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

Optimizing Treatment Facility Locations in Oklahoma Using Haversine, Euclidean, Manhattan, and Chebyshev Distance Optimization | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Optimizing Treatment Facility Locations in Oklahoma Using Haversine, Euclidean, Manhattan, and Chebyshev Distance Optimization Karen Roberts-Licklider, Theodore Trafalis This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4530065/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version 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. Nonlinear Multicriteria Optimization Computational Criminology Facility Location Problem Hoover Index Gini Coefficient Haversine/Euclidean/Manhattan/Chebyshev Distance Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4530065","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":316965580,"identity":"1235152b-ad9c-401f-a751-e56369b9fe43","order_by":0,"name":"Karen Roberts-Licklider","email":"","orcid":"","institution":"University of Oklahoma","correspondingAuthor":false,"prefix":"","firstName":"Karen","middleName":"","lastName":"Roberts-Licklider","suffix":""},{"id":316965581,"identity":"739fc4cc-802c-48ba-aa3b-85534cd3c75f","order_by":1,"name":"Theodore Trafalis","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAt0lEQVRIiWNgGAWjYBAC+/sPGBgqGCx4GNgbQHxmwlrYQGrOMEjwMPAcIFELA4NEAtFaeB9+OFAjISM/8/ExCYYK68QGwlrYjSUOHJPgMbidlibBcCadGC1sDNIf2IBapHPMJBjbDhOlhfnHgX8SPPIzzwC1/CNOC5vEwTZgiN3gAWppIFKLxcE+oMPOpCVbJBxLNybKYTcOfLOxl28/fPDGhxprWYJaUEECacpHwSgYBaNgFOACANzWM2O5AeD5AAAAAElFTkSuQmCC","orcid":"","institution":"University of Oklahoma","correspondingAuthor":true,"prefix":"","firstName":"Theodore","middleName":"","lastName":"Trafalis","suffix":""}],"badges":[],"createdAt":"2024-06-04 19:41:54","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4530065/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4530065/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":58893594,"identity":"1deb46d3-3ec6-4796-8b21-d5d1d44839ed","added_by":"auto","created_at":"2024-06-23 15:17:25","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":980650,"visible":true,"origin":"","legend":"","description":"","filename":"LocationModelHaversineProjectSpringerJournal1.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4530065/v1_covered_eb368d24-2633-477a-bf05-7b185a93dd1f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Optimizing Treatment Facility Locations in Oklahoma Using Haversine, Euclidean, Manhattan, and Chebyshev Distance Optimization","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Nonlinear Multicriteria Optimization, Computational Criminology, Facility Location Problem, Hoover Index, Gini Coefficient, Haversine/Euclidean/Manhattan/Chebyshev Distance","lastPublishedDoi":"10.21203/rs.3.rs-4530065/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4530065/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"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.","manuscriptTitle":"Optimizing Treatment Facility Locations in Oklahoma Using Haversine, Euclidean, Manhattan, and Chebyshev Distance Optimization","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-06-21 03:27:38","doi":"10.21203/rs.3.rs-4530065/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"65a92bb5-f281-4539-9a99-68276b6667ef","owner":[],"postedDate":"June 21st, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-09-25T00:08:15+00:00","versionOfRecord":[],"versionCreatedAt":"2024-06-21 03:27:38","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4530065","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4530065","identity":"rs-4530065","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}