  Inspired by the recent COVID-19 pandemic, we study a generalization of the
multi-resource allocation problem with heterogeneous demands and Leontief
utilities. Unlike existing settings, we allow each agent to specify
requirements to only accept allocations from a subset of the total supply for
each resource. These requirements can take form in location constraints (e.g. A
hospital can only accept volunteers who live nearby due to commute
limitations). This can also model a type of substitution effect where some
agents need 1 unit of resource A \emph{or} B, both belonging to the same
meta-type. But some agents specifically want A, and others specifically want B.
We propose a new mechanism called Dominant Resource Fairness with Meta Types
which determines the allocations by solving a small number of linear programs.
The proposed method satisfies Pareto optimality, envy-freeness,
strategy-proofness, and a notion of sharing incentive for our setting. To the
best of our knowledge, we are the first to study this problem formulation,
which improved upon existing work by capturing more constraints that often
arise in real life situations. Finally, we show numerically that our method
scales better to large problems than alternative approaches.
