A matheuristic approach to integrated multi-Range lot-sizing and vehicle routing problems with time windows for perishable products

A matheuristic approach to integrated multi-Range lot-sizing and vehicle routing problems with time windows for perishable products | 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 A matheuristic approach to integrated multi-Range lot-sizing and vehicle routing problems with time windows for perishable products Ridha Erromdhani, Abdelwaheb Rebaï This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6701965/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 Our starting point in this paper was based on the overview of recent developments in the field of modeling multi-range capacitated lot-Sizing problem and vehicle routing problem with time windows. However, the objective is to synchronize the two problems and to build a better overall solution applied to a real case study. We propose a mixed-integer linear programming (MILP) model that incorporates the new dimension of product range along with time windows, specifically applied to the distribution of perishable products. An iterative two-phase matheuristic, combining mathematical programming and a variable neighborhood search algorithm, is employed to solve these NP-hard problems. In this study, we assigned a product to each production range while respecting capacity constraints and minimizing the total costs of production, shortage, backlog, and storage. Additionally, we optimized vehicle routing to deliver the product ranges while accounting for vehicle capacity constraints and the time windows assigned to each customer. We demonstrate the efficiency of our mathematical formulation through numerical experiments conducted on real-world data. Matheuristic Approach Production Routing Problem Multi-Range Lot-Sizing Problem Mixed Integer Programming Perishability Variable Neighborhood Search Local Search Vehicle Routing Problem with Time Windows 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-6701965","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":471333574,"identity":"84452796-e349-48f4-9af3-5ee49883cfbf","order_by":0,"name":"Ridha Erromdhani","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+0lEQVRIiWNgGAWjYNACtgMMDMwMDAd4GxjkGBh4QEJyxGsxhmoxJkILCAC1JDYQ0sIvffbhoxtld+TN2XkfHni7wy59w/GzBx98YDDIx6VFsi/d2Djn3DPDnc3sBgfnnknO3XAmL9lwBoOBZQMOLQZn2Nikc9sOM244zMZwmLeNOXfDgRwzaR6GPwa4bLGHarGHaqlPNzj/BqTFAKcWAx6IlkSolsMJBjdy8GuROMPGDPTL4WSQloNz244bzrzxxthwhgFuLfw9bIyPc8oO2244f4z5w9u2anm+8zmGDz5U4NaCCRQOgB1MvAYGBvkGUlSPglEwCkbBSAAAHlNYEil06ocAAAAASUVORK5CYII=","orcid":"","institution":"University of Sfax","correspondingAuthor":true,"prefix":"","firstName":"Ridha","middleName":"","lastName":"Erromdhani","suffix":""},{"id":471333575,"identity":"9c911e51-bd80-428f-9fd1-58bf8d19e331","order_by":1,"name":"Abdelwaheb Rebaï","email":"","orcid":"","institution":"University of Sfax","correspondingAuthor":false,"prefix":"","firstName":"Abdelwaheb","middleName":"","lastName":"Rebaï","suffix":""}],"badges":[],"createdAt":"2025-05-19 21:08:06","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6701965/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6701965/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":86190293,"identity":"292eadfa-8703-478c-8829-4a9e0ed6a50e","added_by":"auto","created_at":"2025-07-07 18:53:28","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":476501,"visible":true,"origin":"","legend":"","description":"","filename":"OperationsResearchForum.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6701965/v1_covered_ea1c1785-5d21-4c22-8b7c-fa88aeab4631.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A matheuristic approach to integrated multi-Range lot-sizing and vehicle routing problems with time windows for perishable products","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":"Matheuristic Approach, Production Routing Problem, Multi-Range Lot-Sizing Problem, Mixed Integer Programming, Perishability, Variable Neighborhood Search, Local Search, Vehicle Routing Problem with Time Windows","lastPublishedDoi":"10.21203/rs.3.rs-6701965/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6701965/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eOur starting point in this paper was based on the overview of recent developments in the field of modeling multi-range capacitated lot-Sizing problem and vehicle routing problem with time windows. 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