Entropy Based Uncertain Multi Objective Multi-Item Fixed Charge 4D Transportation Problem Involving Breakable and Substitute Items

Entropy Based Uncertain Multi Objective Multi-Item Fixed Charge 4D Transportation Problem Involving Breakable and Substitute Items | 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 Entropy Based Uncertain Multi Objective Multi-Item Fixed Charge 4D Transportation Problem Involving Breakable and Substitute Items Awdhesh Kumar Bind, Deepika Rani, Kapil Kumar Goyal This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3588941/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 Decision-makers always strive to build transport systems that are both profitable and sustainable. Such systems seek to satisfy transportation requirements while minimizing adverse environmental effects and enhancing economic viability. Cost savings and the reduction of the environmental impact can be boosted by improving the supply chain management and freight transportation efficiency. In the transportation systems, energy conservation, waste reduction, recyclable packaging, plastic reduction and sustainable transportation can majorly contribute to the environmental sustainability. During transportation, several types of vehicles are used and generally these vehicles use different type of fuels like petrol, diesel, CNG etc. These vehicles emit green house gases that pollute the environment. In this study, an entropy based multi-objective 4D transportation problem with breakable and substitute items is developed and examined in order to maximize profit and reduce the carbon emissions. The items have been purchased at various depots at various prices. Different types of breakable/replacement items are delivered via different routes using various types of vehicles having varying capacities. All the parameters have been taken to be zigzag uncertain variables. Different models are developed in accordance with the management and the customer decisions regarding the substitutability of items. Chance-constrained programming has been used to transform the equivalent crisp models. All the models have been solved using the intuitionistic fuzzy programming technique using the LINGO 19.0 optimization solver with x64-based system type and Intel(R) Pentium(R) CPU 4405U @ 2.10GHz, 2100 Mhz, 2 Core(s) Processor. A real life based numerical problem is presented and solved to validate the concept and the results are compared with respect to the nature of the obtained solution. 4D transportation problem entropy function multi-objective programming chance constrained optimistic pessimistic expected value carbon emission Full Text 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-3588941","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":284765365,"identity":"4b67e389-be5c-475a-8ed4-536d22e825b9","order_by":0,"name":"Awdhesh Kumar Bind","email":"","orcid":"","institution":"National Institute of Technology Jalandhar: Dr BR Ambedkar National Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Awdhesh","middleName":"Kumar","lastName":"Bind","suffix":""},{"id":284765366,"identity":"2417c86f-ad54-40a2-8b44-edf5e89592ee","order_by":1,"name":"Deepika Rani","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAs0lEQVRIiWNgGAWjYJCCAzwVDDxACsSWIFbLGQYeHpK0MPC2MYCsIRKYt589eODtvDsy9owHGD/8YLDII6hF5kxewsG5256BHMYs2cMgUUxQiwRDjsFh3m2HwX6RBvITGwhq4X8D1DIHrIX5N3FaJEC2NIC1sBFpi8Qbg4NzjgG1HDjYZtljQJTDcow/vKk5bM8+4/DhGz8q6ghrQdJ8EKjYgHj1QMBPgvGjYBSMglEwsgAAANg5Zywm1EQAAAAASUVORK5CYII=","orcid":"","institution":"Dr BR Ambedkar National Institute of Technology","correspondingAuthor":true,"prefix":"","firstName":"Deepika","middleName":"","lastName":"Rani","suffix":""},{"id":284765368,"identity":"f09311f4-8b55-4631-8f2d-7a41861c2e7f","order_by":2,"name":"Kapil Kumar Goyal","email":"","orcid":"","institution":"National Institute of Technology Jalandhar: Dr BR Ambedkar National Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Kapil","middleName":"Kumar","lastName":"Goyal","suffix":""}],"badges":[],"createdAt":"2023-11-10 06:33:20","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3588941/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3588941/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":61219234,"identity":"1737062f-be2a-46f0-a719-102f76c699c7","added_by":"auto","created_at":"2024-07-27 10:36:57","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1691605,"visible":true,"origin":"","legend":"","description":"","filename":"EntropybasedTP.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3588941/v1_covered_c2bd0b40-0c89-476f-8cc5-7d02c65d4434.pdf"}],"financialInterests":"","formattedTitle":"Entropy Based Uncertain Multi Objective Multi-Item Fixed Charge 4D Transportation\nProblem Involving Breakable and Substitute Items","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":"4D transportation problem, entropy function, multi-objective programming, chance constrained, optimistic, pessimistic, expected value, carbon emission","lastPublishedDoi":"10.21203/rs.3.rs-3588941/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3588941/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Decision-makers always strive to build transport systems that are both profitable and sustainable. Such systems\nseek to satisfy transportation requirements while minimizing adverse environmental effects and enhancing economic\nviability. Cost savings and the reduction of the environmental impact can be boosted by improving the\nsupply chain management and freight transportation efficiency. In the transportation systems, energy conservation,\nwaste reduction, recyclable packaging, plastic reduction and sustainable transportation can majorly contribute to\nthe environmental sustainability. During transportation, several types of vehicles are used and generally these vehicles\nuse different type of fuels like petrol, diesel, CNG etc. These vehicles emit green house gases that pollute the\nenvironment. In this study, an entropy based multi-objective 4D transportation problem with breakable and substitute\nitems is developed and examined in order to maximize profit and reduce the carbon emissions. The items have\nbeen purchased at various depots at various prices. Different types of breakable/replacement items are delivered via\ndifferent routes using various types of vehicles having varying capacities. All the parameters have been taken to be\nzigzag uncertain variables. Different models are developed in accordance with the management and the customer\ndecisions regarding the substitutability of items. Chance-constrained programming has been used to transform the\nequivalent crisp models. All the models have been solved using the intuitionistic fuzzy programming technique\nusing the LINGO 19.0 optimization solver with x64-based system type and Intel(R) Pentium(R) CPU 4405U @\n2.10GHz, 2100 Mhz, 2 Core(s) Processor. 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