Fair allocation of personal protective equipment to health centers during early phases of a pandemic

Abstract

We consider the problem of allocating personal protective equipment, namely surgical and respiratory masks, to health centers under extremely limited supply. We formulate a multi-objective multi-period non-linear resource allocation model for this problem with the objectives of minimizing the number of infected health workers, the number of infected patients and minimizing a deprivation cost function defined over shortages. We solve the resulting problem using the ε-constraint algorithm so as to obtain the exact Pareto set. We also develop a customized genetic algorithm to obtain an approximate Pareto frontier in reasonable time for larger instances. We provide a comparative analysis of the exact and heuristic methods under various scenarios and give insights on how the suggested allocations outperform the ones obtained through a set of rule-of-thumb policies, policies that are implemented owing to their simplicity and ease-of-implementation. Our comparative analysis shows that as the circumstances get worse, the trade-off between the deprivation cost and the ratio of infections deepens and that the proposed heuristic algorithm gives very close solutions to the exact Pareto frontier, especially under pessimistic scenarios. We also observed that while some rule-of-thumb policies such as a last-in-first-receives type policy work well in terms of deprivation costs in optimistic scenarios, others like split policies perform well in terms of number of infections under neutral or pessimistic settings. While favoring one of the objectives, these policies typically fail to provide good solutions in terms of the other objective; hence if such policies are to be implemented the choice would depend on the problem characteristics and the priorities of the policy makers. Overall, the solutions obtained by the proposed methods imply that more complicated distribution schemes that are not induced by these policies would be needed for best results.