Friday, January 13 2023
10:30am - 12:30pm
PhD Thesis Presentation
Thesis Proposal for Drew Horton - Considering Equity in Facility Location Optimization Models

Date: Friday January 13th, 10:30 am

Location: In person- ACAD-4017, Zoom- contact MathStats-Staff@ucdenver.edu for link

Committee: Emily Speakman (Advisor), Steffen Borgwardt (Chair), Stephen Hartke, Florian Pfender, Daphne Skipper

Title: Considering Equity in Facility Location Optimization Models

Abstract:
The urban design of our communities significantly impacts how burdens, such as exposure to pollution, and resources, like supermarkets, are distributed among residents. Studies consistently indicate that historically disadvantaged groups are exposed to larger burdens and have inferior access to resources. The inequitable structure of our cities needs to be addressed, and the climate crisis has increased the urgency of this task. One key to reducing emissions is moving from automobile-oriented development to bring services back into neighborhoods. However, history shows that without careful planning, urban development only benefits the wealthy. Therefore, being proactive during the planning process is crucial.

In the environmental justice literature, the Kolm-Pollak Equally Distributed Equivalent (EDE) is the preferred metric for quantifying the experience of a population. The metric incorporates both the center and the spread of the distribution of the individual experiences, and therefore, captures the experience of an ``average" individual more accurately than the population mean. In particular, the mean is unable to measure the equity of a distribution, while the Kolm-Pollak EDE is designed to penalize for inequity. Unfortunately, optimizing over the Kolm-Pollak EDE in a mathematical programming model is not trivial because of the nonlinearity of the function. We have developed a linear proxy function which allows us to achieve the solution we would obtain when optimizing the Kolm Pollak EDE over a standard facility location model but with the same computational burden as optimizing over the population mean. We present a case study of the 500 largest U.S. cities and provide key information for those working to transform our cities and eradicate food deserts.

We propose to extend this work by considering disamenities, such as pollution, in an obnoxious facility location model. We will also model the case of ‘split demands’ where each origin may be served by multiple facilities. Additionally, we will explore the robustness of our model as we increase or decrease the decision makers’ aversion to inequality. This is equivalent to varying a specific parameter in the definition of the Kolm-Pollak EDE. We will generalize our original model and expand the choice of potential facility locations to allow placement anywhere in the city network, rather than only a discrete set of options. In this generalization, the linear proxy we developed will no longer be appropriate and we will need alternative tools to overcome the computational burden of the optimization. We propose to consider the perspective relaxation of our formulation and also explore a piecewise linear underestimator of this perspective reformulation. We will run computational experiments on randomly generated networks of varying sizes to assess the quality of bounds obtained from both relaxations with the aim of solving the generalized model on real-world data.
Speaker:Drew Horton
Affiliation:Department of Mathematical and Statistical Sciences, University of Colorado Denver
Location:ACAD-4017


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