Determination of optimised cut-off grade utilising non-linear programming
One of the most fundamental problems in a mining operation is how to recognise an optimum cut-off grade, which defines the grade for discriminating between ore and waste in an ore body, including ore that is extracted at different periods over a mine life period. Therefore, the identification of an...
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| Published in | Arabian journal of geosciences Vol. 8; no. 10; pp. 8963 - 8967 |
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| Main Authors | , , , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.10.2015
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1866-7511 1866-7538 |
| DOI | 10.1007/s12517-014-1756-5 |
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| Abstract | One of the most fundamental problems in a mining operation is how to recognise an optimum cut-off grade, which defines the grade for discriminating between ore and waste in an ore body, including ore that is extracted at different periods over a mine life period. Therefore, the identification of an optimised cut-off grade (COG) is a crucial function which has to be monitored during the mine life. The main aim of this study is to propose a modified optimum COG model in order to maximise the profit value (PV) for mining projects. Maximising the PV of a mining operation, which is a non-linear programming, is subject to different constraints involving a general grade distribution within a deposit and three stages of production namely mining, concentrating and refining. The proposed computer-based model is more effective in long-term planning of the open pit mines. To provide a better understanding of the algorithm efficiency, a numerical example is given and subsequently solved based on the Lane algorithm. In order to achieve this, the LINGO software was employed. |
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| AbstractList | One of the most fundamental problems in a mining operation is how to recognise an optimum cut-off grade, which defines the grade for discriminating between ore and waste in an ore body, including ore that is extracted at different periods over a mine life period. Therefore, the identification of an optimised cut-off grade (COG) is a crucial function which has to be monitored during the mine life. The main aim of this study is to propose a modified optimum COG model in order to maximise the profit value (PV) for mining projects. Maximising the PV of a mining operation, which is a non-linear programming, is subject to different constraints involving a general grade distribution within a deposit and three stages of production namely mining, concentrating and refining. The proposed computer-based model is more effective in long-term planning of the open pit mines. To provide a better understanding of the algorithm efficiency, a numerical example is given and subsequently solved based on the Lane algorithm. In order to achieve this, the LINGO software was employed. |
| Author | Asadi, Ahmad Wetherelt, Andy Kennedy, Gareth Afzal, Peyman Foster, Patrick Yasrebi, Amir Bijan Kaveh Ahangaran, Dariush |
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| Cites_doi | 10.1201/9781439833407.pt5 10.1016/j.resourpol.2004.06.002 10.1108/02644400710817961 10.1016/S0892-6875(03)00163-8 10.1007/s12517-010-0275-2 10.1016/j.eswa.2008.09.018 10.1080/13895260500258661 10.1016/j.resourpol.2008.06.001 10.1023/A:1018958209290 10.1016/j.ejor.2010.12.008 10.1016/j.ejor.2012.01.012 |
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| Keywords | Lane algorithm Profit value (PV) Cut-off grade (COG) Non-linear programming |
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| References | CairnsRDShinkumaTThe choice of the cut-off grade in miningResour Policy200329758110.1016/j.resourpol.2004.06.002 BascetinADetermination of optimal cut-off grade policy to optimize NPV using a new approach with optimization factorJ S Afr Inst Min Metall20071078794 Dagdelen K, Kawahata K, Eduardo J, M. eds. (2007) Opportunities in multi-mine planning through large scale mixed integer programming optimisation. Proceeding of 33rd International Symposium on the Application of Computers and Operations Research in the Mineral Industry (APCOM). Santiago, University of Chile ParhizkarAAtaeiMMoarefvandPRasouliVA probabilistic model to improve reconciliation of estimated and actual grade in open-pit miningArab J Geosci201251279128810.1007/s12517-010-0275-2 Cetin E, Dowd P A, Sukumar B, eds. (2002) The use of genetic algorithms for multiple cut-off grade optimization. Proceeding of 30th International Symposium on the Application of Computers and Operations Research in the Mineral Industry (APCOM). Littleton, The Society for Mining, Metallurgy, and Exploration, 769–780 p LaneKFChoosing the optimum cut-off grade1964GoldenQuarterly of the Colorado School of Mines811829 YasrebiABWethereltAFosterPAfzalPEskikayaŞDetermination and analysis of final pit limit of Esfordi phosphate open pit mine. Proceeding of 22nd World Mining Congress and Expo2011IstanbulAydoğdu Ofset513522 YingliangXSunFOptimization of cut-off grade in open-pit based on control theory. Proceeding of 5th international symposium on neural networks2008BeijingSpringer589597 Akaike A, Dagdelen K (1999) A strategic production scheduling method for an open pit mine. Proceeding of the 28th APCOM. Golden, Colorado, 729–738 p Asad M W A, Dessureault S, et al. eds. (2005a) Cut-off grade optimisation algorithm for open pit mining operations with consideration of dynamic metal price and cost escalation during mine life. Proceeding of 32nd international symposium on the Application of Computers and Operations Research in the Mineral Industry (APCOM), Tucson, A.A. Balkema Publishers, 273–277 p AsadMWACut-off grade optimization algorithm with stockpiling option for open pit mining operations of two economic mineralsInt J Surf Min Reclam Environ20051917618710.1080/13895260500258661 LaneKFThe economic definition of ore-cut-off grades in theory and practice1988LondonMining Journal Books Limited145 SinghGSierDErnstATGavrilioukOOystonRGilesTWelgamaPAMixed integer programming model for long term capacity expansion planning: a case study from The Hunter Valley Coal ChainEur J Oper Res201222021022410.1016/j.ejor.2012.01.012 MartinezMANewmanAMA solution approach for optimizing long- and short-term production scheduling at LKAB’s Kiruna mineEur J Oper Res201121118419710.1016/j.ejor.2010.12.008 AzimiYOsanlooMDetermination of open pit mining cut-off grade strategy using combination of nonlinear programming and genetic algorithmArch Min Sci201156189212 DowdPAApplication of dynamic and stochastic programming to optimize cut-off grades and production ratesMin Technol IMM Trans Sect A1976852231 OsanlooMRashidinejadFRezaiBIncorporating environmental issues into optimum cut-off grades modeling at porphyry copper depositsResour Policy20083322222910.1016/j.resourpol.2008.06.001 AsadMWAOptimum cut-off grade policy for open pit mining operations through net present value algorithm considering metal price and cost escalationEng Comput (Swansea, Wales)20072472373610.1108/02644400710817961 HustrulidWAKuchtaMOpen pit mine planning and design20062LondonTaylor & Francis PendharkarPRodgerJNon-linear programming and genetic search application for production scheduling in coal minesAnn Oper Res20002325126710.1023/A:1018958209290 HeYZhuKGaoSLiuTLiYTheory and method of genetic-neural optimizing cut-off grade and grade of crude oreExp Syst Appl2009367617762310.1016/j.eswa.2008.09.018 AzimiYOsanlooMEsfahanipourASelection of the open pit mining cut-off grade strategy under price uncertainty using a risk based multi-criteria ranking systemArch Min Sci201257741768 OsanlooMAtaeiMUsing equivalent grade factors to find the optimum cut-off grades of multiple metal depositsMiner Eng20031677177610.1016/S0892-6875(03)00163-8 1756_CR10 MWA Asad (1756_CR4) 2007; 24 PA Dowd (1756_CR11) 1976; 85 KF Lane (1756_CR15) 1988 MWA Asad (1756_CR3) 2005; 19 G Singh (1756_CR21) 2012; 220 (1756_CR23) 2008 M Osanloo (1756_CR18) 2008; 33 1756_CR1 Y Azimi (1756_CR5) 2011; 56 1756_CR2 A Parhizkar (1756_CR19) 2012; 5 RD Cairns (1756_CR9) 2003; 29 Y Azimi (1756_CR6) 2012; 57 1756_CR8 A Bascetin (1756_CR7) 2007; 107 WA Hustrulid (1756_CR13) 2006 Y He (1756_CR12) 2009; 36 MA Martinez (1756_CR16) 2011; 211 (1756_CR22) 2011 P Pendharkar (1756_CR20) 2000; 23 KF Lane (1756_CR14) 1964 M Osanloo (1756_CR17) 2003; 16 |
| References_xml | – reference: SinghGSierDErnstATGavrilioukOOystonRGilesTWelgamaPAMixed integer programming model for long term capacity expansion planning: a case study from The Hunter Valley Coal ChainEur J Oper Res201222021022410.1016/j.ejor.2012.01.012 – reference: CairnsRDShinkumaTThe choice of the cut-off grade in miningResour Policy200329758110.1016/j.resourpol.2004.06.002 – reference: Akaike A, Dagdelen K (1999) A strategic production scheduling method for an open pit mine. Proceeding of the 28th APCOM. Golden, Colorado, 729–738 p – reference: Cetin E, Dowd P A, Sukumar B, eds. (2002) The use of genetic algorithms for multiple cut-off grade optimization. Proceeding of 30th International Symposium on the Application of Computers and Operations Research in the Mineral Industry (APCOM). Littleton, The Society for Mining, Metallurgy, and Exploration, 769–780 p – reference: Asad M W A, Dessureault S, et al. eds. (2005a) Cut-off grade optimisation algorithm for open pit mining operations with consideration of dynamic metal price and cost escalation during mine life. Proceeding of 32nd international symposium on the Application of Computers and Operations Research in the Mineral Industry (APCOM), Tucson, A.A. Balkema Publishers, 273–277 p – reference: ParhizkarAAtaeiMMoarefvandPRasouliVA probabilistic model to improve reconciliation of estimated and actual grade in open-pit miningArab J Geosci201251279128810.1007/s12517-010-0275-2 – reference: AzimiYOsanlooMEsfahanipourASelection of the open pit mining cut-off grade strategy under price uncertainty using a risk based multi-criteria ranking systemArch Min Sci201257741768 – reference: OsanlooMRashidinejadFRezaiBIncorporating environmental issues into optimum cut-off grades modeling at porphyry copper depositsResour Policy20083322222910.1016/j.resourpol.2008.06.001 – reference: YasrebiABWethereltAFosterPAfzalPEskikayaŞDetermination and analysis of final pit limit of Esfordi phosphate open pit mine. Proceeding of 22nd World Mining Congress and Expo2011IstanbulAydoğdu Ofset513522 – reference: YingliangXSunFOptimization of cut-off grade in open-pit based on control theory. Proceeding of 5th international symposium on neural networks2008BeijingSpringer589597 – reference: LaneKFChoosing the optimum cut-off grade1964GoldenQuarterly of the Colorado School of Mines811829 – reference: AsadMWAOptimum cut-off grade policy for open pit mining operations through net present value algorithm considering metal price and cost escalationEng Comput (Swansea, Wales)20072472373610.1108/02644400710817961 – reference: LaneKFThe economic definition of ore-cut-off grades in theory and practice1988LondonMining Journal Books Limited145 – reference: BascetinADetermination of optimal cut-off grade policy to optimize NPV using a new approach with optimization factorJ S Afr Inst Min Metall20071078794 – reference: DowdPAApplication of dynamic and stochastic programming to optimize cut-off grades and production ratesMin Technol IMM Trans Sect A1976852231 – reference: MartinezMANewmanAMA solution approach for optimizing long- and short-term production scheduling at LKAB’s Kiruna mineEur J Oper Res201121118419710.1016/j.ejor.2010.12.008 – reference: AsadMWACut-off grade optimization algorithm with stockpiling option for open pit mining operations of two economic mineralsInt J Surf Min Reclam Environ20051917618710.1080/13895260500258661 – reference: PendharkarPRodgerJNon-linear programming and genetic search application for production scheduling in coal minesAnn Oper Res20002325126710.1023/A:1018958209290 – reference: AzimiYOsanlooMDetermination of open pit mining cut-off grade strategy using combination of nonlinear programming and genetic algorithmArch Min Sci201156189212 – reference: Dagdelen K, Kawahata K, Eduardo J, M. eds. (2007) Opportunities in multi-mine planning through large scale mixed integer programming optimisation. Proceeding of 33rd International Symposium on the Application of Computers and Operations Research in the Mineral Industry (APCOM). Santiago, University of Chile – reference: HustrulidWAKuchtaMOpen pit mine planning and design20062LondonTaylor & Francis – reference: HeYZhuKGaoSLiuTLiYTheory and method of genetic-neural optimizing cut-off grade and grade of crude oreExp Syst Appl2009367617762310.1016/j.eswa.2008.09.018 – reference: OsanlooMAtaeiMUsing equivalent grade factors to find the optimum cut-off grades of multiple metal depositsMiner Eng20031677177610.1016/S0892-6875(03)00163-8 – ident: 1756_CR2 doi: 10.1201/9781439833407.pt5 – ident: 1756_CR1 – volume: 29 start-page: 75 year: 2003 ident: 1756_CR9 publication-title: Resour Policy doi: 10.1016/j.resourpol.2004.06.002 – volume-title: Open pit mine planning and design year: 2006 ident: 1756_CR13 – volume: 24 start-page: 723 year: 2007 ident: 1756_CR4 publication-title: Eng Comput (Swansea, Wales) doi: 10.1108/02644400710817961 – volume: 16 start-page: 771 year: 2003 ident: 1756_CR17 publication-title: Miner Eng doi: 10.1016/S0892-6875(03)00163-8 – volume: 85 start-page: 22 year: 1976 ident: 1756_CR11 publication-title: Min Technol IMM Trans Sect A – start-page: 513 volume-title: Determination and analysis of final pit limit of Esfordi phosphate open pit mine. Proceeding of 22nd World Mining Congress and Expo year: 2011 ident: 1756_CR22 – start-page: 589 volume-title: Optimization of cut-off grade in open-pit based on control theory. Proceeding of 5th international symposium on neural networks year: 2008 ident: 1756_CR23 – volume: 5 start-page: 1279 year: 2012 ident: 1756_CR19 publication-title: Arab J Geosci doi: 10.1007/s12517-010-0275-2 – volume: 57 start-page: 741 year: 2012 ident: 1756_CR6 publication-title: Arch Min Sci – volume: 56 start-page: 189 year: 2011 ident: 1756_CR5 publication-title: Arch Min Sci – volume: 107 start-page: 87 year: 2007 ident: 1756_CR7 publication-title: J S Afr Inst Min Metall – start-page: 145 volume-title: The economic definition of ore-cut-off grades in theory and practice year: 1988 ident: 1756_CR15 – volume: 36 start-page: 7617 year: 2009 ident: 1756_CR12 publication-title: Exp Syst Appl doi: 10.1016/j.eswa.2008.09.018 – ident: 1756_CR8 – volume: 19 start-page: 176 year: 2005 ident: 1756_CR3 publication-title: Int J Surf Min Reclam Environ doi: 10.1080/13895260500258661 – ident: 1756_CR10 – volume: 33 start-page: 222 year: 2008 ident: 1756_CR18 publication-title: Resour Policy doi: 10.1016/j.resourpol.2008.06.001 – volume: 23 start-page: 251 year: 2000 ident: 1756_CR20 publication-title: Ann Oper Res doi: 10.1023/A:1018958209290 – start-page: 811 volume-title: Choosing the optimum cut-off grade year: 1964 ident: 1756_CR14 – volume: 211 start-page: 184 year: 2011 ident: 1756_CR16 publication-title: Eur J Oper Res doi: 10.1016/j.ejor.2010.12.008 – volume: 220 start-page: 210 year: 2012 ident: 1756_CR21 publication-title: Eur J Oper Res doi: 10.1016/j.ejor.2012.01.012 |
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| Title | Determination of optimised cut-off grade utilising non-linear programming |
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