An axiomatic production model for circular directional indirect network technologies with undesirable output production and relational NDEA models

An axiomatic production model for circular directional indirect network technologies with undesirable output production and relational NDEA models | 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 axiomatic production model for circular directional indirect network technologies with undesirable output production and relational NDEA models Claudio Pinto This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4788363/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 In the production economics, the behavior’s assumptions on the production’s unit with production of final undesirable output can be very numerous. For example, it is possible to assume the simple maximization of revenues as well as assuming maximization of revenues net of costs generated by undesirable outputs. Alternatively, it is possible to assume simple minimizing costs or assuming minimizing costs added by those generated by undesirable outputs. Yet, it is possible to assume simple maximizing profits or assuming maximizing profits net of costs generated by undesirable outputs. As well as it is possible to assume the simple minimization of inputs, or minimization of undesirable outputs or the maximization of desirable final outputs as well as their combinations. Therefore, we will have many ways to build an optimization models. The behavior’s assumptions can be technologically and economically constrained. Among these latter, budgetary constraints and revenue targets are the more common. However, models may also take into account other types of constraints, such as those that model the laws of governing the production of undesirable outputs and/or those that model their relationships with other outputs and inputs (as is the case with the constraint of material balance). In addition models can have constraints on the circularity of a subset of outputs (intermediate or final), or constraints on free availability or not of a subset of intermediate outputs and inputs and so on. In this paper, we will present an axiomatic production model for an interconnected linear DEA technology with final reversed outputs (mainly undesirable) subject to three different types of economic constraints. Then we will build optimization models exploiting the network data envelopment analysis approach. One solved the NDEA models we will use the optimal solutions for the calculation of economic quantities such as shadow price of undesirable output. To build our NDEA models we will exploit the duality relationship between indirect technological set, indirect directional distance functions and indirect profit functions. indirect network technologies set indirect directional distance functions indirect directional profit functions reverse final undesirable output production axioms production duality network data envelopment analysis 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. 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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-4788363","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":336098033,"identity":"881ae7b7-e288-448e-a400-ebe57fd8414f","order_by":0,"name":"Claudio Pinto","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4klEQVRIiWNgGAWjYDACdiDmMWBgYGNgPgYWYAOKHMCrhRmuhS2NgSEByACKHMCrB6wFzOIxA2sBi+DTwt/M/EziTYFNHp90z7cHH39sk+djZmA8/AGPFonDbGaScwzSitlkzm43nJFw27CNkMMMmBnMpHkMDie2SeRuk+ZJuM1IhBb2b1AtOc9AWuyJ0MIDsyWHDaQlkaAWicM8xZZgv0ikmUnOSLud3MbM2HDgDB4t/O3tG2+8+WOTJz8j+ZnEB5vbtvPbmw9/qMCjBQYSkNiMDURoQNUyCkbBKBgFowAVAAB9Vkb2UbWUjQAAAABJRU5ErkJggg==","orcid":"","institution":"University of Salerno","correspondingAuthor":true,"prefix":"","firstName":"Claudio","middleName":"","lastName":"Pinto","suffix":""}],"badges":[],"createdAt":"2024-07-23 11:29:23","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4788363/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4788363/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":61955915,"identity":"cb90e650-e6e7-4259-9831-6ac9a89c5f4a","added_by":"auto","created_at":"2024-08-07 13:35:34","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":786345,"visible":true,"origin":"","legend":"","description":"","filename":"Pintomanuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4788363/v1_covered_40eb44c6-9540-4a1f-8733-b0b4d763f407.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"An axiomatic production model for circular directional indirect network technologies with undesirable output production and relational NDEA models","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"indirect network technologies set, indirect directional distance functions, indirect directional profit functions reverse, final undesirable output, production axioms, production duality, network data envelopment analysis","lastPublishedDoi":"10.21203/rs.3.rs-4788363/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4788363/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn the production economics, the behavior\u0026rsquo;s assumptions on the production\u0026rsquo;s unit with production of final undesirable output can be very numerous. For example, it is possible to assume the simple maximization of revenues as well as assuming maximization of revenues net of costs generated by undesirable outputs. Alternatively, it is possible to assume simple minimizing costs or assuming minimizing costs added by those generated by undesirable outputs. Yet, it is possible to assume simple maximizing profits or assuming maximizing profits net of costs generated by undesirable outputs. As well as it is possible to assume the simple minimization of inputs, or minimization of undesirable outputs or the maximization of desirable final outputs as well as their combinations. Therefore, we will have many ways to build an optimization models. The behavior\u0026rsquo;s assumptions can be technologically and economically constrained. Among these latter, budgetary constraints and revenue targets are the more common. 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