Segmented Multi-Tiered Capacitated Median-Covering Problem

Segmented Multi-Tiered Capacitated Median-Covering Problem | 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 Segmented Multi-Tiered Capacitated Median-Covering Problem Britta Stemmler, Andreas Kleine, Markus André Hilbert This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8893575/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 The German banking landscape has undergone profound structural changes over the past two decades. Driven by digitalization, shifting customer behavior, and cost pressures, the number of physical bank branches has declined substantially. Despite this contraction, physical presence remains strategically important for regional institutions such as the Savings Banks (Sparkassen), which operate under a public mandate to ensure inclusive access to financial services, particularly in structurally weak regions. Against this background, this paper introduces the Segmented Multi-Tiered Capacitated Median-Covering Problem, or SMTC-MCP for short, a discrete, nested, and hierarchical location allocation model for the optimization of existing bank branch networks. Building on the classical $p$-median framework, the model integrates heterogeneous customer segments, differentiated facility types with service-specific accessibility radii, and a flexible multi-tiered capacity structure. The proposed capacity formulation allows for controlled overload, segment-to-segment reallocation, and penalized capacity extensions, enabling a realistic representation of advisory workloads and staffing constraints. The hybrid median-covering structure jointly balances distance minimization and service accessibility requirements. The applicability of the proposed framework is demonstrated through an empirical case study using real-world data from a German Savings Bank. The results provide actionable insights for operational and strategic branch network optimization under contemporary regulatory, demographic, and capacity constraints. JEL Classification: C61 , D24 , L20 , R30 Operations Research hierarchical facility location median-covering model branch network optimization multi-tiered capacity 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. 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-8893575","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":592195131,"identity":"1b57f7c3-361f-4273-a2db-559db5c5dfca","order_by":0,"name":"Britta Stemmler","email":"","orcid":"https://orcid.org/0009-0006-1526-1790","institution":"Fernuniversität in Hagen","correspondingAuthor":false,"prefix":"","firstName":"Britta","middleName":"","lastName":"Stemmler","suffix":""},{"id":592195941,"identity":"53464ebf-a810-4f77-a5ad-39ed35836a30","order_by":1,"name":"Andreas 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mandate to ensure inclusive access to financial services, particularly in structurally weak regions.\u003c/p\u003e\n\u003cp\u003eAgainst this background, this paper introduces the Segmented Multi-Tiered Capacitated Median-Covering Problem, or SMTC-MCP for short, a discrete, nested, and hierarchical location allocation model for the optimization of existing bank branch networks.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eBuilding on the classical $p$-median framework, the model integrates heterogeneous customer segments, differentiated facility types with service-specific accessibility radii, and a flexible multi-tiered capacity structure.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe proposed capacity formulation allows for controlled overload, segment-to-segment reallocation, and penalized capacity extensions, enabling a realistic representation of advisory workloads and staffing constraints.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe hybrid median-covering structure jointly balances distance minimization and service accessibility requirements.\u003c/p\u003e\n\u003cp\u003eThe applicability of the proposed framework is demonstrated through an empirical case study using real-world data from a German Savings Bank. The results provide actionable insights for operational and strategic branch network optimization under contemporary regulatory, demographic, and capacity constraints.\u003c/p\u003e\n\u003cp\u003eJEL Classification: C61 , D24 , L20 , R30\u003c/p\u003e","manuscriptTitle":"Segmented Multi-Tiered Capacitated Median-Covering Problem","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-18 06:26:50","doi":"10.21203/rs.3.rs-8893575/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":"e780424b-79dc-4c1d-9fab-23b8f863a534","owner":[],"postedDate":"February 18th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":63013683,"name":"Operations Research"}],"tags":[],"updatedAt":"2026-02-18T06:26:50+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-18 06:26:50","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8893575","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8893575","identity":"rs-8893575","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}