A p-robust mathematical model for a sustainable vaccine supply chain

الموضوعات :

Saed Fazayeli ¹ , Mahmoud Pormollaahmad ² , Ali Doniavi ³

1 - Faculty of Engineering, Urmia University, Urmia, West Azerbaijan Province, Iran
2 - Master of Science in engineering, Urmia University, Urmia, West Azerbaijan Province, Iran
3 - Faculty of Engineering, Urmia University, Urmia, West Azerbaijan Province, Iran

تاريخ الإرسال : 26 الثلاثاء , ربيع الثاني, 1446 تاريخ التأكيد : 26 الثلاثاء , ربيع الثاني, 1446 تاريخ الإصدار : 26 الثلاثاء , ربيع الثاني, 1446

الکلمات المفتاحية: Words: vaccine supply Chain, sustainability, p-robust model,

ملخص المقالة :

This paper introduces a multi-product, multi-period, and multi-level sustainable supply chain (SC) network problem, including several production centers. It includes stocking technology and different transportation methods in conditions of uncertainty. The increasing demand for vaccines in the conditions of the corona virus epidemic and the existing sensitivities towards the stability characteristics as well as the unique characteristics of the vaccine SC are the reasons for redesigning this network. The economic, environmental and social goals are considered in presented mathematical model in order to achieve organization's sustainability strategy and stakeholder satisfaction. The economic objective function includes two types of tactical and strategic costs to avoid creating sub-optimal solutions. The environmental objective function calculates the total emission of pollution in SC. The social objective is to maximize the social responsiveness of the SC. Three indicators including job opportunity creation (positive effect), employee health and safety (negative effect) and customer health as risk of harm to customer using product (negative effect). LP metric and epsilon limit methods are used to solve the model in small dimensions and Pareto front drawing method is used to draw the conflict of interest diagram. A numerical example has been proposed to evaluate and test the model, and in order to deal with non-deterministic parameters and reduce its impact on the optimal solution, a robust optimization model has been proposed. Finally, the results in deterministic and robust state has been compared.

المصادر:

[1] Aminifar Z., Arabi M. (2014) Sustainable supply chain management and the need to investigate it, International Conference on New Researches in Industrial Management and Engineering, Tehran.
[2] Nayeri S., Torabi A., Tavakoli M., Sazvar Z. (2021) A multi-objective fuzzy robust stochastic model for designing a sustainable-resilient-responsive supply chain network, Journal of Cleaner Production, 311, 126-691.
[3] Sazvar Z., Tafakkori k., Oladzad N., Nayeri S. (2021) A capacity planning approach for sustainable-resilient supply chain network design under uncertainty: A case study of vaccine supply chain, Computers & Industrial Engineering, 159, 107-406.
[4] Karmakar M., Lantz P. M., Tipirneni R. (2021) Association of Social and Demographic Factors With COVID-19 Incidence and Death Rates in the US, JAMA Netw Open. 4(1):e2036462. doi:10.1001/jamanetworkopen.2020.36462.
[5] P-Georgiadis G., C-Georgiadis A. (2021) Optimal planning of the COVID-19 vaccine supply chain, Volume 39, Issue 37, Pages 5302-5312. DOI: 10. 1016/j. vaccine. 2021. 07. 068.
[6] Y- Lee B., A-Haidari L. (2017) The importance of vaccine supply chains to everyone in the vaccine world, Journal of Vaccine, https: //doi. org/10. 1016/j. vaccine. 2017. 05. 096.
[7] Mofijur M., Fattah I. R., Alam M. A., Islam A. S., Ong H. C., Rahman S. A., Najafi G., Ahmed S. F., Uddin M. A., Mahlia T. M. I. (2021) Impact of COVID-19 on the social, economic, environmental and energy domains: lessons learnt from a global pandemic, Sustain. Prod. Consum, 26, 343–359.
[8] Ivanov D., Dolgui A. (2021) OR-methods for coping with the ripple effect in supply chains during COVID-19 pandemic: Managerial insights and research implica- tions. International Journal of Production Economics 232,107921.
[9] Gholipoor A., Paydar M. M., Safaei A. S. (2019) a faucet closed-loop supply chain network design considering used faucet exchange plan, J. Clean. Prod, 235, 503–518.
[10] Babazadeh R., Razmi J., Pishvaee M. S., Rabbani M. (2017) A sustainable second-generation biodiesel supply chain network design problem under risk, Omega (United Kingdom), 66, 258–277.
[11] Mousavi Ahranjani P., Ghaderi S. F., Azadeh A., Babazadeh R. (2018) Hybrid multiobjective robust possibilistic programming approach to a sustainable bioethanol sup ply chain network design, Ind. Eng. Chem. Res, 57, (44), 15066–15083.
[12] Zahiri B., Zhuang J., Mohammadi M. (2017) Toward an integrated sustainable-resilient supply chain: A pharmaceutical case study, Journal of Transportation Research Part E, 103, 109-142.
[13] Eskandarpour M., Dejax P., Miemczyk J., Péton O. (2015) Sustainable supply chain network design: an optimization-oriented review, Omega, 54, 11–32.
[14] Habib M. S., Asghar O., Hussain A., Imran M., Mughal M. P., Sarkar B. (2021) A robust possibilistic programming approach toward animal fat-based biodiesel supply chain network design under uncertain environment, J. Clean. Prod. 122-403.
[15] Yu H., Solvang W. D. (2020) A fuzzy-stochastic multi-objective model for sustainable planning of a closed-loop supply chain considering mixed uncertainty and network flex- ibility, J. Clean. Prod. 266 121702.
[16] Shen J. (2020) An uncertain sustainable supply chain network, Appl. Math. Comput. 378, 125213.
[17] Sherafati M., Bashiri M., Tavakkoli-Moghaddam R., Pishvaee M. S. (2020) Achieving sustainable development of supply chain by incorporating various carbon reg- ulatory mechanisms, Transport. Res. Part D 102253.
[18] Mota B., Gomes M. I., carvalho A., Barbosa-Povoa A. P. (2018) Sustainable supply chains: A integrated modeling approach under uncertainty, Omega 77, 32–57.
[19] Mahmud P., Ahmed M., Janan F., Xames D., Chowdhury N.R. (2023) Strategies to develop a sustainable and resilient vaccine supply chain in the context of a developing economy, Socio-Economic Planning Sciences, 87, Part B.
[20] Gilani H., Sahebi H. (2023) A data-driven robust optimization model by cutting hyperplanes on vaccine access uncertainty in COVID-19 vaccine supply chain, Omega, Volume 110.
[21] Babaee Tirkolaee E., Ebadi Torkayesh E., Tavana M., Goli A., Simic V., Ding W. (2023) An integrated decision support framework for resilient vaccine supply chain network design, Engineering Applications of Artificial Intelligence, Volume 126, Part B.
[22] Gan Q., Zhang, Y. Zhang Z., Chen M., Zhao J., Wang X. (2023) Influencing factors of cooling performance of portable cold storage box for vaccine supply chain: An experimental study, Journal of Energy Storage, Volume 72, Part A.
[23] Khodaee V., Kayvanfar V., Haji A. (2022) A humanitarian cold supply chain distribution model with equity consideration: The case of COVID-19 vaccine distribution in the European Union, Decision Analytics Journal, Volume 4.
[24] Lin Q., Zhao Q., Lev B. (2020) Cold chain transportation decision in the vaccine supply chain, European Journal of Operational Research, Volume 283, Issue 1.
[25] Kumar S., Mvundura M., Ray A., Haldar P., Lennon P., Muller N., Roy A., Rewaria S (2023) Using new cold chain technologies to extend the vaccine cold chain in India: Equipment performance, acceptability, systems fit, and costs, Vaccine: X, Volume 15.
[26] Ahi P., Searcy C. (2014) an analysis of metrics used to measure performance in green and sustainable supply chains, Journal of Cleaner Production, 1-18.
[27] Ivo de Carvalho M., Ribeiro D., Paula Barbosa-Povoa A. (2019) Design and Planning of Sustainable Vaccine Supply Chain, DOI: 10. 1007/978-3-030-15398-4_2.
[28] Taleizadeh A. A., Haghighi F., Niaki S. T. A. (2019) Modeling and solving a sustainable closed-loop supply chain problem with pricing decisions and discounts on returned products, Journal of Cleaner Production, 207, 163–181.
[29] Vali-Siar M. M., Roghanian E. (2022) Sustainable, resilient and responsive mixed supply chain network design under hybrid uncertainty with considering COVID-19 pandemic disruption, Sustainable Production and Consumption, 30, 278–300.
[30] Kaur H., Singh S. P., Garza-Reyes J. A., Mishra N. (2019) Sustainable Stochastic Production and Procurement Problem for Resilient Supply Chain, Computers & Industrial Engineering, doi: https: //doi. org/10. 1016/j. cie. 2018. 12. 007
[31] Bairamzadeh S., Pishvaee M. S., Saidi-Mehrabad M. (2016) Multiobjective robust possibilistic programming approach to sustainable bioethanol supply chain design under multiple uncertainties, Ind. Eng. Chem. Res, 55 (1), 237-256.
[32] Fathollahi-Fard A. M., Ahmadi A., Mirzapour Al-e-Hashem S. M. J. (2020) Sustainable closed-loop supply chain network for an integrated water supply and wastewater collection system under uncertainty, Journal of Environmental Management 275, 111-277.
[33] Gholami-Zanjani S. M., Jabalameli M. S., Pishvaee M. S. (2021) A resilient-green model for multi-echelon meat supply chain planning. Computers and Industrial Engineering, 152, 107018.
[34] Kaur H., Singh S. P., Garza-Reyes J. A., & Mishra N. (2020) Sustainable stochastic production and procurement problem for resilient supply chain, Computers and Industrial Engineering, 139.
[35] Pavlov A., Ivanov D., Pavlov D., Slinko A. (2019) Optimization of network redundancy and contingency planning in sustainable and resilient supply chain resource management under conditions of structural dynamics, Annals of Operations Research.
[36] Kogler C., Rauch P. (2019) A discrete-event simulation model to test multimodal strategies for a greener and more resilient wood supply, Canadian Journal of Forest Research, 49(10), 1298–1310.
[37] Jabbarzadeh A., Fahimnia B., Rastegar S. (2019) Green and resilient design of electricity supply chain networks: A multiobjective robust optimization approach, IEEE Transactions on Engineering, 66(1).
[38] Dorneanu B., Masham E., Mechleri E., Arellano-Garcia H. (2019) Centralised versus localised supply chain management using a flow configuration model, In Computer Aided Chemical Engineering (Vol. 46) Elsevier Masson SAS.
[39] Jabbarzadeh A., Fahimnia B., Sabouhi F. (2018) Resilient and sustainable supply chain design: sustainability analysis under disruption risks, Int. J. Prod. Res. 56, (17), 5945–5968.
[40] Ivanov D. (2018) Revealing interfaces of supply chain resilience and sustainability: a simulation study, International Journal of Production Research, 56(10), 3507–3523.
[41] Mari S. I., Lee Y. H., Memon M. S. (2016) Sustainable and resilient garment supply chain network design with fuzzy multi-objectives under uncertainty, Sustainability (Switzerland), 8(10).
[42] Fahimnia B., Jabbarzadeh A. (2016) Marrying supply chain sustainability and resilience: A match made in heaven, Transportation Research Part E: Logistics and Transportation Review, 91, 306–324.
[43] Yılmaz Balaman S., Selim H. (2016) Sustainable design of renewable energy supply chains integrated with district heating systems: A fuzzy optimization approach, Journal of Cleaner Production,133, 863–885.
[44] Cardoso S. R., Paula Barbosa-P´ovoa A., Relvas S., Novais A. Q. (2015) Resilience metrics in the assessment of complex supply-chains performance operating under demand uncertainty, Omega (United Kingdom), 56, 53–73.
[45] Tavana M., Kian H., Khalili Nasr A., Govindan K., Mina H. (2022) A comprehensive framework for sustainable closed-loop supply chain network design, Journal of Cleaner Production, 332, 129777.
[46] Ghaderi, A., Khanzadeh, C. (2019) A Combined Stochastic Programming and Robust Optimization Approach for Location-Routing Problem and Solving it via Variable Neighborhood Search algorithm. Journal of Operational Research and Its Applications, 16(4), 15-36.
[47] Mazidi M., Rezaei N., Ghaderi A. (2019) Simultaneous power and heat scheduling of microgrids considering operational uncertainties: A new stochastic p-robust optimization approach, Energy, 185, 239-253.

نص كامل:



Islamic Azad University Rasht Branch ISSN: 2588-5723        E-ISSN:2008-5427

Optimization Iranian Journal of Optimization Volume 15, Issue 2, 2023, 99-124 Research Paper

 

 

                                        Online version is available on: www.ijo.rasht.iau.ir

 

A p-robust mathematical model for a sustainable vaccine supply chain

Saed fazayeli1*, Mahmoud Pormollaahmad2 and Ali Doniavi1

1Faculty of Engineering, Urmia University, Urmia, West Azerbaijan Province, Iran

2 Master of Science in engineering, Urmia University, Urmia, West Azerbaijan Province, Iran

 

Revise Date: 06 December 2024   Abstract

*Correspondence E‐mail: [e-mail]

Keywords: vaccine supply Chain sustainability p-robust model

            Accept Date: 29 October 2024   This paper introduces a multi-product, multi-period, and multi-level sustainable supply chain (SC) network problem, including several production centers. It includes stocking technology and different transportation methods in conditions of uncertainty. The increasing demand for vaccines in the conditions of the corona virus epidemic and the existing sensitivities towards the stability characteristics as well as the unique characteristics of the vaccine SC are the reasons for redesigning this network. The economic, environmental and social goals are considered in presented mathematical model in order to achieve organization's sustainability strategy and stakeholder satisfaction. The economic objective function includes two types of tactical and strategic costs to avoid creating sub-optimal solutions. The environmental objective function calculates the total emission of pollution in SC. The social objective is to maximize the social responsiveness of the SC. Three indicators including job opportunity creation (positive effect), employee health and safety (negative effect) and customer health as risk of harm to customer using product (negative effect). LP metric and epsilon limit methods are used to solve the model in small dimensions and Pareto front drawing method is used to draw the conflict of interest diagram. A numerical example has been proposed to evaluate and test the model, and in order to deal with non-deterministic parameters and reduce its impact on the optimal solution, a robust optimization model has been proposed. Finally, the results in deterministic and robust state has been compared.

 

 

INTRODUCTION

Governments and societies have concerns about global warming, loss of natural resources, excessive use of non-renewable resources and increasing industrial activities in developed and developing countries caused many managers to consider sustainable businesses [1]. In order to survive in a competitive market, organizations have to reduce operating costs, improve service levels, simultaneous attention to economic, environmental and social aspects of SC. Therefore, organizations are trying to optimize their supply chain network (SCN) considering all elements of sustainability (i.e. economic, environmental and social aspects) [2]. Consequently, a company that is oriented to join global SC, should consider sustainability in its SC [3].

Recently, the world community has faced COVID-19 pandemic, which is the most destructive disease in recent decades. SCs have faced various challenges and this destructive and widespread disease has adversely affected SCs worldwide [4]. Many researchers have investigated the significant effects of COVID-19 on SCs. Productivity, efficiency, and responsiveness of SCs have suffered due to material shortages, delivery delays, disruptions in logistics and transportation systems, facility capacities reduction and other disruption-related harms. The positive point of the occurrence of this disease is the special attention paid to the sustainability of SC [5]. As mentioned, while world focused on developing new vaccines and measuring their effects on humans, the lack of understanding and correct handling of vaccine supply chain issues, can greatly reduce the effectiveness of any vaccine. Therefore, any agency involved in vaccine decision-making should consider vaccine SCs when making key decisions [6]. This disease caused several problems and beside its affection on human lives such as quarantines and other restrictions, industries also had to reduce their activities. This mandatory decision had different economic, social and environmental results such as job loss, revenue reduction, bankruptcy and recycling activity stop [7]. Also, for some SCs, the demand has increased dramatically so that the supply cannot respond and the organization faced shortage. In general, the epidemic of COVID-19 was a test for resilience and sustainability of SCs by impacting on various aspects of the economy and society [8].

This study tries to expand the existing models in the design of the vaccine SC network and the dimensions of sustainability that were less mentioned in the previous researches. The objectives of this research are to identify and examine the dimensions, paradigms and concepts of sustainable SCN design that have been used by academics and experts in the past, and to examine the impact of including sustainability in vaccine SC and how to address it. This study aims to present a mathematical model for the vaccine SC, which includes the SC stability issue. To consider uncertainty in the parameters, a relatively new probabilistic-robust approach is used to overcome the disadvantages of the two probabilistic and robust approaches to gain optimal answers.

The main question of this study is whether it is possible to present a mathematical model for the design of a vaccine SCN that includes location decisions (storage centers, manufacturing centers and packaging centers) and routing decision, where model parameters such as demand and other parameters considered uncertain. Other questions can also be raised as follows: Can sustainability be included in the vaccine supply chain (VSN)? Can providing a sustainable VSC model have better results in the organization's strategic and operational planning? Will considering the problem in a non-deterministic way provide better results? Does considering the probabilistic-robust method for uncertainty in the parameters of the problem produce more realistic results?

 

LITERATURE REVIEW

Various researchers focused on sustainable SC in recent years. Some researchers paid attention to the uncertainty in the SC. Nayeri et al. presented a multi-objective MIP model to configure a sustainable SC network under uncertainty, while considering flexibility and responsiveness measures. To deal with the uncertainty, they proposed an improved version of the fuzzy stochastic optimization model [2]. Gholipoor et al. stated that companies are creating closed loop SCs to increase their profit and the sustainability. To deal with this, a single-objective, multi-product, multi-period MIP model under fuzzy demand proposed by the authors [9]. Babazadeh et al. designed a SC by modeling a mixed integer nonlinear problem under risk. The aim of this study is to minimize environmental impacts and total costs under supply and demand uncertainties [10]. It is stated in Mousavi et al.'s article that when all three aspects of sustainability are considered, uncertainties are rarely addressed. In this paper, a multi-objective MILP model generated for a robust sustainable SC network problem with uncertainty in all three sustainability objectives including cost and greenhouse gas emission minimization and job creation maximization [11]. Another paper presented by Zahiri et al. introduces an integrated and stable multi-objective MILP model for a pharmaceutical SC under uncertainty. To deal with the uncertainty, a new fuzzy probabilistic-stochastic programming approach is developed [12]. Eskandarpour et al. reviewed 87 articles in the field of SC network design. They believe that the borders of environmental and social researches should move beyond the greenhouse gas emissions to the optimum use of life cycle approaches and new social criteria should be included in the models. More effective inclusion of uncertainty and risk in models with improved multi-objective approaches is also needed [13]. Habib et al. proposed a MILP model to minimize total cost and carbon emissions. In this paper, a robust probabilistic programming approach has been used to address supply and demand uncertainties in the network [14].

Some studies integrated economic and environmental aspects to reduce environmental pollution levels with financial stability. Yu & Solvang developed a closed-loop SCN and modeled a multi-objective optimization problem with fuzzy and stochastic parameters. The main objective of this study was to optimize the trade-off between cost effectiveness and environmental performance [15]. Shen investigated a sustainable SC in an uncertain environment [16]. Sherafati et al. designed an SCN by developing all three dimensions of sustainability while imposing an appropriate carbon regulatory mechanism. The social aspects considered in this study were unemployment rate, corruption, crimes, etc. [17]. The research conducted by Mota et al. generates a multi-objective MILP model which integrates several interconnected decisions including facility location, capacity determination, supplier selection, definition of purchase levels, technology selection and allocation, and defining the transportation network that includes unimodal and intermodal options [18]. Mahmud et al. identified key VSC strategies and their interrelationships under four groups: Intra-organizational, Inter-organizational, Legislative, and Environmental, based on previous literature and the expert opinions of industrial practitioners and policymakers [19]. Gilani and Sahebi presented a mathematical model of a sustainable SC for the COVID-19 vaccine that covers the economic, environmental and social aspects and provides vaccine both domestically and internationally. They also proposed a robust data-driven model based on a polyhedral uncertainty set to address the unjust worldwide vaccine distribution as an uncertain parameter [20]. Tirkolaee et al. developed a novel two-stage decision support framework for configuring multi-echelon VSC, resilient supplier selection, and order allocation under uncertainty. A robust multi-objective optimization model is then built for order allocation considering resiliency scores, reliability of facilities, and uncertain supply and demand [21].

On the other hand, vaccine supply chain should implement as a cold supply chain for health reasons. Gan et al. investigated the cooling performance of vaccine cold storage boxes integrated with phase change material bottles [22]. Khodaee et al. presented a humanitarian cold supply chain distribution model for COVID-19 vaccine distribution in the European Union [23]. Lin et al. considered cold chain transportation decision in the vaccine supply chain [24]. Kumar et al. studied using new cold chain technologies to extend the vaccine cold chain in India [25].

Corporate sustainability metrics are widely available and used by numerous organizations around the world. These metrics are often shared with the public in corporate sustainability reports. Examples of absolute and relative metrics are widely available, including through the Global Reporting Initiative (GRI), which lists more than 90 indicators.

Analysis of criteria based on 13 key features of SSCM proposed by Ahi & Searcy, indicates that more than one-third of the criteria focused on environmental issues, 17% focuses on economic issues and 12.1% focused on social issues. "Air emissions" with 28 repetitions, "energy consumption" with 24 repetitions, and "greenhouse gas emissions" with 24 repetitions are some of the high-frequency environmental measures used. "Cost" (12 times), "return on investment" (11 times) and "operating cost" (11 times) were the most frequently used economic criteria. Examples of social criteria with high frequency are "discrimination" (6 times), "health and safety incidents" (5 times), and "supervisory and public services" (4 times) [26].

According to the Ahi & Searcy, environmental issues, economic issues and social issues are the most frequently used criteria and received most of the attention of researchers. In this study, these 3 sustainability paradigms are used to design a sustainable VSC [26]. Also, by reviewing sustainable SC articles, from the years 2015 to 2022 according to table (1), few of the existing articles have used an integrated approach for strategic and tactical decision-making levels for the design of multi-product and multi-period SC networks.

 

Table 1: Comparison of sustainability evaluation indicators in articles

papers	uncertainty approach	solving method	transportation	technology level	time period	Case study	Product	Decision		model
								Strategic	Tactical	Simulation	optimization
[2]	FRS	E	*	*	M	WH	M	*	-	*	*
[3]	F	E	*	*	M	H	M	*	*	-	*
[12]	FS	H	*	*	M	H	M	*	*	-	*
[14]	RPP	H	-	-	M	B	M	*	*	-	*
[27]	-	E	*	*	M	H	M	-	*	-	*
[18]	S	E	*	*	M	EC	M	-	-	-	*
[28]	F	E	*	*	M	EC	S	-	*	-	*
[29]	FS	H	-	*	M	TI	M	-	*	-	*
[30]	F	E	-	-	M	-	M	-	*	*	*
[31]	RPP	H	-	*	S	LB	S	*	*	-	*
[32]	S	H	-	-	-	-	-	*	*	*	-
[33]	S	E	*	-	M	-	M	-	*	-	*
[34]	S	E	-	-	M	-	M	-	*	-	*
[35]	S	E	*	*	M	S	M	-	*	-	*
[36]	-	-	-	-	M	W	S	-	*	*	-
[37]	R	E	-	-	M	E	S	*	*	-	*
[38]	-	E	-	-	M	F	M	*	*	-	*
[39]	S	E	-	-	S	I	S	*	*	-	*
[40]	-	-	-	-	M	-	S	-	*	*	-
[41]	F	E	-	-	M	C	M	*	*	-	*
[42]	S	E	*	-	S	C	M	*	-	-	*
[43]	F	E	-	-	M	E	M	*	*	-	*
[44]	S	E	-	*	M	-	M	*	*	-	*
[45]	FS	E	*	-	M	-	M	*	*	-	*
This study	RPP	E	*	*	M	P	M	*	*	-	*

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Note: For time period and product, M stands for "Multi" and S stands for "Single". For uncertainty handling methods: random S, robust R, fuzzy F. (example. FRS: Fuzzy Robust Stochastic, RPP: robust possibility programming). For solution methods, H stands for "heuristic, meta-heuristic", E stands for "exact". For case studies, A: Automotive, C: Apparel, H: Healthcare, E: Energy, P: Pharmaceutical, I: Pipe Industry, F: Food Industry, W: Wood Industry, S: Seaports, TI: Tire Industry, LB: Lignocellulose bioethanol.        

papers	Sustainability
	Economic		Environmental issue			Social issue
	Total cost	Net present value	CO2 emission	Resource waste	Life cycle analysis	Product responsibility	Labor payment	Job creation	Social anxious	Deprivation	GDP
[2]	*	-	*	-	-	-	-	*	*	-	-
[3]	*	-	*	-	-	-	-	*	*	*	-
[12]	*	-	*	-	-	-	-	*	-	-	-
[14]	*	-	*	-	-	-	-	-	-	-	-
[27]	-	*	-	-	*	-	-	-	-	-	*
[18]	-	*	-	-	*	-	-	-	-	-	*
[28]	*	-	*	-	-	*	*	*	-	-	-
[29]	*	-	-	-	*	-	-	*	*	-	-
[30]	*	-	*	-	-	-	-	*	-	-	-
[31]	-	*	-	-	*	*	-	*	*	-	-
[32]	*	-	-	-	*	-	-	*	-	-	-
[33]	*	-	*	-	-	-	-	-	-	-	-
[34]	*	-	*	-	-	-	-	-	-	-	-
[35]	*	-	*	-	-	-	-	-	-	-	-
[36]	*	-	*	-	-	-	-	-	-	-	-
[37]	*	-	-	-	-	-	-	-	-	-	-
[38]	*	-	*	-	-	-	-	-	-	-	-
[39]	*	-	*	*	-	*	*	*	-	-	-
[40]	*	-	*	*	-	-	-	-	-	-	-
[41]	*	-	*	-	-	-	-	-	-	-	-
[42]	*	-	*	*	-	*	*	*	-	-	-
[43]	*	-	-	-	-	-	-	-	-	-	-
[44]	*	*	-	-	-	-	-	-	-	-	-
[45]	*	-	*	-	-	-	-	*	*	*	-
This study	*	-	*	-	-	*	*	*	*	-	-

Table 2: Model review table of the most relevant researches

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

In the presented model, cost indicates economic aspect; emission of greenhouse gases (carbon dioxide gas and refrigerant gas) indicates environmental aspect and number of lost working days due to work injuries as well as the number of created jobs indicates the social aspect of sustainable SC management. According to sustainable SC and VSC literature review, only few studies considered the integration of sustainability in the VSC. Also, in dealing with the uncertainty in VSC, this research is one of the first studies. It is a relatively new probabilistic approach that uses the advantages of both stochastic and robust optimization approaches to deal with uncertainties. Also, considering the harmful effects of other greenhouse gases, especially the HFC refrigerant gases used in industrial refrigerators in the cold SC, this study discusses the harmful effects of HFC gases and their role in global warming along with CO2 emissions in the environment.

MATHEMATICAL MODEL

problem description

The production and distribution processes are two main features of VSC, which is important to safe and healthy communities, requires special attention for design and planning. Figure 1 shows a VSC including domestic and foreign manufacturers, international packaging centers, storage and distribution centers and provincial health centers as demand points. Due to limited capacity of domestic vaccines producer, main producer in a foreign country transfers products to international packaging centers, and sends and stores them in the destination country after packaging. Finally, vaccines are transferred to provincial medical centers as demand points by internal transportation. Vaccines can be stored in production, packaging and distribution centers, and this model determines the optimal storage level during the planning time horizon. It is possible to store the vaccine with cold storage and freezing, and it is possible to build storage and distribution centers based on each of them. products are moved between SC echelons by road/rail modes for domestic transport and sea/air modes for external transport. In the proposed SC, strategic and tactical decisions are taken into account at the same time. It should be noted that the present model is written by adapting the model presented by Gilani & Sahebi, 2022.

 

 

 

 

Fig. 1. VSC

 

Assumptions

The model is multi-level, multi-product and multi-period. The flow of products exists only between different consecutive facilities and the flow of products between similar facilities is not possible. The location of foreign production factories and suppliers is fixed and known. Shortage is possible according to customer demand and a cost is considered for unsatisfied customer demand. The locations of potential domestic production and distribution centers are known. Inventory in domestic and foreign production centers, distribution and packaging centers for products is considered. Only one storage center should be assigned to each customer area. No shipping from foreign factory to customer areas is possible. Transport streams and vaccine storage facilities emit CO2 and HFC-based pollutants.

Symbols

 

 

 

 

. Objective functions in non-deterministic mode

The presented model includes three objective functions: minimizing total costs, minimizing environmental effects, and maximizing social effects of the SC. The first objective function (economic objective function) includes two types of costs: tactical and strategic costs. Strategic costs include establishment (factories and warehouses while tactical costs include purchasing, production, inventory (holding and shortages), and transportation (between SC entities) costs. The objective is as described in equatio (1):

 

Sets
I	Set of foreign producers	L	Set of transportation modes
J	Set of potential foreign packaging centers	P	Set of vaccines
K	Set of potential for domestic storage centers	M	Set of vaccine holding technology
R	Set of provincial health centers	T	Set of time periods
V	Set of potential domestic producer centers	S	Set of scenarios
Parameters
	Fixed cost of developing packaging center j
	Fixed cost of developing distribution center k with holding technology m
	Fixed cost of developing domestic producer p in location v
	Variable cost of foreign producer for vaccine p in location i and time period t
	Variable cost of packaging center j for vaccine p and time period t
	Variable cost of distribution center k with holding technology m for vaccine p and time period t
	Variable cost of domestic producing vaccine p in location v and time period t
	Variable cost of foreign producing vaccine p in factory i and time period t under scenario s
	Variable cost of domestic producing vaccine p in factory v and time period t under scenario s
	Distribution cost per foreign vaccine for distribution center k with holding technology m and time period t
	Distribution cost per domestic vaccine for producer v and time period t
	Packaging cost per foreign vaccine p in packaging center j and time period t
	Holding cost per foreign vaccine p for foreign producer i and time period t
	Holding cost per foreign vaccine p for foreign producer i and time period t
	Holding cost per foreign vaccine p for distribution center k with holding technology m and time period t
	Holding cost per domestic vaccine p for domestic producer v and time period t
	Transportation cost per foreign vaccine p from foreign producer i to packaging center j with mode l
	Transportation cost per foreign vaccine p from packaging center j to distribution center k with mode l
	Transportation cost per foreign vaccine p from distribution center k to provincial health center r with mode l
	Transportation cost per domestic vaccine p from domestic producer v to provincial health center r with mode l
	Capacity increase cost per foreign vaccine p for foreign producer i in time period t
	Capacity increase cost per foreign vaccine p for packaging center j in time period t
	Capacity increase cost per foreign vaccine p for distribution center k with holding technology m in time period t
	Capacity increase cost per domestic vaccine p for domestic producer v in time period t
	Market value of vehicle l
	Interest rate
	Number of time periods
	Maximum order size of raw materials used for foreign vaccine p production in time period t
	Maximum order size of raw materials used for domestic vaccine p production in time period t
	Raw material cost for foreign vaccine p produced in foreign producer i in time period t under scenario s
	Raw material cost for domestic vaccine p produced in domestic producer v in time period t under scenario s
	Transportation cost per mode l (truck only)
	Minimum capacity for foreign vaccine p in foreign producer i
	Minimum capacity for domestic vaccine p in domestic producer v
	Minimum capacity for foreign vaccine p in packaging center j
	Minimum capacity for foreign vaccine p in distribution center k with holding technology m
	Maximum capacity for foreign vaccine p in foreign producer i
	Maximum capacity for domestic vaccine p in domestic producer v
	Maximum capacity for foreign vaccine p in packaging center j
	Maximum capacity for foreign vaccine p in distribution center k with holding technology m
	Raw material to foreign vaccine p exchange rate
	Raw material to domestic vaccine p exchange rate
	Packaging coefficient for vaccine p
	Demand of customer region r in time period t under scenario s
	Vehicle capacity l in time period t
	Number of jobs created by developing a domestic producer v
	Number of jobs created by developing a packaging center j
	Number of jobs created by developing a distribution center k with holding technology m
	Shortage cost under scenario s
	Total CO2 emission resulted from holding a foreign vaccine p at storage center k with holding technology m
	Maximum inventory for foreign vaccine p at foreign producer i
	Maximum inventory for foreign vaccine p at packaging center j
	Maximum inventory for foreign vaccine p at distribution center k with holding technology m
	Maximum inventory for domestic vaccine p at domestic producer v
	Total CO2 emission resulted from foreign vaccine p transportation between foreign producer i and packaging center j with mode l
	Total refrigerant gas (HFC) emission leaked from vehicle l transporting foreign vaccine p between foreign producer i and packaging center j
	Total CO2 emission resulted from foreign vaccine p transportation between packaging center j and distribution center k with mode l
	Total refrigerant gas (HFC) emission leaked from vehicle l transporting foreign vaccine p between packaging center j and distribution center k
	Total CO2 emission resulted from foreign vaccine p transportation between distribution center k and provincial health center r with mode l
	Total refrigerant gas (HFC) emission leaked from vehicle l transporting foreign vaccine p between distribution center k and provincial health center r
	Total CO2 emission resulted from domestic vaccine p transportation between domestic producer v and provincial health center r with mode l
	Total refrigerant gas (HFC) emission leaked from vehicle l transporting domestic vaccine p between domestic producer v and provincial health center r
	Total CO2 emission resulted from foreign vaccine p production at foreign producer i
	Total CO2 emission resulted from domestic vaccine p production at domestic producer v
	Total CO2 emission resulted from foreign vaccine p production at packaging center j
	Total CO2 emission resulted from packaging center building j
	Total CO2 emission resulted from distribution center building k with holding technology m
	Total refrigerant gas (HFC) emission leaked from distribution center building k with holding technology m per year
	Total CO2 emission resulted from domestic vaccine p at producer v
	Total CO2 emission resulted from holding of foreign vaccine p at producer i
	Total refrigerant gas (HFC) emission leaked from holding of foreign vaccine p at producer i
	Total CO2 emission resulted from holding of foreign vaccine p at packaging center j
	Total refrigerant gas (HFC) emission from holding of foreign vaccine p at distribution center k with technology m
	Total CO2 emission resulted from holding of domestic vaccine p at producer v
	Total refrigerant gas (HFC) emission from holding of domestic vaccine p at producer v
	Total jobs created by sending foreign vaccine p from producer I to packaging center j with mode l
	Total jobs created by sending foreign vaccine p from packaging center j to distribution center k with mode l
	Total jobs created by sending foreign vaccine p from distribution center k to provincial health center r with mode l
	Total jobs created by sending domestic vaccine p from producer v to provincial health center r with mode l
	Total yearly local jobs created by producing foreign vaccine p at producer i
	Total yearly local jobs created by producing domestic vaccine p at producer v
	Total yearly local jobs created by packaging foreign vaccine p at packaging center j
	Total yearly local jobs created by distributing foreign vaccine p at distributer k with technology m
	Total yearly local jobs created by distributing domestic vaccine p at producer v
	Average number of days lost per year in the vaccine transportation process by transportation mode l
	Average number of days lost per year in the vaccine production
	Average number of days lost per year in the vaccine packaging
	Average number of days lost per year in the vaccine distribution
	The average fraction of dangerous foreign vaccines p in the foreign vaccine production center i
	The average fraction of dangerous domestic vaccines p in the domestic vaccine production center v
	Weighted coefficient of the total number of local jobs created
	Weighted coefficient of the total number of days lost due to work injuries
	Weighted coefficient of the total number of potentially dangerous vaccines
	The probability of each existing scenarios
	Total refrigerant gas (HFC) emission leaked from holding of foreign vaccine p at packaging center j
Variables
	The number of vehicles l purchased to transport materials (trucks only) under scenario s
	The capacity designed to produce foreign vaccine p at producer i in time period t under scenario s
	The capacity designed to pack foreign vaccine p at packing center j in time period t under scenario s
	The capacity designed to store foreign vaccine p in the distribution and storage center k with technology m in period t under scenario s
	The designed capacity for domestic vaccine p at the domestic manufacturing facility v in time period t under scenario s
	The amount of foreign vaccine p produced in manufacturing plant i in period t under scenario s
	The amount of domestic vaccine p produced in manufacturing plant v in period t under scenario s
	Amount of foreign vaccine p distributed from distribution center k with technology m in period t under scenario s
	Amount of foreign vaccine p packed in packing center j in period t under scenario s
	The amount of foreign vaccine raw materials of type p purchased at foreign vaccine factory i in period t under scenario s
	The amount of domestic vaccine raw materials of type p purchased at domestic vaccine factory v in period t under scenario s
	The amount of foreign vaccine p transferred from foreign vaccine production center i to packaging center j with transportation mode l in period t under scenario s
	The amount of foreign vaccine p transported from packaging center j to distribution center k with transportation mode l in period t under scenario s
	The amount of foreign vaccine p transferred from distribution center k to provincial health centers r with mode l in period t under scenario s
	The amount of domestic vaccine p transferred from the domestic production of vaccine v to provincial medical centers r by method l in period t under scenario s
	Inventory of foreign vaccine p in foreign vaccine production center i in period t under scenario s
	Inventory of foreign vaccine p in packing center j in period t under scenario s
	Inventory of foreign vaccine p in distribution center k with storage technology m in period t under scenario s
	Inventory of domestic vaccine p in the domestic vaccine production center v in period t under scenario s
	Capacity increase for production of foreign vaccine p in producer i in period t under scenario s
	Capacity increase for packaging foreign vaccine p in packaging center j in period t under scenario s
	Capacity increase for distribute foreign vaccine p in distribution and storage centers k with technology m in period t under scenario s
	Capacity increase for producing domestic vaccine p at producer v in period t under scenario s
	Vaccine shortage rate in customer areas (provincial health centers r) in period t under scenario s
	If packing center j is opened takes 1 otherwise 0
	If packing center k with maintenance technology m is opened, takes 1 otherwise 0
	If domestic vaccine production center v is opened, takes 1 otherwise it is 0

+ +++ +++ +++ + + +++ ++ +  + +  +  +  +  +  -  (1)      In the cold SC, products must be stored and transported at near or below freezing temperatures. This requires the use of refrigerated warehouses and trucks that consume large amounts of energy for refrigeration. More energy consumption is associated with more carbon dioxide (CO2) emissions in power generation facilities. In addition, refrigeration systems use large amounts of hydrofluorocarbon (HFC) gases, which have a high global warming potential and long lifetime in the atmosphere. The regular and catastrophic leakage of HFC gases from the cold SC, constitutes a significant part of global warming impact. Therefore, these gases must be considered in design and operation of a cold SC. In the cold SC, products must be stored and transported at near or below freezing temperatures. This requires the use of refrigerated warehouses and trucks that consume large amounts of energy for refrigeration. More energy consumption is associated with more carbon dioxide (CO2) emissions in power generation facilities. In addition, refrigeration systems use large amounts of hydrofluorocarbon (HFC) gases, which have a high global warming potential and long lifetime in the atmosphere. The regular and catastrophic leakage of HFC gases from the cold SC, constitutes a significant part of global warming impact. Therefore, these gases must be considered in design and operation of a cold SC.    The second objective function calculates the total emission of pollution resulting from all traverses in SC. In this objective function, it is tried to minimize the environmental effects that have adverse effects on the environment. Facilities and flow transfer between facilities have an important effect on environmental pollution. It was observed in the literature review, most of the previous researches have considered the minimization of carbon dioxide gas emission as the objective function. But in the cold SC, due to the high energy consumption and leakage of refrigerant gases, which leads to high levels of greenhouse gas emissions, it is necessary to pay attention to refrigerant greenhouse gases (HFC) in addition to carbon dioxide gas. Equation number (2) is the mathematical representation of environmental goal. This goal should be minimized to design an environmentally friendly (green) SC.   ++ + +++++++++++++  (2)      According to equation (3), the third objective function is to maximize the social responsiveness of the SC. This objective function includes the indicators of creating job opportunities (positive effect), lost working days due to illness and accidents (negative effect; related to health and safety of employees) and risk of using products for customers (negative effect; related to customer health). Job opportunities are classified into two fixed and variable categories. Permanent job opportunities, such as managerial jobs, are not dependent on capacity of facilities, but variable jobs, such as workers' job, are different depends on facility’s capacity and rate of production. In this objective function fixed and variable job opportunities are model separately. Regarding the health and safety of employees, the average number of working days lost due to injury is used.     (++ + + ++++++ +) -*(+ +  + )+ (+ )+ ()+ ())-* (+ )   (3)   All social effects of SC are formulated by giving weight to each component. θ1 with (+) sign used to maximize the number of jobs, θ2 with a (-) sign used to minimize number of days lost due to work-related injuries, θ3 with a sign (-) used to minimize environmental risks. Model constraints in non-deterministic mode