Optimisation of the Distribution of COVID-19 Vaccines

Abstract: This paper explores how to optimally distribute vaccines by deciding what middle warehouses to use for storage. For this purpose, a network has been designed with a central warehouse, a set of middle warehouses and a set of local hospitals. The supply has been defined by two different types of vaccines to incorporate their logistical requirements, and the demand has been defined by the elderly population of Sweden. The model was constructed as a mixed-integer program in the optimisation programming language GAMS. The results was a set of 13 middle warehouses allocated such that the total distances when distributing the vaccines are minimised. It was also identified how much of each type of vaccines that was being shipped. The integer program was then relaxed to test whether the optimal value was in fact a global optima. Both the objective value for the original problem and for the relaxed problem was 10189.8 km, which means that it could be identified as a global optima. Furthermore, this paper explored ways to mitigate the supply chain risks with the help of mathematical methods and supply chain management literature. This paper presents scenario-based stochastic programming, how to construct a supplier portfolio, reliability engineering and distribution-based stochastic programming as useful methods when dealing with the risks.  In essence, the purpose of this paper was to evaluate modeling opportunities for distributions of vaccines rather than the quantitative results since the data was limited. The aim was to present a general model that could be used with different sets of data, and provide the most optimal allocation of warehouses. Recommended improvements to the paper are greater accuracy in data, in probability distributions and expansion of model with consideration of time.