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Optimizing Treatment Facility Locations in Oklahoma Using Haversine, Euclidean, Manhattan, and Chebyshev Distance Optimization

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  • Karen Roberts-Licklider

    (University of Oklahoma)

  • Theodore Trafalis

    (University of Oklahoma)

Abstract

In this study, we are optimizing the treatment facility locations in the eight regions of Oklahoma based on the homeland security map. Drug court data was used for each county in Oklahoma to optimize the placement of treatment facilities. The objectives of this model are to optimally place treatment facilities minimizing cost, total of various distance metrics and maximizing the total number of facilities located in each region, while not exceeding the number of facilities allowed to be located according to the maximum covering location problem. An integer priority based multi-criteria nonlinear programming model is utilized with several models comparing the results with and without fairness constraints, using fairness measures such as Hoover index and Gini coefficient at various thresholds. Gurobi was the solver used to solve each model. The Euclidean, Haversine, Manhattan, and Chebyshev distance metrics are used and compared to see which metric performs the best when coupled with Hoover and Gini index fairness measures.

Suggested Citation

  • Karen Roberts-Licklider & Theodore Trafalis, 2025. "Optimizing Treatment Facility Locations in Oklahoma Using Haversine, Euclidean, Manhattan, and Chebyshev Distance Optimization," SN Operations Research Forum, Springer, vol. 6(3), pages 1-32, September.
    • Handle: RePEc:spr:snopef:v:6:y:2025:i:3:d:10.1007_s43069-025-00448-7
    DOI: 10.1007/s43069-025-00448-7
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    References listed on IDEAS

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    1. Cowell, Frank, 2011. "Measuring Inequality," OUP Catalogue, Oxford University Press, edition 3, number 9780199594047.
    2. Violet Xinying Chen & J. N. Hooker, 2023. "A guide to formulating fairness in an optimization model," Annals of Operations Research, Springer, vol. 326(1), pages 581-619, July.
    3. Higinio Mora & Jerónimo M Mora-Pascual & Alberto García-García & Pablo Martínez-González, 2016. "Computational Analysis of Distance Operators for the Iterative Closest Point Algorithm," PLOS ONE, Public Library of Science, vol. 11(10), pages 1-19, October.
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