean $\mu tcd_{k,l,t}^o$ and the variance $\sigma^2 tcd_{k,l,t}^o$
$\widetilde{tdp_{l,i,t}^q } $ : Unit transportation cost for products with the technology $t\in T$ from the DC $l\in L$ to the manufacturing plant $i\in I$ with the transportation mode $v\in V$, the mean $\mu tdp_{l,i}^v$ and the variance $\sigma^2 tdp_{l,i}^v$
${ep_{i,t}} $ : The rate of the released $co_2$ to produce unit of product with the technology $t\in T$ in the manufacturing plant $i\in I$
$ew_{j,t}$ : The rate of the released $co_2$ to handle and storage unit of product with the technology $t\in T$ in the warehouse $j\in J$
$ed_{l,t}$ : The rate of the released $co_2$ to disassemble unit of product with the technology $t\in T$ to be disposed in the DC $l\in L$
$er_{i,t}$ : The rate of the released $co_2$ to remanufacture unit of product with the technology $t\in T$ to be dismantled in the manufacturing plant $i\in I$
$etp_m$ : $co_2$ released by the transportation mode $m\in M$ to forward a unit of product from a manufacturing plant to a warehouse for a unit distance
$etw_n$ : $co_2$ released by the transportation mode $n\in N$ to forward a unit of product from a warehouse to a customer for a unit distance
$etc_o $ : $co_2$ released by the transportation mode $o\in O$ to collect a unit disposal from a customer to a DC for a unit distance
$etd_q $ : $co_2$ released by the transportation mode $q\in Q$ to ship a unit of product to be dismantled from a DC to a manufacturing plant for a unit distance
$cp_{i,t} $ : Maximum production capacity of the manufacturing plant $i\in I$ for products with the technology $t\in T$
$cw_{j,t}$ : Maximum storage and handling, and the processing capacity of the warehouse $j\in J$ for products with the technology $t\in T$
$cd_{l,t}$ : Maximum disassembly capacity of DC $l\in L$ for products with the technology $t\in T$
$cr_{i,t}$ : Maximum reproduction capacity of the manufacturing plant $i\in I$ for products with the technology $t\in T$
$\xi p_{i,j}^m$ : Transportation rate from the manufacturing plant $i\in I$ to the warehouse $j\in J$ with the transportation mode $m\in M$
$\xi w_{j,k}^n$ : Transportation rate from the warehouse $j\in J$ to the customer $k\in K$ with the transportation mode $n\in N$
$\xi c_{k,l}^o$ : Transportation rate cost for collecting the unit of product from the customer $k\in K$ to the DC $l\in L$ with the transportation mode $o\in O$
$\xi d_{l,i}^q$ : Transportation rate from the DC $l\in L$ to the manufacturing plant $i\in I$ with the transportation mode $q\in Q$
$dpw_{i,j}$ : Distance between the manufacturing plant $i\in I$ and the warehouse $j\in J$
$dwc_{j,k}$ : Distance between the warehouse $j\in J$ and the customer $k\in K$
$dcd_{k,l}$ : Distance between the customer $k\in K$ and the DC $l\in L$
$ddp_{l,i}$ : Distance between the DC $l\in L$ and the manufacturing plant $i\in I$
$\tilde{\delta}$ : Minimum percentage of the units of product to be disposed to be collected from a customer with the mean $\mu \delta$ and the variance $\sigma \delta$
$\tilde{\delta'}$ : Minimum percentage of the units of product to be dismantled to be shipped from a DC with the mean $\mu \delta'$ and the variance $\sigma^2 \delta'$
$\widetilde{dem_{k,t}} $ : Demand of the customer $k\in K$ for products with technology $t\in T$ with the mean $\mu dem_{k,t}$ and the variance $\sigma^2 dem_{k,t}$
$ \widetilde{UBE}$ : The upper bound of the emission capacity of $co_2$ released, which is determined by the government and regulatory bodies with the mean $\mu UBE$ and the variance $\sigma UBE$
$UBD$ : The upper bound of the number of products to be disposed
$1-\sigma,1-\omega,1-\xi$ : The chance of rejecting a solution that does not satisfy the constraint
$Z_{1-\sigma},Z_{1-\omega},Z_{1- \xi}$ : The lower critical point of the standard normal distribution used for a $( 1-\sigma\%, 1-\omega\%, 1- \xi\%)$ chance constraint on the solution obtained
$fjp_{i,t}$ : 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 $i\in I$ with the technology $t\in T$
$fjw_j$ : The number of fixed job opportunities (i.e., job opportunities which are independent of the production capacity like managerial positions) created by the warehouse $j\in J$
$fjd_l$ : The number of fixed job opportunities (i.e., job opportunities which are independent of the production capacity like managerial positions) created by the DC $l\in L$
$vjp_{i,t}$ : 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 $i\in I$ with the technology $t\in T$
$vjh_j$ : The number of variable job opportunities created through handling at the warehouse $j\in J$
$vjd_l$ : The number of variable job opportunities created through disassembling at the DC $l\in L$
$vjr_{i,t}$ : The number of variable job opportunities created through remanufacturing at the manufacturing plant $i\in I$ with the technology $t\in T$
$ph_t$ : Average fraction of the potentially hazardous products when the technology $u\in U$ is used
$eldp_{i,t}$ : The lost days caused from work's damages during the establishment of the technology $u\in U$ at the manufacturing plant $i\in I$
$eldw_j$ : The lost days caused from the work's damages during the establishment of the warehouse $j\in J $
$eldd_l$ : The lost days caused from the work's damages during the establishment of the DC $l\in L$
$vldp_{i,t}$ : The lost days caused from the work's damages during production at the manufacturing plant $i\in I$ with the technology $u$
$vldh_j$ : The lost days caused from the work's damages during handling at the warehouse $j\in J$
$vldd_l$ : The lost days caused from the work's damages during disassembling at the DC $l\in L$
$vldr_{i,u}$ : The lost days caused from the work's damages during remanufacturing at the manufacturing plant $i\in I$ with the technology $u\in U$
$wj$ : Weighting the factor of the total number of the produced job opportunities
$wp$ : Weighting the factor of the total number of the potentially hazardous products
$wl$ : Weighting the factor of the total number of lost days caused from the work's damages
Table 4.  Binary and continuous decision variables
Decision variables Description
$YA_{i,t}$ : 1 if the manufacturing plant $i\in I$ with the production technology $t\in T$ is established, otherwise is 0
$YB_j$ : 1 if the warehouse $j\in J$ is established, otherwise is 0
$YD_l$ : 1 if DC $l\in L$ is established, otherwise is 0
$XA_{i,j,t}^m$ : The number of the unit product shipped from the manufacturing plant $i\in I$ with technology $t\in T$ to the warehouse $j\in J$ with the transportation mode $m\in M$
$XB_{j,k,t}^n $ : The number of the unit product shipped from the warehouse $j\in J$ with technology $t\in T$ to the customer $k\in K$ with the transportation mode $n\in N$
$XC_{k,l,t}^0$ : he number of the unit product to be disposed and collected from the customer $k\in K$ with technology $t\in T$ to the DC $l\in L$ with the transportation mode $o\in O$
$XD_{l,i,t}^q$ : The number of the unit product to be dismantled and shipped from the DC $l\in L$ with technology $t\in T$ to the manufacturing plant $i\in I$ with the production technology $t\in T$ and the transportation mode $q\in Q$
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Decision variables Description
$YA_{i,t}$ : 1 if the manufacturing plant $i\in I$ with the production technology $t\in T$ is established, otherwise is 0
$YB_j$ : 1 if the warehouse $j\in J$ is established, otherwise is 0
$YD_l$ : 1 if DC $l\in L$ is established, otherwise is 0
$XA_{i,j,t}^m$ : The number of the unit product shipped from the manufacturing plant $i\in I$ with technology $t\in T$ to the warehouse $j\in J$ with the transportation mode $m\in M$
$XB_{j,k,t}^n $ : The number of the unit product shipped from the warehouse $j\in J$ with technology $t\in T$ to the customer $k\in K$ with the transportation mode $n\in N$
$XC_{k,l,t}^0$ : he number of the unit product to be disposed and collected from the customer $k\in K$ with technology $t\in T$ to the DC $l\in L$ with the transportation mode $o\in O$
$XD_{l,i,t}^q$ : The number of the unit product to be dismantled and shipped from the DC $l\in L$ with technology $t\in T$ to the manufacturing plant $i\in I$ with the production technology $t\in T$ and the transportation mode $q\in Q$
Table 5.  The mean and variance of the uncertain demands
University of Medical Sciences(customer zones) Mean of the stochastic demand (unit per month) Variance of the stochastic demand
$ c_1 $ (Tehran) 500 400
$ c_2 $ (Markazi) 260 90
$ c_3 $ (Esfahan) 150 40
$ c_4 $ (Fars) 210 160
$ c_5 $ (Yazd) 160 40
$ c_6 $ (Tabriz) 200 90
$ c_7 $ (Mazandaran) 180 250
$ c_8 $ (Mashahd) 170 250
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University of Medical Sciences(customer zones) Mean of the stochastic demand (unit per month) Variance of the stochastic demand
$ c_1 $ (Tehran) 500 400
$ c_2 $ (Markazi) 260 90
$ c_3 $ (Esfahan) 150 40
$ c_4 $ (Fars) 210 160
$ c_5 $ (Yazd) 160 40
$ c_6 $ (Tabriz) 200 90
$ c_7 $ (Mazandaran) 180 250
$ c_8 $ (Mashahd) 170 250
Table 6.  Mean and variance of the fixed costs, the number of fixed opportunities created by establishing the manufacturing plants and the number of variable jobs created through manufacturing and remanufacturing
Factories(i) Production technology(m) Mean of the Stochastic fixed cost (million Rials) Variance of the Stochastic fixed cost (million Rials)$^2$ Number of fixed job opportunities Number of variable job opportunities created through manufacturing Number of variable job opportunities created through remanufacturing
$f_1$ (Tehran province) ICU 120000 169000 70 15 10
MRI 123000 144000 60 17 9
$f_2$ (Tabriz province) ICU 143000 121000 78 17 9
MRI 143000 100000 73 16 12
$f_3$ (Yazd province) ICU 132000 100000 78 16 10
MRI 170000 121000 79 18 9
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Factories(i) Production technology(m) Mean of the Stochastic fixed cost (million Rials) Variance of the Stochastic fixed cost (million Rials)$^2$ Number of fixed job opportunities Number of variable job opportunities created through manufacturing Number of variable job opportunities created through remanufacturing
$f_1$ (Tehran province) ICU 120000 169000 70 15 10
MRI 123000 144000 60 17 9
$f_2$ (Tabriz province) ICU 143000 121000 78 17 9
MRI 143000 100000 73 16 12
$f_3$ (Yazd province) ICU 132000 100000 78 16 10
MRI 170000 121000 79 18 9
Table 7.  Mean and variance of the fixed costs, the number of fixed opportunities created by establishing warehouses and the number of variable jobs created through handling
Medical equipment storage centers (j) Mean of the Stochastic fixed cost (million Rials) Variance of the Stochastic fixed cost(million Rials)$^2$ Number of fixed job opportunities Number of variable job opportunities created through handling
$w_1$ (Hamedan province) 112000 121000 50 13
$w_2$ (Qom province) 140000 144000 55 14
$w_3$ (Esfahan province) 112000 100000 58 12
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Medical equipment storage centers (j) Mean of the Stochastic fixed cost (million Rials) Variance of the Stochastic fixed cost(million Rials)$^2$ Number of fixed job opportunities Number of variable job opportunities created through handling
$w_1$ (Hamedan province) 112000 121000 50 13
$w_2$ (Qom province) 140000 144000 55 14
$w_3$ (Esfahan province) 112000 100000 58 12
Table 8.  Mean and variance of the fixed costs, the number of fixed opportunities created by establishing DCs and the number of variable jobs created through disassembling
Disassembly centers (l) Mean of the Stochastic fixed cost (million Rials) Variance of the Stochastic fixed cost(million Rials)$^2$ Number of fixed job opportunities Number of variable job opportunities created through disassembling
$d_1$ (Tehran province) 70000 49000 39 15
$d_2$ (Ardabil province) 75000 36000 32 13
$d_3$ (Yazd province) 72000 36000 42 15
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Disassembly centers (l) Mean of the Stochastic fixed cost (million Rials) Variance of the Stochastic fixed cost(million Rials)$^2$ Number of fixed job opportunities Number of variable job opportunities created through disassembling
$d_1$ (Tehran province) 70000 49000 39 15
$d_2$ (Ardabil province) 75000 36000 32 13
$d_3$ (Yazd province) 72000 36000 42 15
Table 9.  Coefficient confidence of the chance-constraints
Environmental constraints ($\alpha$) Customer demands constraints ($\beta$) Return flow establishing constraints ($\gamma$)
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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Environmental constraints ($\alpha$) Customer demands constraints ($\beta$) Return flow establishing constraints ($\gamma$)
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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