Meeting production targets in terms of ore quantity and quality is critical for a successful mining operation. In-situ grade variability and uncertainty about the spatial distribution of ore and quality parameter cause both deviations from production targets and general financial deficits. A stochastic integer programming formulation (SIP) is developed herein to integrate geological uncertainty described by sets of equally possible scenarios of the unknown orebody. The SIP formulation accounts not only for discounted cashflows and deviations from production targets, discounts geological risk, while accounting for practical mining. Application at an iron ore deposit in Western Australia shows the ability of the approach to control a risk of deviating from production targets over time. Comparison shows that the stochastically generated mine plan exhibits less risk in deviating from quality targets than the traditional mine planning approach based on a single interpolated orebody model.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
David, M., Geostatistical Ore Reserve Estimation, Amsterdam: Elsevier, 1977.
David, M., Handbook of Applied Advanced Geostatistical Ore Reserve Estimation, Amsterdam: Elsevier, 1988.
Goovaerts, P., Geostatistics for Natural Resources Evaluation, New York: Oxford University Press, 1997.
Rondon, O., Teaching Aid: Minimum/Maximum Autocorrelation Factors for Joint Simulation of Attributes, Mathematical Geosciences, 2012, vol. 44.
Dimitrakopoulos, R., Risk Analysis in Ore Reserves and Mine Planning: Conditional Simulation Concepts and Applications for the Mining Industry, AusIMM-McGill 2007 Professional Development Seminar Series, 2007.
Ravenscroft, J.P., Risk Analysis for Mine Scheduling by Conditional Simulation, Transactions of the Institute of Mining and Metallurgy, Section A, 1992, vol. 101.
Dowd, P.A., Risk in Minerals Projects: Analysis, Perception and Management, Transactions of the Institutions of Mining and Metallurgy, Section A: Mining Technology, 1997, vol. 106.
Dimitrakopoulos, R., Farrelly, C.T. and Godoy, M.C., Moving forward from Traditional Optimization: Grade Uncertainty and Risk Effects in Open-Pit Design, Transactions of the Institutions of Mining and Metallurgy, Section A: Mining Technology, 2002, vol. 111.
Godoy, M.C. and Dimitrakopoulos, R., Managing Risk and Waste Mining in Long-Term Production Scheduling, SME Transactions, 2004, vol. 316.
Leite, A. and Dimitrakopoulos, R., A Stochastic Optimization Model for Open Pit Mine Planning: Application and Risk Analysis at a Copper Deposit, IMM Transactions, Mining Technology, 2007, vol. 116.
Albor, F. and Dimitrakopoulos, R., Stochastic Mine Design Optimization Based on Simulated Annealing: Pit Limits, Production Schedules, Multiple Orebody Scenarios and Sensitivity Analysis, IMM Transactions, Mining Technology, 2009, vol. 118.
Birge, J.R. and Louveaux, F., Introduction to Stochastic Programming, New York: Springer-Verlag, 1997.
Ramazan, S. and Dimitrakopoulos, R., Production Scheduling with Uncertain Supply: A New Solution to the Open Pit Mining Problem, Optimization and Engineering, DOI 10.1007/s11081-012-9186-2, 2012.
Dimitrakopoulos, R., Stochastic Optimization for Strategic Mine Planning: A Decade of Developments, Journal of Mining Science, 2011, vol. 47, no. 2, pp. 138–150.
Albor, F. and Dimitrakopoulos, R., Algorithmic Approach to Pushback Design Based on Stochastic Programming: Method, Application and Comparisons, IMM Transactions, Mining Technology, 2010, vol. 119.
Lamghari, A. and Dimitrakopoulos, R., A Diversified Tabu Search Approach for the Open-Pit Mine Production Scheduling Problem with Metal Uncertainty, European Journal of Operational Research, 2012, vol. 222.
Asad, M.W.A. and Dimitrakopoulos, R., Implementing a Parametric Maximum Flow Algorithm for Optimal Open Pit Mine Design under Uncertain Supply and Demand,” Journal of the Operational Research Society, DOI:10.1057/jors.2012.26, 2012.
Whittle, G., Global Asset Optimization. Orebody Modeling and Strategic Mine Planning: Uncertainty and Risk Management Models, The Australian Institute of Mining and Metallurgy, Spectrum Series, 2nd Edition, 2007, vol. 14.
Goodfellow, R. and Dimitrakopoulos, R., Algorithmic Integration of Geological Uncertainty in Pushback Designs for Complex Multiprocess Open Pit Mines, IMM Transactions, Mining Technology, 2013, vol. 122.
Stone, P., Froyland, G., Menabde, M., Law, B., Pasyar, R., and Monkhouse, P., BLASOR-Blended Iron Ore Mine Planning Optimization at Yandi. Orebody Modeling and Strategic Mine Planning: Uncertainty and Risk Management Models, The Australian Institute of Mining and Metallurgy, Spectrum Series, 2nd Edition, 2007, vol. 14.
Dimitrakopoulos, R. and Ramazan, S., Uncertainty-Based Production Scheduling in Open Pit Mining, SME Transactions, 2004, vol. 316.
Boucher, A. and Dimitrakopoulos, R., Multivariate Block-Support Simulation of the Yandi Iron Ore Deposit, Western Australia, Mathematical Geosciences, 2012, vol. 44.
Benndorf, J., Efficient Sequential Simulation Methods with Implications on Long-Term Production Scheduling, Unpublished MPh. Thesis, Brisbane: The University of Queensland, 2005.
Original Russian Text © J. Benndorf, R. Dimitrakopoulos, 2013, published in Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, 2013, No. 1, pp. 79–94.
About this article
Cite this article
Benndorf, J., Dimitrakopoulos, R. Stochastic long-term production scheduling of iron ore deposits: Integrating joint multi-element geological uncertainty. J Min Sci 49, 68–81 (2013). https://doi.org/10.1134/S1062739149010097
- Open pit optimization
- stochastic simulation
- multi-element deposits
- iron ore