The Optimal Flow in Multicommodity Dynamic Problem using Modified Algorithm

The Optimal Flow in Multicommodity Dynamic Problem using Modified Algorithm | 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 Optimal Flow in Multicommodity Dynamic Problem using Modified Algorithm Gautam Beniwal, Mohammad Rizwanullah This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5144707/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 multicommodity flow problem is classical optimization problem where multi commodities transported from sources to sinks subject to different constraints e.g. distance function, demand function with respect to time expanded capacities. Dynamic approach considering time varying flows to resolve the multicommodity flow problem. In this paper, we investigated a time-dependent, stochastic version of min-cost integer multi-commodity flow problem in context of dynamic resource allocation. The stochastic and time dependent dynamic approach uses to resolve the problem considering flow rates changes over time due to certain parameters such as demand function, distance function, conjugation or changing the cost. Linear approximations result in low-quality solutions. Although we will eventually need to use piecewise-linear or hybrid approximation techniques, their quick runtimes can make them respond in the initial piecewise-linear approximation iterations. For this reason, in present work applied an iterative, adaptive dynamic programming approach that influences both non-linear and linear approximations of value function to efficiently tackle this complex problem. The numerical results show that the proposed model gives optimal solution and is computationally useful for large scale problems. It also allows to efficiently manage and optimize the transportation of multicommodity through complex network overtime. Dynamic network Multicommodity network flow Integer programing shortest distance stochastic 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. 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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-5144707","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":365037221,"identity":"8311a170-545c-4f3c-be7e-2b50096bddc1","order_by":0,"name":"Gautam Beniwal","email":"","orcid":"","institution":"Manipal University Jaipur","correspondingAuthor":false,"prefix":"","firstName":"Gautam","middleName":"","lastName":"Beniwal","suffix":""},{"id":365037225,"identity":"81f825c4-c62a-402e-95d5-70bfb87ce5cb","order_by":1,"name":"Mohammad Rizwanullah","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4ElEQVRIiWNgGAWjYDACZijNx94AZzMcIEoLG88BYrXAAJtEAkILXmDezv5M4ueOOnk2yTeGnwsqbBj42xsYDxfg0SJzmCFNsvfMYcM26Rxj6Rln0hgkzhxgODwDjxYJZoZjN3jbDjACtRhI87YdZjAAuvAwD14tjG03/7bV2bdJnjH+TaQWZrbbvG3MiW0SPGbE2sLG/lu27XByG09amTXPmTQeiTMHG/Br4T/+2PBtW51tP/vhzbd5Kmzk+NubD3/GpwUJcBiASKBixgbiNDAwsD8gVuUoGAWjYBSMMAAAKkxCUkFh8gEAAAAASUVORK5CYII=","orcid":"","institution":"Manipal University Jaipur","correspondingAuthor":true,"prefix":"","firstName":"Mohammad","middleName":"","lastName":"Rizwanullah","suffix":""}],"badges":[],"createdAt":"2024-09-24 11:38:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5144707/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5144707/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":74183726,"identity":"00285839-35d2-4b7f-9916-290c30a8a9be","added_by":"auto","created_at":"2025-01-19 15:31:37","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":388146,"visible":true,"origin":"","legend":"","description":"","filename":"OETheOptimalFlowinMulticommodityDynamicProblemOE.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5144707/v1_covered_e3fdb064-f0da-498e-ac1a-f14cee2981a8.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"The Optimal Flow in Multicommodity Dynamic Problem using Modified Algorithm","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":"Dynamic network, Multicommodity network flow, Integer programing, shortest distance, stochastic","lastPublishedDoi":"10.21203/rs.3.rs-5144707/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5144707/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The multicommodity flow problem is classical optimization problem where multi commodities transported from sources to sinks subject to different constraints e.g. distance function, demand function with respect to time expanded capacities. 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