A Comparative Study of Mathematical Models for Two-Dimensional Cutting Stock Problems and Solving Algorithms

A Comparative Study of Mathematical Models for Two-Dimensional Cutting Stock Problems and Solving Algorithms | 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 Comparative Study of Mathematical Models for Two-Dimensional Cutting Stock Problems and Solving Algorithms Fatemeh Maleki Almani, Mahsa Gholamnazhad This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4367405/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 Two-dimensional cutting problem involves cutting a set of small pieces from large sheets in a way that optimizes one or more objectives. The objective of this problem can be minimizing the number of sheets used, waste, cost, and so forth. These problems have various applications in different industries such as glass, paper, wood, plastic, steel, etc. This paper studies one of the recent exact polynomial models proposed for these problems. Although the presented model, named Original(a), is quite promising for finding a solution, since these problems belong to the mixed integer non-linear programming model (MINLP) group, solving them will be difficult. Therefore, a linearization technique by multiplying continuous variables for this model would be used. The goal is to find an optimum solution. The studied models are implemented in the Matlab environment and the results of numerical experiments are presented. Applied Mathematics Two-dimensional cutting Two-dimensional packaging Linearization MINLP problems 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-4367405","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":298638038,"identity":"b240a3b7-afa9-4be5-aea4-48fc5bc5629a","order_by":0,"name":"Fatemeh Maleki Almani","email":"data:image/png;base64,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","orcid":"https://orcid.org/0009-0003-4802-3041","institution":"University of Guilan","correspondingAuthor":true,"prefix":"","firstName":"Fatemeh","middleName":"Maleki","lastName":"Almani","suffix":""},{"id":298638579,"identity":"d357fadc-146a-494b-a7b8-85656933f0d9","order_by":1,"name":"Mahsa Gholamnazhad","email":"","orcid":"","institution":"University of Science and Technology of Mazandaran","correspondingAuthor":false,"prefix":"","firstName":"Mahsa","middleName":"","lastName":"Gholamnazhad","suffix":""}],"badges":[],"createdAt":"2024-05-04 08:11:41","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-4367405/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4367405/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":55973374,"identity":"adf6f78e-134a-4df1-a6eb-d07ad1875b72","added_by":"auto","created_at":"2024-05-07 04:29:17","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":764043,"visible":true,"origin":"","legend":"","description":"","filename":"MalekiGholamnezhad5.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4367405/v1_covered_dc50576b-0c48-4355-bb6b-478e1e04a64f.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eA Comparative Study of Mathematical Models for Two-Dimensional Cutting Stock Problems and Solving Algorithms\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"University of Guilan","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":"Two-dimensional cutting, Two-dimensional packaging, Linearization, MINLP problems","lastPublishedDoi":"10.21203/rs.3.rs-4367405/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4367405/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eTwo-dimensional cutting problem involves cutting a set of small pieces from large sheets in a way that optimizes one or more objectives. 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