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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
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
Asad MWA (2005) Cut-off grade optimization algorithm with stockpiling option for open pit mining operations of two economic minerals. Int J Surf Min Reclam Environ 19:176–187
Asad MWA (2007) Optimum cut-off grade policy for open pit mining operations through net present value algorithm considering metal price and cost escalation. Eng Comput (Swansea, Wales) 24:723–736
Azimi Y, Osanloo M (2011) Determination of open pit mining cut-off grade strategy using combination of nonlinear programming and genetic algorithm. Arch Min Sci 56:189–212
Azimi Y, Osanloo M, Esfahanipour A (2012) Selection of the open pit mining cut-off grade strategy under price uncertainty using a risk based multi-criteria ranking system. Arch Min Sci 57:741–768
Bascetin A (2007) Determination of optimal cut-off grade policy to optimize NPV using a new approach with optimization factor. J S Afr Inst Min Metall 107:87–94
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
Cairns RD, Shinkuma T (2003) The choice of the cut-off grade in mining. Resour Policy 29:75–81
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
Dowd PA (1976) Application of dynamic and stochastic programming to optimize cut-off grades and production rates. Min Technol IMM Trans Sect A 85:22–31
He Y, Zhu K, Gao S, Liu T, Li Y (2009) Theory and method of genetic-neural optimizing cut-off grade and grade of crude ore. Exp Syst Appl 36:7617–7623
Hustrulid WA, Kuchta M (2006) Open pit mine planning and design, 2nd edn. Taylor & Francis, London
Lane KF (1964) Choosing the optimum cut-off grade. Quarterly of the Colorado School of Mines, Golden, pp 811–829
Lane KF (1988) The economic definition of ore-cut-off grades in theory and practice. Mining Journal Books Limited, London, p 145
Martinez MA, Newman AM (2011) A solution approach for optimizing long- and short-term production scheduling at LKAB’s Kiruna mine. Eur J Oper Res 211:184–197
Osanloo M, Ataei M (2003) Using equivalent grade factors to find the optimum cut-off grades of multiple metal deposits. Miner Eng 16:771–776
Osanloo M, Rashidinejad F, Rezai B (2008) Incorporating environmental issues into optimum cut-off grades modeling at porphyry copper deposits. Resour Policy 33:222–229
Parhizkar A, Ataei M, Moarefvand P, Rasouli V (2012) A probabilistic model to improve reconciliation of estimated and actual grade in open-pit mining. Arab J Geosci 5:1279–1288
Pendharkar P, Rodger J (2000) Non-linear programming and genetic search application for production scheduling in coal mines. Ann Oper Res 23:251–267
Singh G, Sier D, Ernst AT, Gavriliouk O, Oyston R, Giles T, Welgama PA (2012) Mixed integer programming model for long term capacity expansion planning: a case study from The Hunter Valley Coal Chain. Eur J Oper Res 220:210–224
Yasrebi AB, Wetherelt A, Foster P, Afzal P, Eskikaya Ş (eds) (2011) Determination and analysis of final pit limit of Esfordi phosphate open pit mine. Proceeding of 22nd World Mining Congress and Expo. Aydoğdu Ofset, Istanbul, pp 513–522
Yingliang X, Sun F et al (eds) (2008) Optimization of cut-off grade in open-pit based on control theory. Proceeding of 5th international symposium on neural networks. Springer, Beijing, pp 589–597
Acknowledgments
The authors are hugely thankful to the Institute of Materials, Minerals and Mining (IOM3) for its financial support in order to conduct this research.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yasrebi, A.B., Wetherelt, A., Foster, P. et al. Determination of optimised cut-off grade utilising non-linear programming. Arab J Geosci 8, 8963–8967 (2015). https://doi.org/10.1007/s12517-014-1756-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12517-014-1756-5