  We study the problem of learning, from observational data, fair and
interpretable policies that effectively match heterogeneous individuals to
scarce resources of different types. We model this problem as a multi-class
multi-server queuing system where both individuals and resources arrive
stochastically over time. Each individual, upon arrival, is assigned to a queue
where they wait to be matched to a resource. The resources are assigned in a
first come first served (FCFS) fashion according to an eligibility structure
that encodes the resource types that serve each queue. We propose a methodology
based on techniques in modern causal inference to construct the individual
queues as well as learn the matching outcomes and provide a mixed-integer
optimization (MIO) formulation to optimize the eligibility structure. The MIO
problem maximizes policy outcome subject to wait time and fairness constraints.
It is very flexible, allowing for additional linear domain constraints. We
conduct extensive analyses using synthetic and real-world data. In particular,
we evaluate our framework using data from the U.S. Homeless Management
Information System (HMIS). We obtain wait times as low as an FCFS policy while
improving the rate of exit from homelessness for underserved or vulnerable
groups (7% higher for the Black individuals and 15% higher for those below 17
years old) and overall.
