Table B.2.

A selective summary of most recent literature on optimisation of vaccine distribution design. .

Authors	Objectives	Methodology	Assumptions	Findings
Balcik et al. (2008)	To deliver relief supplies from local distribution centre(LDC) to beneficiaries affected by disasters efficiently using a vehicle-based last mile distribution system	A mixed integer programming model that determines delivery schedules for vehicles and equitably allocates resources, based on supply, vehicle capacity, and delivery time restrictions	Location of the LDC is predetermined. Its capacity is sufficient to serve its service region	Number of nodes, routes and partial-allocation options, penalty costs, LDC-supply and vehicle capacities, vehicles’ characteristics, etc. can make the problem very complex and difficult to find a preferred solution.
Medlock and Galvani (2009)	To determine optimal vaccine allocation for five outcome measures: deaths, infections, years of life lost, contingent valuation, and economic costs.	A mathematical model parametrised with survey-based contact data and mortality data from influenza pandemics	Limited supply of vaccines; Vaccinate the most valued based on age structure but not risk or occupation; Nonlinear constrained optimisation.	Optimal vaccination is achieved by prioritisation of schoolchildren and adults aged 30 to 39 years. Consideration of age-specific transmission dynamics is paramount in the desired allocation of influenza vaccines.
Lee et al. (2011)	To examine the impacts of new vaccines on existing vaccine supply chain in terms of storage or transport capacity.	Discrete-event simulation model based on HERMES and deterministic mathematical equation-based model (EBM models to simulate introducing various new vaccines to a district in Thailand	Children would present to clinics for immunisation when they reach the appropriate age	New vaccine introduction can exceed refrigerator space transport cold space at district and sub-district levels As such, additional storage capacity at the provincial level would be required.
Abrahams and Ragsdale (2012)	To design a decision support tool for clerical staff in a healthcare clinic using a familiar, affordable, and accessible software platform.	A binary integer programming model and a genetic algorithm solution technique with conventional scheduling approaches	Multiple vaccines; Single time slot of constant duration; All patients receive the needed vaccines; Number of patients is less than or equal to the number of available time slots; Single patient queue and a single server	Computational results show that significant cost savings can be achieved with the decision support system while simultaneously considering scheduling preferences of patients and mitigating scheduling inconvenience.
Özdamar and Demir (2012)	To develop transportation plans of the last mile delivery and pick-up problem in large-scale disaster relief	A hierarchical cluster and route procedure (HOGCR) for coordinating vehicle routing in large-scale post-disaster distribution and evacuation activities	Operational logistics plans are devised based on estimates of deliveries and evacuations necessary information such as population is known with certainty	The proposed optimisation approach can obtain in 15 min CPU time solutions within a percentage deviation of less than 12% from a strong lower bound for large-scale relief networks.
Dessouky et al. (2013)	To help design an efficient pharmaceutical supply chain with strategic locations to place warehouses and inventories and optimal routes for distribution vehicles	Mathematical models to solve facility location and vehicle routing problems in the context of a response to a large-scale emergency	The plans need to be flexible enough to accommodate contingencies of daily operations. They must consider the stochastic nature of the problem, such as uncertain demand, traffic conditions, etc.	Analysis using a hypothetical anthrax emergency in Los Angeles County shows the approach can help design a effective pharmaceutical supply chain to meet urgent needs.
Brown et al. (2014)	To explore different potential redesigns of the Benin vaccine supply chain and how they would compare with simply adding refrigerators and freezers to the current vaccine supply chain.	A discrete-event simulation model called HERMES (Highly Extensible Resource for Modelling Event-Driven Supply Chains)	Demand for vaccines is modelled stochastically at each location through vaccination sessions Data are drawn from a Poisson distribution around the expected number of patients from yearly census estimates	Operational costs can be reduced while vaccine availability increased by streamlining the distribution system from four to three levels.
Ceselli et al. (2014)	To determine the efficient distribution of vaccines or drugs through the simultaneous and coordinated use of distribution centres and vehicles	A mathematical model to solve a combined location and routing problem. An exact algorithm based on column generation with three different types of columns and branch-and-bound is devised to find the best solution.	Once a delivery site is visited, all people assigned to it will get the drugs within a very short time. Assignment of delivery sites to distribution centres is known beforehand. All vehicles travel at the same speed	Results of numerical experiments show that the proposed algorithm is able to quickly find the optimal value in most of the instances.
Li et al. (2016)	To minimise the overall cost (including refrigeration storage cost, vehicle fixed cost, and transportation cost) of medicine distribution in a certain region	A transport-distance-constrained local community medicine distribution route optimising model is established and solved using a tabu-search-based algorithm	Not stated.	Simulated results show that the proposed algorithm is able to obtain an optimum distribution scheme cost with minimum transportation cost.
Shittu et al. (2016)	To explore the effects of variance in supply of and demand for vaccines in Nigeria on storage capacity requirements	An improved discrete-event simulation model based on HERMES	Monthly requirements are independent random variables. Any required vaccines not available are back ordered and delivered as soon as possible	More vaccine storage capacity is needed than is currently available to cope with the variation; Situation can be improved with proper redesign of the vaccine supply chain.
Gamchi et al. (2020)	To distribute vaccines among different regions to control the spread of communicable diseases in the aftermath of a disaster	A bi-objective mathematical model to simultaneously minimise the total social cost incurred by infected individuals before and after vaccination as well as the cost of assigning appropriate vehicles to routes considering their capacity	The epidemic process follows the SIR model before receiving the vaccines; Vaccine demand for each priority group in each region should be fully satisfied; One vehicle only serves one particular route	With only limited amounts of vaccines, considering high-risk groups as priority groups would help practitioners effectively assign the available vaccine doses. This will help to minimise the social cost incurred by infected individuals.