The Planar p-Median Problem with Uniform Demand Density Over an Area

The Planar p-Median Problem with Uniform Demand Density Over an Area | 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 The Planar p-Median Problem with Uniform Demand Density Over an Area Jack Brimberg, Pawel Kalczynski, Taly Drezner, Zvi Drezner This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9570392/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 Most location papers assume that demand is generated at points. This is convenient for designing models and solution methods. In many real applications, demand is generated in an area. For example, when planning to locate service facilities such as public schools in a large area, there may be a very large number of students in the area, and it is impractical to represent them as individual demand points. Also, students graduate every year and new students start schooling. It is reasonable to model the problem as demand generated at every point in the area. A recommended practical approach suggested in this paper, when very little information is known and future demand is unpredictable, is to assume a uniform demand density and to create a configuration of facilities, using the model and methods presented here. The size of each facility, for example, the number of teachers and classrooms, would be determined every year once there is more demand information. In this paper we derive explicit expressions for calculating the exact value of the objective function, the average distance between all the points in the area to their closest facility, when locating multiple facilities inside a convex polygon. Based on these formulations, heuristic procedures for finding the best locations of facilities are developed and tested with good results. Location analysis p-median area demand models and solutions 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-9570392","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":640149828,"identity":"2ce67415-ddcc-4520-b792-12ffd5af9433","order_by":0,"name":"Jack Brimberg","email":"","orcid":"","institution":"Royal Military College of Canada","correspondingAuthor":false,"prefix":"","firstName":"Jack","middleName":"","lastName":"Brimberg","suffix":""},{"id":640149830,"identity":"f22d8d69-13e8-4379-8857-7c883eebbe03","order_by":1,"name":"Pawel Kalczynski","email":"","orcid":"","institution":"California State University, Fullerton","correspondingAuthor":false,"prefix":"","firstName":"Pawel","middleName":"","lastName":"Kalczynski","suffix":""},{"id":640149831,"identity":"9f0c7d73-5d0c-4602-b6a7-a4fa20ee0da7","order_by":2,"name":"Taly Drezner","email":"","orcid":"","institution":"College of Southern Nevada","correspondingAuthor":false,"prefix":"","firstName":"Taly","middleName":"","lastName":"Drezner","suffix":""},{"id":640149832,"identity":"67b16553-78fb-43fd-9dbc-a5f34b6ab1d3","order_by":3,"name":"Zvi Drezner","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA7ElEQVRIiWNgGAWjYFCCBAjFz3yA8cADmCAPMVok2xIYDgDZEsRrMThGrBb59tyHD3/usMk3PsZjcCCh4l4dv3QD44O3bbi1MPY8NzaQPJNmuQ2s5UyxhOScA8yGc/FoYZZIY5MwbDtsYHa/x+BAYluChMGNBDZpXjxa2CTS2H8ktv03MG4D2pL4D6yF/Tc+LTxAWxgOth0wMGADaWmA2MKMT4sEzzNmyca2ZAOJY2wFBxKOJUjOnJHYLDnnHG4t8u1pjB9/ttkZ8Lcxb3zwoSaBn18i+eCHN2W4tWADjA2kqR8Fo2AUjIJRgAEAwsFPENqIiHcAAAAASUVORK5CYII=","orcid":"","institution":"California State University, Fullerton","correspondingAuthor":true,"prefix":"","firstName":"Zvi","middleName":"","lastName":"Drezner","suffix":""}],"badges":[],"createdAt":"2026-04-30 00:08:44","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9570392/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9570392/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":109405389,"identity":"b19695ad-a5ba-44b9-980c-80d1d6f45f66","added_by":"auto","created_at":"2026-05-17 13:17:46","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1118923,"visible":true,"origin":"","legend":"","description":"","filename":"zipped.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9570392/v1_covered_0035ffd2-50ff-45b7-a1f9-d1aa8c3771ca.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"The Planar p-Median Problem with Uniform Demand Density Over an Area","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":"Location analysis, p-median, area demand, models and solutions","lastPublishedDoi":"10.21203/rs.3.rs-9570392/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9570392/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eMost location papers assume that demand is generated at points. 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