Table 2.

Literature review on the distribution stage of vaccine supply chain.

Authors	Objectives	Research method	Variables	Stationary or Mobile DC	Findings
Halper and Raghavan (2011)	To maximize the service provided by mobile facilities	Routing problem	Demand service by each route, cumulative rate of demand	Mobile	The proposed heuristics show optimal routes for mobile facilities especially when demand changes over time.
Ramirez-Nafarrate et al. (2015)	To minimize the waiting time and travel distance to optimize the vaccine distribution	Genetic algorithm	Arrival rate to the point-of-dispensing sites (PODs), number of servers and census track assigned to POD	Stationary	While the proposed model generates output comparable to other similar approaches it is also able to explore a range of alternatives in case the resources are not sufficient to meet the performance objectives.
Araz et al. (2012)	Geographic prioritization of distributing pandemic influenza vaccines	Mathematical model	Mortality rate, social contact, infectious and incubation periods, transmission probability and location	unknown	In case vaccines are unavailable at late stage of pandemic it is recommended to prioritize those areas that are expected to have the latest waves of transmission.
Lee et al. (2013)	To identify the vaccine optimal location for vaccine distribution centers using RealOpt tool	SEPAIR six-stage model	Use of six stage of SEPAIR model: susceptible; exposed; infectious; asymptomatic; symptomatic; recovered	Stationary	Challenges and the benefits of RealOpt tools are discussed.
Aaby et al. (2006)	To optimize the allocation of vaccine distribution centers	Simulation models, capacity-planning and queuing models	Arrival rate, time spent for vaccination, MC capacity, served residents, staff number	Stationary	The proposed models were validated using real data.
Rachaniotis et al. (2012)	To minimize the total; number of infections	Scheduling problem	Number of susceptible and infected individuals, processing time, size of subpopulation	Mobile	The optimal schedule using mobile facility could significantly outperforms random scheduling.
Emu et al. (2021)	To select optimal distribution centers considering two factors of priority and distance	Optimization model (PD-VDM)	Total population to be vaccinated, number of DCs, DC capacities, priority levels	Stationary	The efficiency of the proposed model was shown using real data.
Enayati and Özaltın (2020)	To optimally distribute the vaccine in heterogeneous population	Non-linear optimization problem	Contact rate, group size, infectiousness of infected individuals, infectiousness of exposed individuals, recovery rate, vaccine coverage	Stationary	The group-specific transmission dynamics such as geographic location and age play an important role in the optimal allocation of influenza vaccine.
Larson and Teytelman (2012)	To analyze the effect of timing on the vaccine distribution	Mathematical model	Susceptibility, infectivity, and activity levels	Stationary	Vaccines must be administered well before the pandemic reaches its peak. In allocating vaccine, factors such as stage of pandemic in geographical regions should be taken into account.
Dessouky et al. (2013)	To optimize the facility location and vehicle routing decisions in large-scale disaster relief	Mathematical modeling	Population size, distance, number of facilities and vehicle, vehicle capacity	Stationary	It is shown how the proposed model is considered in an anthrax emergency.
Matrajt et al. (2013)	To optimize vaccine distribution in a group of cities	Mathematical model	Illness attack rate, recovery rate, fraction of symptomatic, contact rates, vaccine efficacies, probability of transmission	unknown	The results indicate that the optimal allocation strategy changes depend on the status of the pandemic. They argue that children as a high transmission group should be given the highest priority during the early stages of the pandemic. This would help to break the transmission cycle early on. However, the priority group will shift to the high transmission group once too many people have already been infected.
Brown et al. (2014)	To explore redesigning the vaccine supply chain in Benin through adding freezer and refrigerators to the chain	HERMES simulation model	Labour, storage, transportation, and building costs	Stationary	Both capital and operating costs were reduced by eliminating redundancies in locations’ personnel, equipment, and routes.
Ceselli et al. (2014)	To optimize the distribution of vaccine	Mathematical problem: Generalized Location and Distribution Problem	Types and number of vehicles, distance between nodes, capacity and number of distribution center	Mixed	The proposed approach outperforms the existing methods with higher levels of flexibility
Gamchi et al. (2021)	To minimize the social cost and the cost of vehicles used in controlling the spread of infectious decease	vehicle routing problem	Number of susceptible, infected and recovered individuals, transmission fate, distance, vehicle capacity, vaccine doses	Stationary	Test problems served to assess the performance of the proposed model.
Goodarzian et al. (2021)	To design a sustainable-resilience health care network during the COVID-19 pandemic	Mathematical problem: MILP	Quantity of transported medicines, inventory level	Unknown	The impact of transportation cost on social responsibility of staff and total cost of the model.