An Inventory Model for partial backlogging Items with memory effect

An Inventory Model for partial backlogging Items with memory effect | 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 An Inventory Model for partial backlogging Items with memory effect RITUPARNA PAKHIRA, UTTAM GHOSH, HARISH GARG, Vishnu Narayan Mishra This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-1877587/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 03 May, 2023 Read the published version in Soft Computing → Version 1 posted 5 You are reading this latest preprint version Abstract In this paper, an EOQ model has been considered where the demand rate is constant for both the stock period and stock out period (i.e. for the period of shortage) and during shortage i.e. stock out period, demand is partially fulfilled at a constant rate. The holding cost here is assumed as time-dependent.The effect of constant backlogging rate and variable backlogging rate are discussed depending on the previous model and present model.Inventory and related phenomena are of agreat importance in the study memory effect.To incorporate memory effect,the model can not be described by the standard ordinary differential equation,it should be developed by standard fractional order differential equation.Moreover,in order to show the relationship between fractional models and standard ordinary first order differential equations,two type of memory indices consider(i) Differential memory index,(ii) integral memory index,equationg two indices to 1,the model would be considered as memoryless model.Different type partial backlogging rate i.e. high partial backlogging rate and low partial backlogging rate has been considered and it is observed that at certain order of differential memory index i.e. at a level of memory effect,profit is equal for high partial backlogging rate and low partial backlogging rate.Atlast,some recommendation is given to develop another paper with the help of this paper. Constant partial backlogging Strong and poor memory effect strong and poor memory effect Cost function with memory effect. Full Text Cite Share Download PDF Status: Published Journal Publication published 03 May, 2023 Read the published version in Soft Computing → Version 1 posted Editorial decision: Major Revision 04 Nov, 2022 Reviewers invited by journal 21 Oct, 2022 Reviewers agreed at journal 13 Oct, 2022 Editor assigned by journal 23 Jul, 2022 First submitted to journal 22 Jul, 2022 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-1877587","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":144142753,"identity":"572633eb-1c1d-4e4d-bebb-05fcc9128137","order_by":0,"name":"RITUPARNA PAKHIRA","email":"data:image/png;base64,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","orcid":"https://orcid.org/0000-0001-7274-7793","institution":"Academy of Technology","correspondingAuthor":true,"prefix":"","firstName":"RITUPARNA","middleName":"","lastName":"PAKHIRA","suffix":""},{"id":144142754,"identity":"ebf6fff3-66df-481b-b535-87750597881f","order_by":1,"name":"UTTAM GHOSH","email":"","orcid":"","institution":"University of Calcutta","correspondingAuthor":false,"prefix":"","firstName":"UTTAM","middleName":"","lastName":"GHOSH","suffix":""},{"id":144142755,"identity":"2971c855-b09c-48e3-ae85-460face494e9","order_by":2,"name":"HARISH GARG","email":"","orcid":"","institution":"Thapar Institute of Engineering and Technology","correspondingAuthor":false,"prefix":"","firstName":"HARISH","middleName":"","lastName":"GARG","suffix":""},{"id":144142756,"identity":"e939490e-b258-4e46-a911-35f6ad9e1674","order_by":3,"name":"Vishnu Narayan Mishra","email":"","orcid":"","institution":"Indira Gandhi National Tribal University","correspondingAuthor":false,"prefix":"","firstName":"Vishnu","middleName":"Narayan","lastName":"Mishra","suffix":""}],"badges":[],"createdAt":"2022-07-20 10:57:56","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-1877587/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-1877587/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00500-023-08087-y","type":"published","date":"2023-05-03T20:42:26+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":27943285,"identity":"fb342e60-28b8-481a-9412-3d02006f6927","added_by":"auto","created_at":"2022-10-18 16:16:58","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":612805,"visible":true,"origin":"","legend":"","description":"","filename":"Finalpaper20.7.2022.pdf","url":"https://assets-eu.researchsquare.com/files/rs-1877587/v1_covered.pdf"}],"financialInterests":"","formattedTitle":"An Inventory Model for partial backlogging Items with memory effect","fulltext":[{"header":"Full Text","content":"This preprint is available for \u003ca href='/article/rs-1877587/latest.pdf' target='_blank'\u003edownload as a PDF\u003c/a\u003e."}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"soft-computing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"soco","sideBox":"Learn more about [Soft Computing](https://www.springer.com/journal/500)","snPcode":"500","submissionUrl":"https://submission.nature.com/new-submission/500/3","title":"Soft Computing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Constant partial backlogging, Strong and poor memory effect, strong and poor memory effect, Cost function with memory effect.","lastPublishedDoi":"10.21203/rs.3.rs-1877587/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-1877587/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"In this paper, an EOQ model has been considered where the demand rate is constant for both the stock period and stock out period (i.e. for the period of shortage) and during shortage i.e. stock out period, demand is partially fulfilled at a constant rate. 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