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A scalable optimization approach for equitable facility location: Methodology and transportation applications

Drew Horton, Tom Logan, Joshua Murrell, Daphne Skipper, Emily Speakman

TL;DR

The paper tackles equitable facility location by optimizing the Kolm-Pollak EDE to balance average access and fairness across the distribution of distances. It introduces a linear proxy (KPL) that is equivalent to the nonlinear KP objective, enabling scalable optimization on city-scale networks and extensions to capacity, split demand, and site penalties. Computational experiments show the approach scales to very large instances (e.g., NYC with millions of binary variables) while improving the worst-off residents' outcomes and maintaining near-optimal mean accessibility, with real-world case studies in supermarket access and polling locations. The framework also provides practical guidance for scaling the inequality aversion parameter and incorporating location preferences, making it broadly applicable to transportation planning, urban policy, and related domains requiring equity-aware optimization.

Abstract

Efficient and equitable access to essential services, such as healthcare, food, and education, is an important goal in urban planning, public policy, and transport logistics. However, existing facility location models often do not scale well to large instances, or primarily focus on optimizing average accessibility, neglecting equity concerns, particularly for disadvantaged populations. This paper proposes a novel, scalable framework for equitable facility location, introducing a linearized proxy for the Kolm-Pollak Equally-Distributed Equivalent (EDE) metric to balance efficiency and fairness. Computational experiments demonstrate that our approach scales to extremely large problem instances, while being sensitive enough to account for inequity throughout the distribution, not merely via the maximum value. Moreover, optimal solutions represent significant improvements for the worst-off residents in terms of distance to an open amenity, while also attaining a near-optimal average experience for all users. An extensive real-world case study on supermarket access illustrates the practical applicability of the framework, with additional examples coming from polling applications. As such, the model is extended to handle real-world considerations such as capacity constraints, split demand assignments, and location-specific penalties. By bridging the gap between equity theory and practical optimization, this work offers a robust and versatile tool for researchers and practitioners in urban planning, transportation, and public policy.

A scalable optimization approach for equitable facility location: Methodology and transportation applications

TL;DR

The paper tackles equitable facility location by optimizing the Kolm-Pollak EDE to balance average access and fairness across the distribution of distances. It introduces a linear proxy (KPL) that is equivalent to the nonlinear KP objective, enabling scalable optimization on city-scale networks and extensions to capacity, split demand, and site penalties. Computational experiments show the approach scales to very large instances (e.g., NYC with millions of binary variables) while improving the worst-off residents' outcomes and maintaining near-optimal mean accessibility, with real-world case studies in supermarket access and polling locations. The framework also provides practical guidance for scaling the inequality aversion parameter and incorporating location preferences, making it broadly applicable to transportation planning, urban policy, and related domains requiring equity-aware optimization.

Abstract

Efficient and equitable access to essential services, such as healthcare, food, and education, is an important goal in urban planning, public policy, and transport logistics. However, existing facility location models often do not scale well to large instances, or primarily focus on optimizing average accessibility, neglecting equity concerns, particularly for disadvantaged populations. This paper proposes a novel, scalable framework for equitable facility location, introducing a linearized proxy for the Kolm-Pollak Equally-Distributed Equivalent (EDE) metric to balance efficiency and fairness. Computational experiments demonstrate that our approach scales to extremely large problem instances, while being sensitive enough to account for inequity throughout the distribution, not merely via the maximum value. Moreover, optimal solutions represent significant improvements for the worst-off residents in terms of distance to an open amenity, while also attaining a near-optimal average experience for all users. An extensive real-world case study on supermarket access illustrates the practical applicability of the framework, with additional examples coming from polling applications. As such, the model is extended to handle real-world considerations such as capacity constraints, split demand assignments, and location-specific penalties. By bridging the gap between equity theory and practical optimization, this work offers a robust and versatile tool for researchers and practitioners in urban planning, transportation, and public policy.
Paper Structure (35 sections, 13 theorems, 56 equations, 11 figures, 13 tables)

This paper contains 35 sections, 13 theorems, 56 equations, 11 figures, 13 tables.

Table of Contents

  1. Introduction
  2. Background and Literature Review
  3. Facility Location Models
  4. Incorporating Equity into Facility Location Models
  5. Measuring Inequality
  6. Properties Required for Equity Assessment
  7. Review of Existing Measures (Suitability and Scalability)
  8. The Kolm-Pollak EDE
  9. A Framework for Equitable Facility Location
  10. Base Model Formulation
  11. Model Extensions for Practice
  12. Facility Cost
  13. Facility Capacity
  14. Split Demand Assignment
  15. Incorporating Location Preferences Through Penalties
  16. ...and 20 more sections

Key Result

Proposition 1

Suppose $y_{r,s} \in \{0,1\}$ for all $s \in S$, $r\in R$, and $\sum_{s\in S} y_{r,s} = 1$ for all $r \in R$. Then

Figures (11)

  • Figure 1: This figure shows a hypothetical distribution of residents' distance to a resource, with the average (mean) and Kolm-Pollak Equally-Distributed Equivalent (EDE) indicated by vertical lines. The inequality penalty—shown by the gap between the mean and EDE—increases with the value of the inequality aversion parameter and reflects the presence of residents who are significantly worse off than average.
  • Figure 2: Illustration of the distribution in Example \ref{['ex:KPsplitdemands']}.
  • Figure 3: Optimal locations of 10 additional supermarkets in Santa Rosa, California. The figure on the left displays the solution to (KPL)$^{all}$, and the figure on the right displays the solution to (KPL)$^{p}$.
  • Figure 4: Gwinnett County early voting sites. Red dots represent less-suitable sites (churches and fire stations). Filled dots represent existing early voting sites. Darker background shading indicates residential areas that are farther from an early voting site. Map (a) displays the optimal solution to (KPL$^{rem}$): less-suitable sites are not included as potential locations. In map (b), eight less-suitable sites are selected by (KPL$^{all}$): all sites are included but no penalties are applied. In map (c), the penalized model, (KPL$^t$), achieves a near-optimal Kolm-Pollak score with only 2 less-suitable sites.
  • Figure 5: Distribution of the "true" value of $\epsilon$, after the initial run ($\epsilon_1$) and after the second run ($\epsilon_2$), for $k=1, 5, \text{ and } 10$ new stores placed in 428 US cities. The desired value is $\epsilon=-1$ and is indicated by the red vertical line.
  • ...and 6 more figures

Theorems & Definitions (32)

  • Example 1
  • Proposition 1
  • Corollary 2
  • Example 2
  • Theorem 3
  • Theorem 4
  • Theorem 5
  • Remark 6
  • Definition 7
  • Proposition 8
  • ...and 22 more