Dominant Resource Fairness with Meta-Types.

Inspired by the recent COVID-19 pandemic, we study a generalization of the multi-resource allocation problem with heterogeneous demands and Leontief utilities. Specifically, we assume each agent can only receive allocations from a subset of the total supply for each resource. Such constraints often arise from location constraints (e.g. among all of the volunteer nurses, only a subset of them can work at hospital A due to commute constraints. So hospital A can only receive allocations of volunteers from a subset of the total supply). We propose a new mechanism called Group Dominant Resource Fairness which determines the allocations by solving a small number of linear programs. The proposed method satisfies Pareto optimality, envy-freeness, strategy-proofness, and under an additional mild assumption, also proportionality. We show numerically that our method scales better to large problems than alternative approaches. Finally, although motivated by the problem of medical resource allocation in a pandemic, our mechanism can be applied more broadly to resource allocation under Leontief utilities with external constraints.