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Assessment of costs in cut-off grades optimizationby using grid search method

Cetin Erhan
Gospodarka Surowcami Mineralnymi - Mineral Resources Management | 2018 | vol. 34 | No 2 | DOI: 10.24425/118650
Keywords cut-off grades optimization grid search rehabilitation cost depletion rate
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Abstract

The optimization of cut-off grades is a fundamental issue for metallic ore deposits. The cut-off grade is used to classify the material as ore or waste. Due to the time value of money, in order to achieve the maximum net present value, an optimum schedules of cut-off grades must be used. The depletion rate is the rate of depletion of a mineral deposit. Variable mining costs are to be applied to the really excavated material, as some of the depletion can be left in-situ. Due to access constraints, some of the blocks that have an average grade less than the determined cut-off grade are left in-situ, some of them are excavated and dumped as waste material. Naturally, variable mining costs should be applied to the blocks of a mineral deposit that are actually excavated. The probability density function of an exponential distribution is used to find the portion of the depletion rate over the production rate that is to be left in-situ. As a result, inverse probability density function is to be applied as the portion of the depletion rate over the production rate that is to be excavated and dumped. The parts of a mineral deposit that are excavated but will be dumped as waste material incur some additional cost of rehabilitation that is to be included in the algorithm of the cut-off grades optimization. This paper describes the general problem of cut-off grades optimization and outlines the further extension of the method including various depletion rates and variable rehabilitation cost. The author introduces the general background of the use of grid search in cut-off grades optimization by using various depletion rates and variable rehabilitation cost. The software developed in this subject is checked by means of a case study.
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Authors and Affiliations

Cetin Erhan

The optimization of cut-off grades by means of memetic algorithms

Erhan Cetin Abdurrahman Dalgic
Gospodarka Surowcami Mineralnymi - Mineral Resources Management | 2022 | vol. 38 | No 1 | 107-122 | DOI: 10.24425/gsm.2022.140607
Keywords memetic algorithms optimization cut-off grades depletion rate rehabilitation cost
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Abstract

Cut-off grades optimization is a fundamental issue for mineral deposits. A cut-off grade is any grade that is used to separate two courses of action; to mine or not to mine, to process or to dump. In order to achieve the maximum discounted cash flow, generally a decreasing order of cut-off grades schedule takes place. Variable mining costs are applied to the extracted material, not to all of the depletion rate as some of the depletion can be left in-situ. B ecause of access constraints, some of the blocks that have an average grade less than the determined cut-off grade are left in-situ, some of them are excavated and dumped as waste material. The probability density function of an exponential distribution is used to find the portion of the material below the cut-off used that is left in situ. The parts of a mineral deposit that are excavated but will be dumped as waste material and tailings of ore incur some additional cost of rehabilitation. The method of memetic algorithms is a very robust optimization tool. It is a step further from the genetic algorithms. The crossover, mutation and natural selection behavior of the method ensures it escape from a local optimum point, and a further local search improves the optimum further. This paper describes the general problem of cut-off grades optimization, outlines the use of memetic algorithms in cut-off grades optimization and further extension of the method including partial depletion rates and variable rehabilitation cost. This paper is the first application of memetic algorithms to cut-off grades optimization in this context.
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Bibliography

Cetin, E . 2016. Cut-off grades optimization by means of memetic algorithms with uncertain market conditions. Middle East Journal of Technic 1(1).
Cetin, E . and Dowd, P. A. 2002. The use of genetic algorithms for multiple cut-off grade optimisation. Proceedings of the 30th International Symposium on the Application of Computers and Operations Research in the Minerals Industries, Littleton, Colorado, USA.
Cetin, E . and Dowd, P.A. 2016. M ultiple cut-off grade optimization by genetic algorithms and comparison with grid search method and dynamic programming. The Journal of the South African Institute of Mining and Metallurgy 116(7), pp. 681–688, DOI: 10.17159/2411-9717/2016/v116n7a10.
Dowd, P.A. 1976. Application of dynamic and stochastic programming to optimise cut-off grades and production rates. Transactions of the Institution of Mining and Metallurgy Section A: Mining Industry 81. pp. 160–179.
Dawkins, R. 1976. The Selfish Gene, Oxford University Press.
Garg, P. 2009. A Comparison between Memetic algorithm and Genetic algorithm for the Cryptanalysis of Simplified Data Encryption Standard Algorithm. International Journal of Network Security & Its Applications (IJNSA), 1(1), pp. 34–42.
Gholamnejad, J. 2008. Determination of the optimum cutoff grade considering environmental cost. Journal of International Environmental Application and Science 3(3), pp. 186-194.
Gholamnejad, J. 2009. Incorporation of rehabilitation cost into the optimum cut-off grade determination. The Journal of the South African Institute of Mining and Metallurgy 109(2), pp. 89–94.
Holland, J.H. 1975. Adaptation in N atural and Artificial Systems. University of Michigan Press, USA.
Lane, K.F. 1964. Choosing the optimum cutoff grade. Colorado School of Mines Quarterly 59(4), pp. 811–829.
Lane, K.F. 1988. The Economic Definition of Ore. Mining Journals Books Ltd., L ondon, UK.
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Authors and Affiliations

Erhan Cetin
1
ORCID: ORCID
Abdurrahman Dalgic
2
  1. Dicle University, Diyarbakır, Turkey
  2. Alanya Alaaddin Keykubat University, Alanya, Turkey

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