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Decision trees are among the most interpretable and popular machine learning models that are used routinely in applications ranging from revenue management to medicine. Traditional heuristic methods, although fast, lack modeling flexibility for incorporating constraints such as fairness and do not guarantee optimality. Recent efforts aim to overcome these limitations using mixed-integer optimization (MIO) for better modeling flexibility and optimality, but speed remains an issue. In “Strong Optimal Classification Trees,” Aghaei, Gómez, and Vayanos use integer optimization and polyhedral theory to create an MIO-based formulation with a strong LO relaxation resulting in a 29% speed-up in training time compared with state-of-the-art MIO-based formulations, as well as up to an 8% improvement in out-of-sample accuracy. 

We study critical systems that allocate scarce resources to satisfy basic needs, such as homeless services that provide housing. These systems often support communities disproportionately affected by systemic racial, gender, or other injustices, so it is crucial to design these systems with fairness considerations in mind. To address this problem, we propose a framework for evaluating fairness in contextual resource allocation systems that is inspired by fairness metrics in machine learning. This framework can be applied to evaluate the fairness properties of a historical policy, as well as to impose constraints in the design of new (counterfactual) allocation policies. Our work culminates with a set of incompatibility results that investigate the interplay between the different fairness metrics we propose. Notably, we demonstrate that: 1) fairness in allocation and fairness in outcomes are usually incompatible; 2) policies that prioritize based on a vulnerability score will usually result in unequal outcomes across groups, even if the score is perfectly calibrated; 3) policies using contextual information beyond what is needed to characterize baseline risk and treatment effects can be fairer in their outcomes than those using just baseline risk and treatment effects; and 4) policies using group status in addition to baseline risk and treatment effects are as fair as possible given all available information. Our framework can help guide the discussion among stakeholders in deciding which fairness metrics to impose when allocating scarce resources.