A new global optimum solution model based on multi-value dynamic programming for the cut-off grade optimization in a surface mining complex

A new global optimum solution model based on multi-value dynamic programming for the cut-off grade optimization in a surface mining complex | 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 new global optimum solution model based on multi-value dynamic programming for the cut-off grade optimization in a surface mining complex Pritam Biswas, Rabindra Kumar Sinha, Phalguni Sen This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-1171028/v2 This work is licensed under a CC BY 4.0 License Status: Posted Version 2 posted You are reading this latest preprint version Show more versions Abstract In techno-economic concern, cut-off grade (COG) optimization is the key for efficient mineral liquidation from the huge metalliferous surface mining sector. In this paper, a sequentially advancing algorithm based on discrete multi-value dynamic programming (MDP) has been developed to calculate the global optimum COG of a large-scale open-pit metalliferous deposit. The proposed COG optimization algorithm aims to overcome the limitations of straightforward classical techniques in determining the optimum COG. This discrete COG-MDP model is the first of its kind and has the novelty of dealing with the simulation of eight dynamic possibilities to achieve the maximal global Net Present Value (NPV). A high-level programming language (Python) has been used to develop the computer model to deal with the complexity of handling a minimum of 500 series of dynamic variables. This model can generate results in polynomial-time from the complex of mining, milling, and smelting and refining system corresponding to various limiting conditions. The prime objective considered in the model is to optimize the COG of a metalliferous deposit. A working open-pit copper mining complex from India has been used to validate the model. In this study, the optimum COG for the Malanjkhand copper deposit has been found to be (0.33%, 0.23%, 0.52%, 0.26%, 0.27%, 0.22%, 0.24%) with a maximum NPV of ₹ (12204, 14653, 16948, 14609, 21454, 26717, 38821) million corresponding to various scenarios. The findings also show that the present value gradually hits zero after the project’s life cycle, confirming the typical pattern of other mining firms. Dynamic programming global optimum model cut-off grade (COG) surface mining NPV maximization Full Text Cite Share Download PDF Status: Posted Version 2 posted You are reading this latest preprint version Show more versions 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-1171028","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":71797157,"identity":"db8e4567-fea8-4b04-97d8-728acaca3bea","order_by":0,"name":"Pritam Biswas","email":"","orcid":"","institution":"Indian Institute of Technology (Indian School of Mines): Indian Institute of Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Pritam","middleName":"","lastName":"Biswas","suffix":""},{"id":71797158,"identity":"3fe8cf95-c6f6-4c90-9046-c7797214532c","order_by":1,"name":"Rabindra Kumar Sinha","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0ElEQVRIiWNgGAWjYDACHgaGA4wNDHJszEAGRAjIJUaLMRszMwlaQGoSGxiYiXSXec/xh4cLd9il97HzHzz4M4dBnr+Bue0BPi0yZ3sMDs88k5zbBnTYYd5tDIYzDjC2G+DTIsHPA1TZxgzRwriNgXEDA2ObBH4t7A+AWurTQd4/+HMbgz1hLbwNBkAthxPAIQZ0WCJhLTxnQFqOGwIdBmRsk0iecZiglvTHn3nbquXl+w8+/vhzm41tf3v7M7xaMIxgIDp+RsEoGAWjYBTgBgAX50GGFKR2SwAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0001-8971-4090","institution":"Indian Institute of Technology (Indian School of Mines), Dhanbad","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Rabindra","middleName":"Kumar","lastName":"Sinha","suffix":""},{"id":71797159,"identity":"fa6175a0-18f4-479f-801c-4f02365bac4e","order_by":2,"name":"Phalguni Sen","email":"","orcid":"","institution":"Indian Institute of Technology (Indian School of Mines): Indian Institute of Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Phalguni","middleName":"","lastName":"Sen","suffix":""}],"badges":[],"createdAt":"2021-12-14 16:17:46","currentVersionCode":2,"declarations":"","doi":"10.21203/rs.3.rs-1171028/v2","doiUrl":"https://doi.org/10.21203/rs.3.rs-1171028/v2","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":16773692,"identity":"68c859dc-0ff0-49a3-bf50-19e3267a4c29","added_by":"auto","created_at":"2021-12-27 16:59:04","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1988833,"visible":true,"origin":"","legend":"","description":"","filename":"PROECOS2102655clean.pdf","url":"https://assets-eu.researchsquare.com/files/rs-1171028/v2_covered.pdf"}],"financialInterests":"","formattedTitle":"\u003cp\u003eA new global optimum solution model based on multi-value dynamic programming for the cut-off grade optimization in a surface mining complex\u003c/p\u003e","fulltext":[{"header":"Full Text","content":"This preprint is available for \u003ca href='/article/rs-1171028/latest.pdf' target='_blank'\u003edownload as a PDF\u003c/a\u003e."}],"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":false,"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":"Dynamic programming, global optimum model, cut-off grade (COG), surface mining, NPV maximization","lastPublishedDoi":"10.21203/rs.3.rs-1171028/v2","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-1171028/v2","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn techno-economic concern, cut-off grade (COG) optimization is the key for efficient mineral liquidation from the\u003c/p\u003e\u003cp\u003ehuge metalliferous surface mining sector. In this paper, a sequentially advancing algorithm based on discrete\u003c/p\u003e\u003cp\u003emulti-value dynamic programming (MDP) has been developed to calculate the global optimum COG of a\u003c/p\u003e\u003cp\u003elarge-scale open-pit metalliferous deposit. The proposed COG optimization algorithm aims to overcome the\u003c/p\u003e\u003cp\u003elimitations of straightforward classical techniques in determining the optimum COG. This discrete COG-MDP\u003c/p\u003e\u003cp\u003emodel is the first of its kind and has the novelty of dealing with the simulation of eight dynamic possibilities to\u003c/p\u003e\u003cp\u003eachieve the maximal global Net Present Value (NPV). A high-level programming language (Python) has been used\u003c/p\u003e\u003cp\u003eto develop the computer model to deal with the complexity of handling a minimum of 500 series of dynamic\u003c/p\u003e\u003cp\u003evariables. This model can generate results in polynomial-time from the complex of mining, milling, and smelting\u003c/p\u003e\u003cp\u003eand refining system corresponding to various limiting conditions. The prime objective considered in the model is\u003c/p\u003e\u003cp\u003eto optimize the COG of a metalliferous deposit. A working open-pit copper mining complex from India has been\u003c/p\u003e\u003cp\u003eused to validate the model. In this study, the optimum COG for the Malanjkhand copper deposit has been found to\u003c/p\u003e\u003cp\u003ebe (0.33%, 0.23%, 0.52%, 0.26%, 0.27%, 0.22%, 0.24%) with a maximum NPV of ₹ (12204, 14653, 16948, 14609,\u003c/p\u003e\u003cp\u003e21454, 26717, 38821) million corresponding to various scenarios. The findings also show that the present value\u003c/p\u003e\u003cp\u003egradually hits zero after the project’s life cycle, confirming the typical pattern of other mining firms.\u003c/p\u003e","manuscriptTitle":"A new global optimum solution model based on multi-value dynamic programming for the cut-off grade optimization in a surface mining complex","msid":"","msnumber":"","nonDraftVersions":[{"code":2,"date":"2021-12-27 16:58:47","doi":"10.21203/rs.3.rs-1171028/v2","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}},{"code":1,"date":"2021-12-22 01:55:13","doi":"10.21203/rs.3.rs-1171028/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"38fa3ef3-ccc3-4ce7-adcc-e8322c7d31bc","owner":[],"postedDate":"December 27th, 2021","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2021-12-22T01:55:14+00:00","versionOfRecord":[],"versionCreatedAt":"2021-12-27 16:58:47","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v2","identity":"rs-1171028","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-1171028","identity":"rs-1171028","version":["v2"]},"buildId":"FbvkV6FR0MCFSLy54lSbu","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}