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Analysis and Improvement of Eviction Enforcement

Baris Ata, Yuwei Zhou

TL;DR

The paper addresses eviction enforcement planning by casting daily decisions as a high-dimensional stochastic control problem with a budgeted prize-collecting VRP, where prizes derive from a Brownian control formulation. It develops a deep neural network–based method to approximate the value-function gradient in a Reflected Brownian Motion setting, enabling scalable policy design that balances equity and efficiency. The proposed policy substantially reduces the fraction of eviction orders missing their deadlines (by ~72%) while maintaining comparable daily throughput, and a counterfactual analysis shows further improvements with increased capacity or longer deadlines. Practically, the framework offers a data-driven, dynamically adaptive approach to eviction enforcement planning with potential policy implications for resource allocation and scheduling in large urban counties.

Abstract

Each year, nearly 13,000 eviction orders are issued in Cook County, Illinois. While most of these orders have an enforcement deadline, a portion does not. The Cook County Sheriff's Office (CCSO) is responsible for enforcing these orders, which involves selecting the orders to prioritize and planning daily enforcement routes. This task presents a challenge: balancing "equity" (i.e., prioritizing orders that have been waiting longer) with "efficiency" (i.e., maximizing the number of orders served). Although the current CCSO policy is highly efficient, a significant fraction of eviction orders miss their deadline. Motivated by the CCSO's operations, we study a model of eviction enforcement planning and propose a policy that dynamically prioritizes orders based on their type (deadline or no deadline), location, and waiting time. Our approach employs a budgeted prize-collecting vehicle routing problem (VRP) for daily planning, where the "prizes" are determined by solving a stochastic control problem. This stochastic control problem, which relies on the VRP for determining feasible actions at each decision point, is high-dimensional due to its spatial nature, leading to the curse of dimensionality. We overcome this challenge by building on recent advances in high-dimensional stochastic control using deep neural networks. We compare the performance of our proposed policy with two practical benchmark policies, including one that mimics the current CCSO policy, using data from CCSO. Similar to the CCSO policy, our proposed policy leads to efficient resource utilization, but it also reduces the percentage of orders that miss their deadline by 72.38% without degrading the overall service effort for either type of orders. In a counterfactual study, we show that increasing the service capacity or extending the enforcement deadline further reduces the fraction of orders missing their deadline.

Analysis and Improvement of Eviction Enforcement

TL;DR

The paper addresses eviction enforcement planning by casting daily decisions as a high-dimensional stochastic control problem with a budgeted prize-collecting VRP, where prizes derive from a Brownian control formulation. It develops a deep neural network–based method to approximate the value-function gradient in a Reflected Brownian Motion setting, enabling scalable policy design that balances equity and efficiency. The proposed policy substantially reduces the fraction of eviction orders missing their deadlines (by ~72%) while maintaining comparable daily throughput, and a counterfactual analysis shows further improvements with increased capacity or longer deadlines. Practically, the framework offers a data-driven, dynamically adaptive approach to eviction enforcement planning with potential policy implications for resource allocation and scheduling in large urban counties.

Abstract

Each year, nearly 13,000 eviction orders are issued in Cook County, Illinois. While most of these orders have an enforcement deadline, a portion does not. The Cook County Sheriff's Office (CCSO) is responsible for enforcing these orders, which involves selecting the orders to prioritize and planning daily enforcement routes. This task presents a challenge: balancing "equity" (i.e., prioritizing orders that have been waiting longer) with "efficiency" (i.e., maximizing the number of orders served). Although the current CCSO policy is highly efficient, a significant fraction of eviction orders miss their deadline. Motivated by the CCSO's operations, we study a model of eviction enforcement planning and propose a policy that dynamically prioritizes orders based on their type (deadline or no deadline), location, and waiting time. Our approach employs a budgeted prize-collecting vehicle routing problem (VRP) for daily planning, where the "prizes" are determined by solving a stochastic control problem. This stochastic control problem, which relies on the VRP for determining feasible actions at each decision point, is high-dimensional due to its spatial nature, leading to the curse of dimensionality. We overcome this challenge by building on recent advances in high-dimensional stochastic control using deep neural networks. We compare the performance of our proposed policy with two practical benchmark policies, including one that mimics the current CCSO policy, using data from CCSO. Similar to the CCSO policy, our proposed policy leads to efficient resource utilization, but it also reduces the percentage of orders that miss their deadline by 72.38% without degrading the overall service effort for either type of orders. In a counterfactual study, we show that increasing the service capacity or extending the enforcement deadline further reduces the fraction of orders missing their deadline.

Paper Structure

This paper contains 88 sections, 4 theorems, 70 equations, 23 figures, 19 tables, 19 algorithms.

Table of Contents

  1. Introduction
  2. The remainder of this paper.
  3. Literature Review
  4. Evictions in the sociology literature.
  5. Vehicle Routing Problem (VRP).
  6. Drift rate control problems.
  7. Solving high-dimensional PDEs.
  8. Model
  9. HJB equation and an equivalent SDE
  10. Approximating the Auxiliary Function $F(z, v)$
  11. Computational Method
  12. Proposed Policy and Benchmarks
  13. Proposed policy.
  14. An urgency-based policy.
  15. Threshold-based zone clearing policy (a benchmark policy motivated by the current practice).
  16. ...and 73 more sections

Key Result

Proposition 1

If $V(\cdot)$ and $\beta$ solve the HJB equation, then the following holds almost surely for $T>0$,

Figures (23)

  • Figure 1: The 12-zone design from the CCSO. The red marker is the CCSO office (which serves as the depot in eviction enforcement planning).
  • Figure 2: Histogram of the number of daily received orders across all zones, depending on whether the eviction orders have a deadline or not.
  • Figure 3: Empirical distribution of the service time of the eviction orders. The mean and standard deviation of the service time is 14.39 and 10.42 minutes, respectively.
  • Figure 4: Number of the teams for daily assignments throughout the history. The mean, median, and standard deviation of the number of teams in a daily assignment is 3.8722, 4, and 1.6408, respectively.
  • Figure 5: Distribution of the duration between the deadline and received date. The mean, median, and standard deviation is 69.17, 72, and 12.64, respectively.
  • ...and 18 more figures

Theorems & Definitions (9)

  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Remark 1
  • Remark 2
  • Definition 1: PCST problem
  • Proposition 3
  • Proposition 4