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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
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 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%.
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doi: 10.24200/sci.2019.21531. |
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Multi-objective ant colony optimisation: A meta-heuristic approach to supply chain design, International Journal of Production Economics, 131 (2011), 407-420.
|
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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. |
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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. |
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Green supply chain design: A mathematical modeling approach based on a multi-objective optimization model, International Journal of Production Economics, 183 (2017), 421-432.
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From a literature review to a conceptual framework for sustainable supply chain management, Journal of Cleaner Production, 16 (2008), 1699-1710.
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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.
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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. |
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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] |
E. B. Tirkolaee, P. Abbasian and G. W. Weber,
Sustainable fuzzy multi-trip location-routing problem for medical waste management during the COVID-19 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 location-allocation-inventory problem to design an urban waste management system under uncertainty, Waste Management, 102 (2020), 340-350.
doi: 10.1016/j.wasman.2019.10.038. |
[45] |
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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, |
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 |
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 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, |
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 |
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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