Covid 19 vaccine order allocation: an optimization model with substitution

Purpose This paper focuses on multi-objective order allocation with product substitution for the vaccine supply chain under uncertainty. Design/methodology/approach The weighted-sum minimization approach is used to find a compromised solution between three objectives of minimizing inefficiently vaccinated people, postponed vaccinations, and purchasing costs. A mixed-integer formulation with substitution quantities is proposed, subject to capacity and demand constraints. The substitution ratios between vaccines are assumed to be exogenous. Besides, uncertainty in supplier reliability is formulated using optimistic, most likely, and pessimistic scenarios in the proposed optimization model. Findings Covid-19 vaccine supply chain process is studied for one government and three vaccine suppliers as an illustrative example. The results provide essential insights for the governments to have proper vaccine allocation and support governments to manage the Covid-19 pandemic. Originality/value This paper considers the minimization of postponement in vaccination plans and inefficient vaccination and purchasing costs for order allocation among different vaccine types. To the best of the authors' knowledge, there is no study in the literature on order allocation of vaccine types with substitution. The analytical hierarchy process structure of the Covid-19 pandemic also contributes to the literature.