Optimal location of additional facilities and reallocation of service areas

Optimal location of additional facilities and reallocation of service areas | 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 Optimal location of additional facilities and reallocation of service areas Maryna Sazonova, Larysa Koriashkina This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4971931/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 This paper addresses the problem of the optimal location of new facilities within an existing service network to alleviate the burden on current enterprises and meet the increasing demand for services. The study considers two critical aspects: 1) the "capacities" of service centers, which determine the maximum number of services or products each center can offer, and 2) the option for customers to be served by one of the k nearest service centers. Alongside the strategic location of new centers, the model also involves the reallocation of service areas, defining zones of responsibility for all facilities in the network. The primary goal is to minimize the total distance between all customers and the k nearest service centers. Typical "service center–customer" relationships include enterprises and consumers, post offices and clients, or medical testing sites and patients, etc. The mathematical model for territorial segmentation is formulated as an Optimal Multiplex Partitioning of Continuum Sets (OMPCS) problem. This approach enables the creation of overlapping service zones, unlike traditional models that result in first-order partitioning where zones are mutually exclusive and operate as territorial monopolies. We present and implement numerical algorithms for solving OMPCS problems in software. The model examples demonstrate how the strategic location of new facilities and the redistribution of service areas across all network entities can effectively reduce the load on existing centers. Applied Mathematics territorial zoning optimal multiplex partitioning of sets continuous model facility location non-differentiable optimization Full Text Additional Declarations The authors declare no competing interests. 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. 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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-4971931","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":344747214,"identity":"fb3605f8-d9dd-44e4-b354-728d7aa1d88c","order_by":0,"name":"Maryna Sazonova","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAArklEQVRIiWNgGAWjYDADfh4GNhK1SPYwk6rF4AyxWuTbjz98XFBxWN74zPljDxj+2BBjeEKy8Ywzhw23nW1mN2BsSyNCC0PCMWnetjTGbeeZ2SQYGw4T4bD+h20gLfab+4FaGP78J6yF4UYyG1CLTeIG3magFrYDRDjsxjNmY54zNslA/5hJJLYlE+Ow9IePeSokbPt7Ep9JfPhjR4TDUEACqRpGwSgYBaNgFGAHADBoM8sP0KXeAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-9513-9659","institution":"KTH Royal Institute of Technology","correspondingAuthor":true,"prefix":"","firstName":"Maryna","middleName":"","lastName":"Sazonova","suffix":""},{"id":344747215,"identity":"ec510702-6855-4112-8941-3f66a94383d3","order_by":1,"name":"Larysa Koriashkina","email":"","orcid":"https://orcid.org/0000-0001-6423-092X","institution":"Dnipro University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Larysa","middleName":"","lastName":"Koriashkina","suffix":""}],"badges":[],"createdAt":"2024-08-25 08:51:32","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-4971931/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4971931/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":63349540,"identity":"cde9ee6f-8eed-480f-90cf-f5e6fc21c391","added_by":"auto","created_at":"2024-08-27 08:07:48","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":600101,"visible":true,"origin":"","legend":"","description":"","filename":"PaperofSazonovaKoriashkinaCor21.08.2024.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4971931/v1_covered_b27d630a-a407-44fc-b1c2-91f5da9fac93.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eOptimal location of additional facilities and reallocation of service areas\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"territorial zoning, optimal multiplex partitioning of sets, continuous model, facility location, non-differentiable optimization","lastPublishedDoi":"10.21203/rs.3.rs-4971931/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4971931/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis paper addresses the problem of the optimal location of new facilities within an existing service network to alleviate the burden on current enterprises and meet the increasing demand for services. The study considers two critical aspects: 1) the \"capacities\" of service centers, which determine the maximum number of services or products each center can offer, and 2) the option for customers to be served by one of the \u003cem\u003ek\u003c/em\u003e nearest service centers. Alongside the strategic location of new centers, the model also involves the reallocation of service areas, defining zones of responsibility for all facilities in the network. The primary goal is to minimize the total distance between all customers and the \u003cem\u003ek\u003c/em\u003e nearest service centers. Typical \"service center\u0026ndash;customer\" relationships include enterprises and consumers, post offices and clients, or medical testing sites and patients, etc.\u003c/p\u003e \u003cp\u003eThe mathematical model for territorial segmentation is formulated as an Optimal Multiplex Partitioning of Continuum Sets (OMPCS) problem. 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