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

Abstract

In this study we are optimizing the treatment facility locations in the eight regions of Oklahoma. Drug court data was used for each county in Oklahoma to optimize the placement of treatment facilities. The objectives of this model were to optimally place treatment facilities minimizing cost, total haversine distance 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 multi-criteria nonlinear programming model was 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 were all used and compared to see which metric performs the best when coupled with Hoover and Gini index fairness measures.