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

TL;DR

The key properties and advantages of the new algorithm, SMaRT (Selecting Mediators that are Right for the Task), are demonstrated compared with baselines on stylized instances of the mediator allocation problem and its application to real-world data on cases and mediators from the Kenyan judiciary is considered.

Abstract

Motivated by the problem of assigning mediators to cases in the Kenyan judicial, we study 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 other resources can be assigned to. 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 over 2000 mediators and a multitude of combinations of geographic locations (87) and case types (12) that each mediator is qualified to work on. Together, these features, unknown quality of new resources, soft capacity constraints, and a high-dimensional state space, make existing scheduling and resource allocation algorithms either inapplicable or inefficient. We formalize the problem in a tractable manner using a quadratic program formulation for assignment and a multi-agent bandit-style framework for learning. We demonstrate the key properties and advantages of our new algorithm, SMaRT (Selecting Mediators that are Right for the Task), compared with baselines on stylized instances of the mediator allocation problem. We then consider its application to real-world data on cases and mediators from the Kenyan judiciary. SMaRT outperforms baselines and allows control over the tradeoff between the strictness of capacity constraints and overall case resolution rates, both in settings where mediator quality is known beforehand and in bandit-like settings where learning is part of the problem definition. On the strength of these results, we plan to run a randomized controlled trial with SMaRT in the judiciary in the near future.

Figures (6)

• Figure 1: Histogram of empirical mediator VA estimates
• Figure 2: A hypothetical situation where holding back the best mediator is beneficial in the long run. Greedily assigning Case 1 in Cell A leads to overload when a new case arrives in Cell B.
• Figure 3: Mediator accreditation among cells
• Figure 4: An example of case allocations (with known med VAs) in Scenario 1 by SMaRT. At lower $\lambda$, SMaRT favors overloading the best mediator (1) to maximize case resolution rate. At higher $\lambda$, SMaRT sacrifices case resolution rate and focuses more on efficient case-load management, evidenced especially by the reduced red bars on Mediator 1 and the increased allocations to Mediator 3.
• Figure 5: Mean shadow price by mediator during allocation by SMaRT on the stylized examples for varying $\lambda$. As $\lambda$ increases, the shadow prices increase, demonstrating increased marginal benefit of holding them back for future cases. Note also Mediator 1's relatively higher value in Scenario 1, where only they can cover cases in Cell B, versus Scenario 2.

Theorems & Definitions (2)

• Lemma 1: Feasibility for QP when $|V_r| =1$
• proof