Optimization of Mode Selection (Road, Rail, and Sea) and Cargo Consolidation in European Freight Transportation: A Game Theory and TSP Approach

Optimization of Mode Selection (Road, Rail, and Sea) and Cargo Consolidation in European Freight Transportation: A Game Theory and TSP Approach | 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 Optimization of Mode Selection (Road, Rail, and Sea) and Cargo Consolidation in European Freight Transportation: A Game Theory and TSP Approach Pavel Malinovskiy This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6949825/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 Background : The European freight transportation landscape, spanning a network of extensive roadways, rail corridors, and major maritime routes, is in constant flux amid the pressures of globalization and evolving trade patterns. The optimization of transportation mode selection (road, rail, or sea) in conjunction with consolidation strategies is critical to reducing operational costs and improving supply chain efficiency across a wide range of industries. Methods : This article provides a comprehensive framework that integrates a game-theoretic approach— specifically, an auction mechanism—to determine cost-optimal mode choices among carriers, together with a Traveling Salesman Problem (TSP) formulation to optimize routing among distribution hubs. Focusing on major logistics centers inWestern and Central Europe, such as Hamburg, Rotterdam, Antwerp, and Duisburg, this study illustrates how mode choice can be adapted based on the cost per distance (“ ”), the infrastructure specifics, and the consolidation potential at strategically positioned hubs. Results : Our extensive analysis, exceeding 10,000 words and supplemented by numerous mathematical formulations, illustrates how an integrated game-theory-cum-TSP model can yield significant cost savings. By systematically comparing road, rail, and sea transport across various route lengths, decision-makers can identify break-even points where a particular mode transitions from less efficient to more efficient. We demonstrate that selective consolidation at hubs such as Hamburg and Duisburg can further enhance cost-effectiveness, leading to marked improvements in overall supply chain performance. Conclusions : Incorporating a strategic choice among road, rail, and maritime options, along with route and consolidation optimization, results in substantive cost reductions and operational efficiencies. Our findings underscore the importance of comprehensive modeling in a rapidly shifting European logistics landscape, offering vital insights for practitioners seeking to balance cost, time, and sustainability. Freight Transportation; Mode Selection; Road, Rail, Maritime Transport; Cargo Consolidation; Game Theory; Auction Method; Traveling Salesman Problem; Route Optimization; Logistics Efficiency; Supply Chain Management; Cost Minimization; Cluster Analysis; European Freight; Transportation Tariffs; Operational Research; Strategic Planning Applied Mathematics 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-6949825","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":474688816,"identity":"d7424126-f168-426a-828f-37e2fae980d0","order_by":0,"name":"Pavel Malinovskiy","email":"data:image/png;base64,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","orcid":"https://orcid.org/0009-0008-3756-5271","institution":"IEEE","correspondingAuthor":true,"prefix":"","firstName":"Pavel","middleName":"","lastName":"Malinovskiy","suffix":""}],"badges":[],"createdAt":"2025-06-22 13:41:09","currentVersionCode":1,"declarations":{"humanSubjects":true,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":true,"humanSubjectConsent":true,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-6949825/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6949825/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":85259853,"identity":"47c45f3d-46fb-4795-bb78-0270e2deca0c","added_by":"auto","created_at":"2025-06-24 03:48:15","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":306813,"visible":true,"origin":"","legend":"","description":"","filename":"OptimizationofModeSelectionRoadRailandSeaandCargoConsolidationinEuropeanFreightTransportationAGameTheoryand.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6949825/v1_covered_571e04f6-4154-4577-920b-edbf62e851b7.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eOptimization of Mode Selection (Road, Rail, and Sea) and Cargo Consolidation in European Freight Transportation: A Game Theory and TSP Approach\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":"","lastPublishedDoi":"10.21203/rs.3.rs-6949825/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6949825/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cstrong\u003eBackground\u003c/strong\u003e: The European freight transportation landscape, spanning a network of extensive roadways, rail corridors, and major maritime routes, is in constant flux amid the pressures of globalization and evolving trade patterns. The optimization of transportation mode selection (road, rail, or sea) in conjunction with consolidation strategies is critical to reducing operational costs and improving supply chain efficiency across a wide range of industries.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMethods\u003c/strong\u003e: This article provides a comprehensive framework that integrates a game-theoretic approach— specifically, an auction mechanism—to determine cost-optimal mode choices among carriers, together with a Traveling Salesman Problem (TSP) formulation to optimize routing among distribution hubs. 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