SMaRT : Online Reusable Resource Assignment and an Application to Mediation in the Kenyan Judiciary

Overview & Synopsis

Motivated by the problem of assigning mediators to cases in the Kenyan judicial system, this paper studies an online resource allocation problem where incoming tasks (cases) must be immediately assigned to available, capacity-constrained resources (mediators). The resources differ in their quality, which may need to be learned. In addition, resources can only be assigned to a subset of tasks that overlaps to varying degrees with the subset of tasks to which other resources can be assigned. The objective is to maximize task completion while satisfying soft capacity constraints across all the resources. The scale of the real-world problem poses substantial challenges, since there are more than 2,000 mediators and a multitude of combinations of geographic locations (87) and case types (12) on which each mediator is qualified to work. Together, these features—unknown quality of new resources (newly onboarded mediators), soft capacity constraints (due to the mandate to assign cases without delay), and high-dimensional state space—make existing scheduling and resource allocation algorithms either inapplicable or inefficient. The paper formalizes the problem in a tractable manner, using a quadratic program formulation for assignment and a multi-agent bandit-style framework for learning. The paper demonstrates the key properties and advantages of the new algorithm, SMaRT (Selecting Mediators that are Right for the Task), compared with baselines on some stylized instances of the mediator allocation problem. The paper then turns to considering its application to real-world data on cases and mediators from the Kenyan judiciary. SMaRT outperforms baselines and allows for controlling the tradeoff between the strictness of the capacity constraints and overall case resolution rates, both in situations where mediator quality is known beforehand and when the problem is bandit-like in that learning is part of the problem definition. On the strength of these results, the study plans to conduct a randomized controlled trial that will deploy SMaRT in the judiciary’s mediation management system.