Modeling a closed-loop vaccine supply chain with transshipments to minimize wastage and threats to the public: a system dynamics approach

Purpose – This study aims to focus on building a conceptual closed-loop vaccine supply chain (CLVSC) to decrease vaccine wastage and counterfeit/ fake vaccines. Design/methodology/approach – Through a focused literature review, the framework for the CLVSC is described, and the system dynamics (SD) research methodology is used to build a causal loop diagram (CLD) of the proposed model. Findings – In the battle against COVID-19, waste management systems have become overwhelmed, which has created negative environmental and extremely hazardous societal impacts. A key contributing factor is unused vaccine doses, shown as a source for counterfeit/fake vaccines. The ﬁ ndings identify a CLVSC design and transshipment operations to decrease vaccine wastage and the potential for vaccine theft. Research limitations/implications – This study contributes to establishing a pandemic-speci ﬁ c VSC structure. The proposed model informs the current COVID-19 pandemic as well as potential future pandemics. Social implications – A large part of the negative impact of counterfeit/fake vaccines is on human well-being, and this can be avoided with proper CLVSC. Originality/value – This study develops a novel overarching SD CLD by integrating the epidemic model of disease transmission, VSC and closed-loop structure. This study enhances the policymakers ’ understanding of the importance of vaccine waste collection, proper handling and threats to the public, which are born through illicit activities that rely on stolen vaccine doses.


Introduction
According to the World Health Organization (WHO) (for full list of abbreviations, see Appendix 1), approximately 510 million COVID-19 cases and 6.3 million deaths worldwide have been reported as of April 2022 [I].Although there are different strategies for combating the COVID-19 pandemic, such as masking and social distancing (Kontogiannis, 2021), vaccination is the primary strategy to battle the coronavirus and decrease fatality rates (Liang et al., 2021).Vaccinations are critical in curbing fatalities; however, the supply chain operations that allow vaccines to reach populations are complicated (Lee and Haidari, 2017).
The number of vaccines required to reach herd immunity changes as complex factors unfold; however, there have been efforts to estimate this quantity.For instance, Kwok et al. (2021) posit that conditions to achieve herd immunity depend on the country, ranging from about 15% to 77%, whereas Randolph and Barreiro (2020) provide an overall global estimate of 67%.Considering the need for at least two doses of the vaccination for each individual, and the world's population of about 7.8 billion, it can be estimated that approximately 16 billion vaccine doses are required.However, as Alam et al. (2021) stated, the vaccine manufacturers' collective capacity The current issue and full text archive of this journal is available on Emerald Insight at: https://www.emerald.com/insight/2042-6747.htm was about 10 billion total doses in May 2021.Therefore, there is a global vaccine shortage (Amankwah-Amoah, 2022).
Despite the vaccine shortage, the WHO reported back in 2005 that 50% of vaccines are wasted annually around the globe [II].More recent estimates on this percentage are scarce.COVID-19 vaccine waste (i.e.expired vaccines and packaging) occurs due to immense purchase orders without estimating vaccine acceptance (intention to get vaccinated), inappropriate allocation models in vaccine supply chains (VSCs), storage requirements (lowtemperature storage), low-capacity syringe design, incorrect dose administration and vaccination appointment no-shows (Klemeš et al., 2021).The vaccine waste is deferred to be handled according to local regulations [III], which does not guarantee a central control or monitoring of waste handling.Moreover, vaccine waste has overwhelmed waste management operations (Klemeš et al., 2020).The amount of vaccine waste coupled with the lack of proper monitoring creates the potential for mishandled vaccine waste, which has also been identified as a possibility for stolen vaccine vials [IV].Some potential illicit activities have been identified by researchers regarding the COVID-19 vaccines, including but not limited to counterfeit/fake vaccines, substandard doses and vaccine theft (Farrell and Johnson, 2020;Bae et al., 2020;Bolton, 2021).
In addition to illicit activities caused by vaccine waste, the proliferation of vials and syringe waste constitutes a significant threat to environmental sustainability (Guillot, 2021).According to Klemeš et al. (2021), approximately 85% of medical waste is non-hazardous waste, including vial and syringe discards.If collected, disinfected and stored appropriately, the vial and syringe waste is recyclable.However, recycling firms are hesitant to collect medical waste, and there may be strict regulations to handle outdated/expired vaccines (Klemeš et al., 2021).Therefore, the firms should focus on supply chain redesign with a closed-loop structure so that VSC waste is handled and appropriately monitored.With only a closed-loop structure, the full extent of the potential vaccine waste reduction cannot be guaranteed, especially given the short shelf life of vaccines after thawing.In addition to the closed-loop infrastructure, a real-time vaccination monitoring system that plans, tracks and monitors vaccine delivery can be used to reduce information asymmetry and vaccine waste (Lejarza and Baldea, 2020;Mast et al., 2021;Weintraub et al., 2021;Fadaki et al., 2022).
Currently, the Centers for Disease Control and Prevention (CDC) uses a vaccine tracking system (VTrckS) to place COVID-19 vaccine orders.VTrckS is an integrated web-based centralized vaccine tracking system that connects the public health sector and private partners to provide successful vaccine allocation, distribution, administration, monitoring, and reporting [V].According to the CDC, some wastage is to be expected for any immunization campaign, and the number of unused vaccine doses (wastage) is tracked.However, the COVID Data Tracker does not yet provide this information [VI].Furthermore, researchers posit that correspondence and coordination between different local and state levels are not always consistent, creating additional challenges for accurate real-time data (Lee and Haidari, 2017;Alam et al., 2021).Moreover, accurately forecasting vaccine demand is quite challenging due to demand uncertainties.There is often trouble matching supply to demand in influenza VSCs (Lin et al., 2021), which also applies to COVID-19 VSC (Alam et al., 2021).Therefore, centralized IT systems must be kept up to date and used by all parties to improve forecasting.
During the COVID-19 pandemic, health-care providers opted for vendor managed inventory (VMI) systems to attain operational efficiencies due to the capability of VMI to apply just-in-time strategies (Patrinley et al., 2020).For instance, VMI systems are used to minimize medical waste in hospitals (Weraikat et al., 2019).The real-time capabilities built to support the VMI systems help uphold the closed-loop nature of the system due to its closer monitoring potential.A transshipment strategy with a VMI system can be used to manage vaccine inventories and reduce wastage (Fadaki et al., 2022).
Transshipment, defined as the movement of goods within the same echelon, can provide benefits such as cost reductions (Herer et al., 2006;Çömez-Dolgan and Fescioglu-Unver, 2015), customer service level improvements due to the balancing of inventory levels (Çömez-Dolgan and Fescioglu-Unver, 2015; Yan and Liu, 2018) and quicker delivery (Çömez-Dolgan and Fescioglu-Unver, 2015).Especially due to the latter two benefits, transshipments would be more than beneficial to use in the VSC (Rudi et al., 2001).Given the remaining shelf life of vaccines, transshipments can allow quick shifts in inventory from areas with excess inventory to regions lacking inventory via the central inventory management system (Fadaki et al., 2022).One of the main challenges with transshipments is the complexity of optimizing transshipment decisions due to the vast number of variables required (Robinson, 1990;Çömez-Dolgan and Fescioglu-Unver, 2015).Moreover, Çömez-Dolgan and Fescioglu-Unver (2015) identify lack of participation as another transshipment challenge in decentralized systems.However, centralized systems with enforced decisionmaking rules can help mitigate the lack of involvement.
The WHO posits that access to genuine and good-quality vaccine doses should be uninterrupted for immunizations to work in VSC.The decoupled and often localized management of medication and vaccine providers challenges this objective.As the WHO asserts in their vision for a "successful immunization program," the goal is to: Strengthen supply chains to ensure that high-quality vaccines are always available in the right quantity and form at the right time, in the right place, and stored and distributed under the right conditions.Promote integration with other supply chains for more effective delivery of primary health care.Invest in systems and infrastructure to safely manage, treat and dispose of vaccine waste to help reduce their environmental footprint.
This vision calls for implementing impeccable logistics strategies along with collaboration among otherwise decoupled VSCs and suggests the need to consider the sustainability of operations via reducing the environmental footprint.While WHO's vision is well-intended, there is a need to take this vision one step further to build a sustainable VSC by integrating social impact considerations into strategies and operations.This integration is specifically proposed here since the threats of negative impacts that exist are not only environmental (Klemeš et al., 2020) but also societal, such as theft and counterfeiting of vaccines (Bae et al., 2020;Bolton, 2021;Amankwah-Amoah, 2022) and human well-being (Alam et al., 2021).
In light of these considerations, this study aims to offer an overarching VSC model that can withstand the challenges of the pandemic by integrating transshipment operations and a closed-loop structure by using system dynamics (SD).The proposed VSC includes supplier, manufacturer/distributor and vaccination site echelons.Figure 1 shows the proposed structure of the closed-loop vaccine supply chain (CLVSC) with the transshipment model.
The remainder of the paper is structured as follows.We first review the literature for SD.Next we build causal loop diagrams (CLDs) to propose our overarching SD model.Finally, we provide discussions and conclusions.

Literature review
Supply chains are complex systems that include information and materials flow within and outside supply chain partners; therefore, a systemic view helps explain supply chain complexity.General systems theory (Von Bertalanffy, 1950Bertalanffy, , 1968) suggests that different parts of complex operations should be evaluated and viewed as a whole.A system has a dynamic nature that allows interactions with sub-systems across boundaries (Caddy and Helou, 2007).
SD (Forrester, 1958(Forrester, , 1961) ) describes the structure of dynamic interactions among informational flows, physical processes and organizational policies and explains how these interactions improve system performance over time (Sterman, 2000).Lane (1999) defines SD as a structural theory of dynamic systems that includes accumulation processes, feedback loops and delays between cause and effect."The development of SD models is a process in which modeling and empirical work take turns, providing a deductive-inductive balance" (Größler et al., 2008).

System dynamics approach in health-care context
The SD approach has gained popularity over the years as one of the most effective approaches to analyzing and managing complex health-care challenges such as the occurrence of significant infectious or noninfectious diseases and the quality of health-care delivery (Homer and Hirsch, 2006;Samuel et al., 2013;Darabi and Hosseinichimeh, 2020).In the vaccine context, Lee et al. (2017) investigate vaccine decision-making using the SD approach.Van Ackere and Schulz (2020) use the SD approach to examine vaccination decisions for measles.The majority of the health-care studies use the SD approach to model diseases, emergency care and delivery systems and health-care policies (Samuel et al., 2010;Kumar and Kumar, 2014).Even though many SD studies contribute to the management and organizational science literature, few focus on managerial issues of health-care delivery (Darabi and Hosseinichimeh, 2020).
After the COVID-19 pandemic, the health-care SD studies' focus turned toward modeling the effects of pandemic mitigation strategies using metrics such as accessibility of medical sources, infection rate and contact rate (Kontogiannis, 2021).According to Kontogiannis (2021), these quantitative SD models do not address the complexity of the social and economic environment's influence on the spread of the disease.Therefore, Kontogiannis (2021) incorporates additional qualitative SD models built from system archetypes and integrates all the archetypes into an overall CLD to explain health-care challenges from a resilience perspective that includes anticipation of threats, resource provision, responses to uncertainties and process assessment within a resilience framework.In this study, we adapt Kontogiannis's (2021) methodology, develop multiple CLDs from an extensive review of the SD literature and combine them into an overarching model.The variables in CLDs are adapted from the models that were validated in previous studies in the literature (Vlachos et al., 2007;Paul and Venkateswaran, 2017;Gonul Kochan et al., 2018).

System dynamics in health-care supply chains
In the supply chain literature, Forrester (1958Forrester ( , 1961) ) developed the first supply chain SD model to evaluate inventory policies in a three-echelon supply chain.Since then, supply chain SD models have increasingly gained attention.These models are mainly used to analyze systems operations that change over time under various managerial policies (Sterman, 2000) and, more specifically, capture the production-inventory order behavior at an aggregate level using feedback-based structures (Venkateswaran and Son, 2007).Most supply chain studies use the SD approach to investigate the effects of coordination mechanisms such as VMI; collaborative planning (CP), forecasting and

Distribution
Used Vaccines

Inventory Control
Recyclable Products replenishment (CPFR); and electronic supply chain management systems (e-SCMs) such as inter-organizational information technology (IT) integration, electronic data interchange (EDI) and cloud computing (Disney and Towill, 2003;Ovalle and Marquez, 2003;Machuca and Barajas, 2004;Fiala, 2005;Agarwal et al., 2006;Wilson, 2007;Gonul Kochan et al., 2018).These studies suggest that when IT is used effectively for coordination and information sharing, supply chain performance metrics such as service levels, inventory levels, costs and the bullwhip effect demonstrate improvement.More importantly, they find that SD modeling is appropriate for examining and understanding the information sharing in the supply chain structure.
In the health-care supply chain literature, only a few studies use the SD modeling approach to capture inter-organizational interactions (Gonul Kochan et al., 2018).The contexts of these studies are waste management in health-care supply chains (Chaerul et al., 2008), health-care service supply chain (Samuel et al., 2013), inventory management and distribution of drugs (Azzi et al., 2013), rural health-care supply chains (Kumar and Kumar, 2014), pharmaceutical supply chains (Asamoah et al., 2011;Behzad et al., 2011;Bam et al., 2017), hospital supply chains (Gonul Kochan et al., 2018) and vaccine supply chain (Kussainov, 2015).Specifically, Paul and Venkateswaran (2017) examine the effect of drug shortages of antiviral treatable disease epidemics on an infectivity/transmissibility parameter using an integrated SD model.The study uses a generic disease diffusion model that generates the supply chain demand and integrates the disease diffusion model (SEITRS) into a generic multi-echelon supply chain model.The combined model studies different supply chain factors such as delays, the number of echelons and ordering policies on the epidemic dynamics.Their findings suggest that these supply chain factors have a significant impact on epidemic dynamics.However, their model does not consider the perishability issues and capacity constraints.In this study, we develop a model that includes perishability and capacity constraints by closing the loop.

System dynamics in closed-loop supply chains
In sustainable SCM (SSCM) literature, SD modeling is lacking compared to analytical modeling and mathematical programming (Govindan et al., 2015).Even though SD models are scarce in SSCM literature, these models help examine complex dynamic systems, identify causal links and mechanisms of environmental issues and facilitate long-term decision-making (Rebs et al., 2019).Numerous studies examine inter-organizational interactions in closed-loop supply chains by using an SD approach.For instance, Vlachos et al. (2007) developed an SD model to examine the long-term behavior of closed-loop supply chains with remanufacturing and suggest efficient remanufacturing and capacity planning policies.Their generalized SD model combines a multiechelon forward supply chain (producer and distributor) and reverse supply chain (remanufacturer and collector) that captures inter-organizational interactions.Later, Georgiadis and Besiou (2008) investigate the effects of ecological motivation and technological innovation on the long-term behavior of the closed-loop electrical and electronic equipment (EEE) supply chain.They introduce a novel closed-loop supply chain SD model comprising a forward supply chain with two echelons (producer and distributor) and a reverse channel encompassing recycling activities.Next, Georgiadis and Besiou (2010) extend their multi-tier closed-loop Waste EEE supply chain SD model to include environmental legislation effects.However, these aforementioned studies involve two echelons, mainly manufacturers and distributors.Our model contributes to the existing closed-loop SD literature by capturing the supply chain as a whole, including an additional echelon: retail (vaccination site).
According to Rebs et al. (2019), existing studies on closedloop SD mainly focus on agriculture, automotive, biofuel, construction, electrical/electronics, energy supply, forestry/ lumber, metal/mining, transportation and water supply industries.To the best of our knowledge, closed-loop supply chain SD modeling in the health-care industry has not been addressed in the literature.
There are many quantitative SD models at the micro-level that address health-care issues, mitigation strategies amid the COVID-19 pandemic, transactions and deliveries in healthcare supply chains, policies and environmental issues in closedloop supply chains.What is missing from the literature is an overarching SD model that addresses the issues in health-care supply chains, especially in VSCs, after the COVID-19 pandemic.
In summary, the major contributions of this study to the literature are as follows:

Methodology
As the first step of the SD modeling process, we first define the problem that encompasses the objective of this study and determine the system boundaries.Next, we identify variables and their interactions by reviewing the SD literature extensively.Finally, we conceptualize the variables and their behaviors by developing CLDs to capture CLVSC.

Description of system dynamics approach and causal loop diagrams
When making any critical choice, observation or modification, a systems approach entails understanding and addressing the entire system.The first and most important stage in a systems approach is to sketch up a broad picture of the whole system.However, comprehending a complex system with several components might be challenging.The direct and instantaneous one-way cause-and-effect links may be obvious, while other effects (such as those involving intermediaries, back-and-forth interactions among all stakeholders and delays) may not be apparent (Lee et al., 2017).Thus, CLDs, qualitative models of SD, are used to capture all the effects that are difficult to foresee (Kontogiannis, 2021).Therefore, we create conceptual CLDs that address the challenges in the VSC.In our approach, similar to Kontogiannis (2021), we first develop several qualitative but quantifiable SD CLDs as the following: compartmental epidemic model of disease transmission that addresses the vaccine shortage (Paul and Venkateswaran, 2017); VSC that balances demand-supply while addressing the cold chain constraints; CLVSC that addresses security and sustainability challenges; and CLVSC with transshipment operations.Next, we incorporate all these models into a combined model to capture the dynamic replenishment of vaccines in a closed-loop environment (See Appendix 2 for table descriptions).

Conceptual causal loop diagrams
In this study, we use CLDs as conceptual modeling components to describe the conceptual feedback structure and better understand VSC behavior.CLDs can reveal feedback mechanisms and leverage points in a system.We adopt Sterman's (2000) stock management structure to develop CLDs and use Vensim software to draw CLDs.CLDs can be expanded further into stock and flow diagrams by applying differential equations.CLDs' feedback loops are developed by causal links among components of reality (Größler et al., 2008).Two feedback loop types are used: balancing (negative) and reinforcing (positive) loop.Each arrow in the CLD represents a causal link or cause and effect relationship between the independent (the variable at the tail of the arrow) and the dependent variable (the variable at the head of the arrow).The positive (1) and negative (À) signs near the arrowhead indicate the direction of the cause-and-effect relationship.A pair of parallel lines imply a delay between the cause and effect.A reinforcing loop enhances the change (increase/decrease !increase/decrease) and creates a growing effect over time.Yet, a balancing loop opposes the change (increase/decrease !decrease/increase) and completes the balancing act over time (Sterman, 2000;Kamath and Roy, 2007).The variables in the boxes express the accumulated quantities (i.e.stocks), dashed arrows show the flow of information and solid arrows indicate the flow of physical goods.

SIR model
The SIR model (Sterman, 2000) is considered one of the most widely used SD models in the health-care domain that can be applied to any infectious disease (Darabi and Hosseinichimeh, 2020).SD modelers keep SIR as the core model and expand it with different levels of complexity and additional feedback loops.The SIR model, developed by Sterman (2000) based on Kermack and McKendrick's (1927) epidemic model, splits the population into three groups: 1 Susceptible Population (S). 2 Infectious Population (I). 3 Recovered (R).
Thus, the SIR model relaxes the second assumption of the SI model by including a balancing (negative) recovery loop.The recovery loop depicts that infected people only stay infected for a specific time, recover and establish long-term immunity.This represents the idea of herd immunity (Randolph and Barreiro, 2020), which is depicted by the recovery loop: the higher the number of infected people, the higher the recovery rate and the lower the number of remaining infected people.The SIR model depicts that when infectious people contact at a certain rate (Contact Rate [CR]) with susceptible people, the number of infectious people increases (contagion loop) by the Infection Rate (IR) (total number of contacts) while the number of susceptible people decreases (depletion loop).Infectivity (IF) represents the likelihood of a person contracting an infection, as not every contact with an infectious person results in infection.The Average Duration of Infectivity (D) is defined as the average length of time people are infectious with the assumption that each person's recovery time is different (some people recover in a short time, but for others, it takes longer), but as people recover, the population of infectious people will decrease exponentially.If the IR is lower than the Recovery Rate (RR), the infectious population will decline.When the infectious population declines, the IR declines.Therefore, the infectious population decreases to zero before the disease transmits to the entire population.

SIV model
Figure 2 depicts our integrated SIV model adopted from Paul and Venkateswaran's (2017) integrated supply chain and epidemics model.In our model, instead of R and RR, we use Vaccinated Population (V) and Vaccination Rate (VR).
The Average Duration of Inoculation (DI) is the average length of time people are inoculated with the assumption that each person's inoculation time is different, but as people are inoculated, the population of infectious people will decrease exponentially.If the IR is lower than the VR, the infectious population will decline.When I declines, the IR also declines.Furthermore, vaccinated people gain immunity for a certain period and become susceptible to COVID-19 and its variants (Vaccinated Population [V] increases the S).In reality, susceptible people do not have to become infected to get vaccinated.Instead, they receive vaccinations to reduce the likelihood of getting infected.Therefore, in our model, S increases VR.We integrate VR into our CLVSC.
The supply rate for a vaccine is generated from the VSC model [adopted from Gonul Kochan et al.'s (2018) hospital supply chain model] and integrated into the SIV model.

Vaccine supply chain order fulfillment
Vaccination site CLD (Figure 3) begins with the Vaccine Demand (VD), the population eligible for receiving vaccines, which leads to a rise in Vaccine Order Rate (VOR).When there is no available inventory in stock to fulfill orders promptly, VOR leads to an increase in Vaccine Order Backlog (VOB) which refers to unsatisfied/ unfulfilled orders (Sterman, 2000;p. 724;Venkateswaran and Son, 2007;Wilson, 2007).A rise in VOB leads to an increase in Vaccine Delivery Delay (VDD), the average delay between the placement and the receipt of the vaccination order.VDD becomes equal to the Target Delivery Delay (TDD), which refers to the vaccination site's target for the interval between placement and receipt of vaccine orders (Sterman, 2000;p. 725) when the Desired Supply Rate for Vaccine (DSRV) (the vaccination site's target supply rate) is equal to the Vaccine Supply Rate (VSR).DSRV is calculated as the ratio of VOB and TDD and confirms that the vaccines are filled within the vaccination site's TDD time.TDD is determined by the vaccination site to meet the VD on time.An increase in TDD increases DSRV while decreasing VOB.A rise in VOB also leads to an increase in DSRV.
DSRV leads to an increase in the VSR when the Vaccine Inventory (VI) in stock is sufficient.Vaccine Inventory (VI) refers to the vaccine inventory on hand at each vaccination site and accumulates vaccines shipped from manufacturers/ distributors and transshipped from other vaccination sites.Inventory in stock is used to supply the vaccination demand at the current vaccination site and supply vaccination sites in need of vaccines.Consequently, VSR leads to an increase in the Vaccine Order Fulfillment Ratio (VOFR) (Kamath and Roy, 2007;Venkateswaran and Son, 2007).Once the orders are fulfilled within time, VOFR, VOB and VDD decrease.

Inventory control
Adequate VI in stock raises the vaccination site's Maximum Vaccine Supply Rate (MVSR).The MVSR is described as the maximum number of supplies given the VI in stock and Vaccine Minimum Order Processing Time (VMOPT).VMOPT refers to the amount of time it takes between the order being placed and shipped.Thus, a rise in VMOPT leads to a decrease in MVSR.MVSR decreases the VSR since a vaccination site cannot supply more than MVSR.Contrarily, a rise in VSR leads to a decrease in VI.It is critical to determine whether a VSR is adequate to meet with the VD to avoid stockouts.Vaccine Inventory Coverage Ratio (VICR) refers to the number of days the vaccination site could supply at the current VSR given VI in stock, revealing the service level of the vaccination site.The lower the VICR, the more a vaccination site desires a rise in the VI level to meet with the VD.The Desired Vaccine Inventory (DVI) is the volume of inventory required to keep a vaccination site's desired service level of full and dependable delivery.DVI is estimated by the Expected Vaccine Demand (EVD) and depends on the vaccination site's Vaccine Safety Stock (VSS) and VMOPT.VSS is challenging due to the highly perishable nature of the vaccines.Cold storage temperature and wastage are the most significant constraints.
EVD and DVI rise in response to an increase in VD over time (Georgiadis et al., 2006).The vaccination site reviews Change in Vaccination Demand (CVD) when setting the DVI level.CVD refers to the discrepancy between EVD and the vaccination site's VOR over a period determined by the Time to Average Order Rate (TAOR).The VD information is used to calculate EVD by smoothing the demand figures with the previous period's perceived demand.A vaccination site wishes to  2007).The DVI level leads to an increase in the Vaccine Inventory Gap (VIG) and the disparity between DVI and VI.Vaccine Inventory Adjustment Time (VIAT), the time required to take the inventory to the desired level, corrects VIG over a period of time.

Order placement
As the VIG increases, Desired Vaccine Order (DVO) increases (Wilson, 2007).DVO translates to the Vaccination Site's Order Rate (VSOR) in the manufacturer/distributor and transshipment echelon.Therefore, DVO results in shipments to the vaccination site denoted as Vaccine Transshipment Rate (VTR), which translates into Vaccine Transshipment Delivery Rate (VTDR).A rise in VTDR increases the VI and the service level, called Vaccine Inventory Coverage Rate (VICR).In the distributor/manufacturing echelon, order fulfillment, inventory control and order placement processes remain the same as in the vaccination site echelon (Gonul Kochan et al., 2018), which is not shown here.
In the VMI setting, the forecasted VD is communicated to all vaccination sites' suppliers, including manufacturers and distributors.Vaccination sites no longer place orders with distributors/manufacturers.Therefore, there are no or minimal order backlogs on vaccination sites (Wilson, 2007).The vaccine order information is automatically sent to the manufacturer/distributor based on the DVO, EVD and VIG.(2018).The manufacturer's CLD (Figure 4) starts with DVO, which triggers an increase in Expected Vaccination Site Demand (EVSD).As EVSD rises, the manufacturer's Desired Production (DP) increases.Production Release Rate (PRR) increases as DP rises (Venkateswaran and Son, 2007) and Work in Process Inventory (WIPI) increases, respectively (Georgiadis et al., 2006).When production begins, the difference between PRR and Production Completion Rate (PCR) is accumulated in WIPI, and WIPI increases the PCR.The pending production line, or WIPGap (WIPG), is the difference between the Desired WIP (DWIP) and WIP Adjustment Time (WIPAT) (Sterman, 2000;p. 714).WIPG adjusts the PRR to keep up with WIPI and the Manufacturer's Inventory (MI) at the DWIP level.Manufacturing Lead Time (MLT) increases the DWIP (Venkateswaran and Son, 2007) due to the third-order delay, resulting in a drop in PCR.The PCR leads to an increase in MI.The MI Gap (MIG) is reduced when the MI level is sufficient (Wilson, 2007).The lower the DP level, the lower the MIG, or vice versa.Increased MI levels also result in higher Maximum Manufacturer Shipment Rate (MMSR) and MS Rate (MSR).
Closing the loop We adopted Vlachos et al.'s (2007) SD CLD model to describe the reverse flow of VSC (Figure 5).VI at the end of their current Vaccine Usage Duration (VUD) (usage until expiration or expired) becomes Used Vaccine (UV) (used or expired vaccines).VUD depends on the vaccine's shelf life.UVs are either disposed of and lead to an increase in Uncontrollable Vaccine Disposal (UVD) or collected for reuse/recycling and lead to an increase in Collection Rate (CR) and Collected Vaccines (CV), respectively.For instance, if opened, vials that still have doses inside can be stored for reuse.Furthermore, if vials are appropriately stored after usage, they can be recycled (Klemeš et al., 2021).

Collection
VCR increases the CV and relies on the Collection Capacity (CC) (e.g.truck capacity, cold storage capacity).CV is decreased by the number of vaccines either accepted after inspection (Vaccines Accepted for Reuse [VAR]) or rejected (Vaccines Rejected for Reuse [VRFR]).Inspection Time (IT) refers to the inspection being completed within a given time.VAR and VRFR increase as IT increases, which indicates that the inspection is performed.The inspection outcome (VAR or VRFR), which takes IT, is formed based on several reuses (remaining non-expired doses) and remaining shelf life, and the Failure Percentage (FR).FR refers to a small fraction, a percentage of failing an inspection.Vaccine Vial Monitors can reduce the inspection failure percentage as these are small, color-changing labels that are affixed to the vials.The colorchanging is governed by temperature changes and is essential in supporting ideal storage monitoring vaccine vials [VII].

Remanufacturing
If the Remanufacturing Capacity (RC), which limits the Vaccine Remanufacturing Rate (VRR), is appropriate, the supply of Reusable Vaccines (RV) can be used for remanufacturing.Controllable Vaccine Disposal (CVD) has been devised to prevent an unending buildup of reusable products by draining them if they remain unused for some time (Reusable Stock Keeping Time [RST]).
The Reuse Ratio (RR), defined as the ratio of the Expected Remanufactured Rate (ERR) to the number of Expected Used Vaccines (EUV), represents the remanufacturing/reuse activities.There are currently no take-back obligations; however, even without the regulations, given the risks associated with improper disposal, vaccines and packaging We omit production capacity in our model, as our focus is on vaccine waste and distribution.

Transshipment
Figure 6 presents a visual representation of the proposed model of transshipments.We suggest using the VMI system to allow for central inventory decisions.Specifically for the vaccine sites, transshipment operations are integrated via VMI, creating a virtual pool of inventory called Aggregate Inventory Level (AIL) displays available inventory levels on each vaccination site.
There are various factors to consider while managing transshipments, such as the timing of transshipments, the allowable number of transshipments within a timeframe, the sender and receiver location pairings and the coordination of the transshipment movements (Archibald et al., 1997; Çömez-Dolgan and Fescioglu-Unver, 2015).
The VMI system is designed to use real-time supply and demand data for vaccine allocation decisions between vaccination sites based on available inventory at each vaccine site via Allocation Inventory (AI).The decisions for the transshipments will be made by considering the potential excess inventory based on Allocation Fill Rate (AFR) (Botha et al., 2017), the remaining shelf life of the vaccine doses, VUD, and the need for inventory in vaccine sites that are within reach depending on Minimum Distance Between Vaccination Sites (MDBV) given the remaining shelf life.As the time window for the transshipment operations is narrow, as indicated by Transshipment Lead Time (TLT), it is critical for the decisions and the operations to be agile and accurate.As AIL increases, the AI decisions lead to a rise in Vaccine Transshipment Rate (VTR).Transshipments made between equivalent locations in the supply chain are called lateral transshipments (Paterson et al., 2011).As Tlili et al. (2012) note, there are two types  (Tlili et al., 2012).In our model, we mainly focus on the latter.
Vehicle capacities are also essential due to cold chain requirements for vaccines.Therefore, we adopted vehicle capacity planning from Rathore et al.The overarching model of closed-loop vaccine supply chain Figure 7 depicts the overarching model of CLVSC.In the literature, most quantitative SD models focus on intraorganizational behavior and do not capture the holistic view of the supply chains (Kontogiannis, 2021).This focus refrains from examining the underlying structure and identifying potential interactions.Therefore, it is essential to incorporate multiple models to depict supply chain operations entirely.This paper builds a qualitative overarching CLD for COVID-19 VSC that contains SIV, vaccination site, manufacturer site, closed-loop and transshipment operations (Figure 7).
CLVSC starts with VD at the vaccination site model.As VI depletes to supply VD, the vaccination site's DVO is automatically triggered in the VMI system and the order information is transferred to all vaccination sites.The connection between the vaccination site model (Figure 3) and the transshipment model (Figure 6) is made via DVO.As DVO increases, VSOR increases in the transshipment model.In the transshipment model, inventory level information of all vaccination sites are aggregated in the system (AIL), the system allocates inventory (AI) and matches vaccination sites' inventory needs based on the minimum distance (MDBV).Based on the vehicle transportation capacity (VC), vaccines are transshipped to vaccination sites (VTR).The vaccine sites supply the demand (VSR).If the vaccines expire due to their VUD, closed-loop operations take place.At the same time, VSR increases VR in the SIV model.As VR increases, UV increases in

Discussion
While epidemics are in decline, vaccinations are instrumental in fending off additional waves (Lee et al., 2010).Applying this thinking to the COVID-19 pandemic, even when numbers of infected individuals and fatalities may decrease, efforts to establish an effective VSC are needed to keep fighting against new waves and variants.Additionally, the capabilities built for the battle against the COVID-19 pandemic would be extremely valuable for future epidemics and pandemics.
Ad hoc systems have been proposed to address inventory shortages (Lee et al., 2010).Nevertheless, ad hoc systems are problematic in the overall design owing to their inconsistency and the inability to monitor and manage such efforts.Our model resolves this issue by offering a flexible approach that can still be controlled, manageable and monitored.
Given the unique challenges of VSCM, establishing and maintaining well-functioning, consistent and reliable databases is extremely critical.Especially in the case of pandemics, timely and accurate geographic data are crucial.However, due to privacy concerns, these data are not usually reported or are not reported with precision.Thus, establishing more consistent, reliable and secure databases is essential (Mast et al., 2021).
Sustainability intersects with individual and society's wellbeing.For example, Griffith (2006) posits that human capital is essential for supply chain success.Supply chain members can use an assessment and matching strategy to place individuals in positions where they would create the most value.However, one of the complex impacts of the COVID-19 pandemic has been workplace changes (Kniffin et al., 2021), and as Alam et al. (2021) discuss, only through proper vaccine demand forecasting people can resume work and contribute to economic growth.
The transshipment element incorporated in the conceptual model was essential to be included because of the significant amount of vaccine doses wasted at the vaccination sites.Additionally, in the face of potential stockouts in any vaccination site, especially in more rural areas where alternative locations may not be easily accessible, it is more efficient for vaccination sites to transship vaccine inventory instead of asking people to travel to other locations to receive vaccines.The circumstances of the pandemic have been challenging to manage.The inherent complexities and poor management have resulted in numerous negative impacts on society, the environment and the economy.The main challenges of the VSCM are the lack of coordination in vaccine supply operations and waste management issues.Although effective management of the COVID-19 VSC requires collaboration throughout the SC, we have observed a lack of collaboration in the current VSCM systems.In addition, a thorough literature review has revealed a lack of research that describes a holistic approach to vaccine supply chain operations (Fadaki et al., 2022).In our study, we propose a model that would integrate components allowing a more holistic view of the VSC amidst a pandemic.To the best of our knowledge, our research is the first to propose a model that integrates VMI, transshipment and a closed-loop structure to the VSC.
The VMI helps monitor supply throughout the system and allows the centralization of inventory decisions.Transshipments enable the inventories to be balanced among vaccination sites and provide opportunities for decreasing wasted vaccines.Additionally, the closed-loop structure allows for monitoring vaccinations and relevant packaging at the endof-life stage, creating two main advantages: 1 decreasing vaccine thefts and counterfeit vaccines; and 2 decreasing negative environmental impact.

Conclusion
The COVID-19 pandemic introduced unprecedented challenges related to factors such as increased global connectivity.Supply chain disruptions and management challenges cause further unrest during pandemic mitigation efforts.Although significant strides have been made in establishing a functioning COVID-19 VSC, some threats have been observed that threaten the safekeeping and delivery of vaccines.
Our paper contributes to the literature by enhancing the understanding of health-care delivery challenges and sustainability during the pandemic through a comprehensive closed-loop SD model designed for VSC.
We propose that establishing a closed-loop structure for the VSC is essential to ensure wasted vaccines are accounted for, monitored and recollected safely.However, one other major objective should be to minimize vaccine doses wasted in the first place.As the number of doses required globally cannot be manufactured quickly, the manufactured doses must be used and not wasted within their shelf life.Therefore, the transshipment operations are instrumental in establishing a way for an agile last-mile vaccine logistics operation.In addition, establishing accurate and reliable real-time data-based information systems is vital for the suggested VSC to work effectively.
The model addresses the issues of negative environmental and societal impacts.The environmental impact is improved, as waste is proposed to be collected and disposed of properly.The societal impact is improved as the potential for vaccine dose theft is diminished, and agile transshipment operations can provide more equitable vaccine distribution.
The model proposed in this study contributes to the literature by integrating new elements into the traditional health-care models, which are essential for handling the case of pandemics.

Limitations and future research
We have built a conceptual model; however, testing it with numeric examples would be beneficial.Additionally, we focused on the US VSC, recognizing that vaccine operations look very different depending on location.Therefore, if applied in other settings, the model may need to be adapted according to the different circumstances as required by the different locations.The biggest challenge of VSCs, especially amidst a pandemic, is establishing a global supply chain structure.Therefore, the issue of data and information system inconsistencies only worsens when the VSC is considered on a global scale.Consequently, when the global VSC is studied, there should be intermediary steps to evaluate the communication of distinct systems.Therefore, the model proposed in this study might not apply to other settings.
We would also like to offer some avenues to guide future research areas.It would be beneficial to study transshipment operations on an international scale for future research.As Alam et al. (2021) note, the inequalities on the global scale increased in the face of inequitable access to vaccines.Therefore, given the differences in opportunities and the capabilities of supply chains, studying the effects of such a strategy in an international setting so that countries within travel distance can support each other's vaccine availability.Klemeš et al. (2020) point out the insufficient waste handling/treatment capacities and note that it is crucial to build capabilities to safely handle the vast amount of waste generated in the VSC.With our proposed closed-loop design, we are addressing the issues of material shortages, safety concerns and diverting waste from landfill.However, for this to work, capacities still need to be improved.Therefore, future work should also include capacity considerations.
Future research could also investigate the impacts of thermostable vaccines on VSCs nationally and, especially, globally.Cold chains are challenging to maintain, especially given the availability and potential disruptions in the global supply chain.Making vaccines thermostable is a possible solution for decreasing cold chain dependency (Chen and Kristensen, 2009).Research for developing thermostable COVID-19 vaccines has been in development (Zhang et al., 2020).As the viability and availability of these vaccines are observed in different countries, researchers can build on the assumptions of vaccines being thermostable into their models.Thus, cold chain constraints could be relaxed along with the relevant time constraints for storing vaccines.

Figure 1
Figure 1 Structure of the CLVSC with transshipment extension of the SIR epidemic model for the COVID-19 pandemic; development of conceptual SD CLDs for vaccine transshipment operations; addressing the problems regarding the reverse flow of the COVID-19 VSC using CLDs; and development of an overarching CLD model to address the underlying structure of VSC, reverse VSC and transshipment operations and their connections and interactions to help organizations better navigate and distribute vaccines during future pandemics.

Figure 2
Figure 2 SIV model

Figure 3
Figure 3 Order fulfilment inventory control and order placement at the vaccination site

Figure 4
Figure 4 Production at the manufacturing site

Figure 5
Figure 5 The reverse flow of VSC (2021).Both VTR and Desired Number of Vehicles (DNV) increase the Vehicle Capacity (VC), and VC should not exceed the Average Capacity of Vehicles (ACV).An increase in VC requires more vehicles, increasing the Number of Available Vehicles (NAV).NAV refers to the discrepancy between VC and Vehicles Used for Transportation (VUT).The more NAV for transshipment, the less the VUT, and vice versa.Similarly, the time to prepare vehicles, Vehicle Adjustment Time (VAT), decreases VUT.

Figure 6
Figure 6 Transshipment at VSC

Figure 7
Figure 7 Overarching model