Novel Models and Improved Algorithms for Fuzzy Joint Replenishment Problem with Carbon Cap-and-trade Policy

Novel Models and Improved Algorithms for Fuzzy Joint Replenishment Problem with Carbon Cap-and-trade Policy | 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 Novel Models and Improved Algorithms for Fuzzy Joint Replenishment Problem with Carbon Cap-and-trade Policy Yuanyuan Liu, Rui Wang, Jian Zhou, Lechen Wu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7485695/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 15 Dec, 2025 Read the published version in Fuzzy Optimization and Decision Making → Version 1 posted You are reading this latest preprint version Abstract A joint replenishment problem (JRP) considering multiple types of uncertainties and carbon emission cost under a carbon cap-and-trade policy is studied in this paper. In particular, a novel fuzzy JRP is primarily formulated, in which the influences on the budget control from uncertainties of product defective rate and fuzzy cost parameters, and the carbon emission during the replenishmentare firstly taken into account simultaneously. Accordingly, a fuzzy dependent-chance programming (DCP) with the aim of maximum the credibility of budget control is constructed. Following that, improved hybrid intelligent algorithms named BIS-DE and Exact-DE are designed to solve the proposed novel fuzzy JRP efficiently by employing the bisection fuzzy simulation method and the differential evolution algorithm. Furthermore, based on advanced inverse operational laws, the novel fuzzy DCP model is transformed into an equivalent deterministic counterpart which could be solved with intelligent algorithms without any simulation process. The effectiveness and superiority of both treatments for novel fuzzy JRP are illustrated by performing numerical experiments and sufficient comparisons. Joint replenishment problem Carbon cap-and-trade policy Fuzzy dependent-chance programming Fuzzy simulation Differential evolution algorithm Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 15 Dec, 2025 Read the published version in Fuzzy Optimization and Decision Making → 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-7485695","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":511935515,"identity":"ba71de85-cfce-42d4-b3d7-7ec9d661a614","order_by":0,"name":"Yuanyuan Liu","email":"","orcid":"","institution":"Shandong University of Finance and Economics","correspondingAuthor":false,"prefix":"","firstName":"Yuanyuan","middleName":"","lastName":"Liu","suffix":""},{"id":511935517,"identity":"74e6d828-0e2b-410b-829d-4de48b2008d0","order_by":1,"name":"Rui Wang","email":"","orcid":"","institution":"Shandong University of Finance and Economics","correspondingAuthor":false,"prefix":"","firstName":"Rui","middleName":"","lastName":"Wang","suffix":""},{"id":511935519,"identity":"16a58a3a-3040-4c01-877d-4f94496d0df4","order_by":2,"name":"Jian Zhou","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2UlEQVRIiWNgGAWjYDACCRDBAyTZG9hATMYG4rXwHCBJC5iRQKQW+dnNxyQYZCzkzSWfP3vMw2Aju+EA87MH+LQwzjmWJgF0mOHO2TnmxjwMacYbDrCZG+DTwiyRYwbSwrjhdg6bNA/D4cQNB3jYJPBpYYNqsd9w8/gzoJb/hLXwQLUkbrjBYAbUcoCwFgmJtGQLoJbkDWdyzCTnGCQbzzzMZoZXi/yM5IM3GHvqbDccP/5M4k2FnWzf8eZneLWAAPPfHhgTFFTMhNSDwQ+iVI2CUTAKRsFIBQA9fjz0/2kfYQAAAABJRU5ErkJggg==","orcid":"","institution":"Shanghai University","correspondingAuthor":true,"prefix":"","firstName":"Jian","middleName":"","lastName":"Zhou","suffix":""},{"id":511935521,"identity":"3cc1f8fc-65cd-466b-9a38-21d242ac9cd1","order_by":3,"name":"Lechen Wu","email":"","orcid":"","institution":"Tsinghua University","correspondingAuthor":false,"prefix":"","firstName":"Lechen","middleName":"","lastName":"Wu","suffix":""}],"badges":[],"createdAt":"2025-08-29 06:53:35","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7485695/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7485695/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10700-025-09468-8","type":"published","date":"2025-12-15T15:58:37+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":98814288,"identity":"0d2a851e-1672-470e-aac6-f4a7a952e46c","added_by":"auto","created_at":"2025-12-22 16:12:15","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":981251,"visible":true,"origin":"","legend":"","description":"","filename":"FuzzyJRPFODM.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7485695/v1_covered_36e13104-f4d2-46a7-a819-0edf04f404ec.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Novel Models and Improved Algorithms for Fuzzy Joint Replenishment Problem with Carbon Cap-and-trade Policy","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":true,"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":"Joint replenishment problem, Carbon cap-and-trade policy, Fuzzy dependent-chance programming, Fuzzy simulation, Differential evolution algorithm","lastPublishedDoi":"10.21203/rs.3.rs-7485695/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7485695/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"A joint replenishment problem (JRP) considering multiple types of uncertainties and carbon emission cost under a carbon cap-and-trade policy is studied in this paper. 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