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

Learning Resource Allocation Policies from Observational Data with an Application to Homeless Services Delivery