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Abstract
This work addresses a fundamental challenge in transportation planning: how to locate facilities equitably across urban networks. Traditional facility location models prioritize operational efficiency but often neglect distributional justice, leaving vulnerable populations underserved. We present a novel approach that incorporates the Kolm-Pollak Equally-Distributed Equivalent (EDE) into facility location optimization, developing a computationally tractable method that scales to city-sized problems while maintaining normative significance for both benefits and burdens.
Our methodological contribution establishes mathematical equivalence between optimizing the non-linear Kolm-Pollak EDE and a linear proxy, enabling solutions for instances as large as New York City with over 200 million binary variables. We extend this framework to accommodate practical constraints including facility capacities, split demands, and location-specific penalties, providing theoretical guarantees and implementation guidelines. Through extensive computational experiments, we demonstrate that our approach effectively balances average access (efficiency) with protection for disadvantaged residents (effectiveness).
To illustrate practical applications, we present a comprehensive case study analyzing supermarket access across the 500 largest U.S. cities, demonstrating how the Kolm-Pollak EDE can support prescriptive decision-making rather than merely descriptive analysis. Additionally, we utilize election data to demonstrate the practicality of the penalty framework to locate polling centers equitably. We further generalize our approach to continuous distances on general networks, addressing the resulting non-convexities through various relaxation techniques. Moreover, we present a unifying framework utilizing both the discrete and continuous models, and demonstrate how it can be used to optimally locate services such as ballot drop boxes. Our methodology has broad applications across transportation facility location problems, including transit stop placement, emergency service coverage, and distribution network design, with potential extensions to other domains requiring equity-based resource allocation.
