Abstract
Recent years have seen increasing efforts to incorporate risk and uncertainty into optimal and heuristic methods for mine planning and scheduling. The recent volatility in the prices of metals and minerals has provided further impetus for developing new methods that facilitate integrated optimization and risk analysis in mining. We consider a long-term problem of determining a plan for above- and underground mining, allowing for different ways in which the material can be extracted, such as choice of cutoff grade and mining speed. We develop a methodology based on a longest-path network framework that allows us to identify the mining plans that produce the k highest values of expected profit, where k can be chosen by the decision-maker. We couple this with a methodology for evaluating each of these plans with respect to various measures of risk, such as variance, probability of achieving a profit target, or conditional value-at-risk. The framework is easily extendible to other risk measures. The methodology provides a means to construct a set of Pareto-optimal solutions with expected profit and the selected risk measure as the two performance metrics. We illustrate our approach using a simple example in which the risk measure is value-at-risk (VaR).
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References
Abdel Sabour, S.A., & Poulin, R. 2010. Mine expansion decisions under uncertainty. International Journal of Mining, Reclamation and Environment, 24(4), 340–349.
Boland, N., Dumitrescu, I.,\& Froyland, G.. 2008. A multistage stochastic programming approach to open pit mine production scheduling with uncertain geology. Working paper, School of Mathematics and Physical Sciences, Australia: University of Newcastle
Chen, J., Gu, D., & Li, J. 2003. Optimization principle of combined surface and underground mining and its applications. Journal of the Central South University of Technology (China), 10(3), 222–225.
Chicoisne, R., Espinosa, M., Goycoolea, M., Moreno, E., & Rubio,E. 2011. A new algorithm for the open-pit mine scheduling problem. Operations Research, 60(1), 4–17.
Chiles, J.-P., & Delfiner, P. 2012. Geostatistics: Modeling spatial uncertainty, Second edition New York: Wiley Interscience.
Denby, B., & Schofield, D. 1995. Inclusion of risk assessment in open-pit design and scheduling. Transactions of the Institution of Mining and Metallurgy. Section A: Mining Industry. 104, A67–A71.
de Lara, M., Morales, N., & Beeker N. 2013. Adaptive strategies for the open-pit mine optimal scheduling problem. Working paper, Centre d’Enseignement et de Recherche en Mathematiques et Calcul Scientifique. France: Universite Paris-Est.
Deutsch, C. V., & Journel, A.G. 1998. GSLIB: Geostatistical software library and user’s guide, Second edition. New York: Oxford University Press.
Dimitrakoupoulos, R. 1998. Conditional simulation algorithms for modeling orebody uncertainty in open pit mines. International Journal of Surface Mining, Reclamation and Environment, 12, 173–179.
Dimitrakoupoulos, R., Martinez, L., & Ramazan S. 2007. Maximum upside / minimum downside approach to the traditional optimization of open pit mine designs. Journal of Mining Science, 43 (1), 73–82.
Dimitrakoupolos, R. 2011. Strategic mine planning under uncertainty. Journal of Mining Science, 47(2), 138–150.
Epstein, R., Goic, M., Weintraub, A., Catalan, J., Santibanez, P., Urrutia, R., Cancino, R., Gaete, S., Aguayo, A.,& Caro, F. 2010. Optimizing long-term production plans in underground and open pit copper mines. Operations Research 60(1), 4–17.
Golamnejad, J., Osanloo, M., & Karimi, B. 2006. A chance-constrained programming approach for open pit long-term production scheduling in stochastic environments. The Journal of the South African Institute of Mining and Metallurgy 106, 105–114.
Hershberger, J., Maxel, M., & Suri, S. 2007. Finding the k shortest simple paths: A new algorithm and its implementation. ACM Transactions on Algorithms, 3(4), 1–9.
Hustrulid, W.A. & Bullock, R.L. (eds). 2001. Underground mining methods: Engineering fundamentals and international case studies. Littleton, Colorado: Society for Mining, Metallurgy and Exploration.
Kumral, M. 2010. Robust stochastic mine production scheduling. Engineering Optimization, 42(6), 567–579.
Lemelin, B., Abdel Sabour, S.A., & Poulin, R. 2006. Valuing Mine 2 at Raglan using real options. International Journal of Mining, Reclamation and Environment, 20(1), 46–56.
Martinez, L.A. 2006. Strategic coal mining planning project using an integrated real options model approach. Proceedings of the Bowen Basin Symposium, McKay, Queensland, Australia, October 6–8, 2010.
Newman, A.M., Rubio, E., Caro, R., Weintraub A., & Eurek, K. 2010. A review of operations research in mine planning. Interfaces, 40(3), 222–246.
Newman, A.M., Yano, C.A., & Rubio, R. 2013. Mining above and below ground: Timing the transition. IIE Transactions 45 (8), 865–882.
Osanloo, M., Golamnejad, J., & Karimi B. 2007. Long-term open pit mine production planning: a review of models and algorithms. International Journal of Mining, Reclamation and Environment, 22(1), 1–33.
Ravenscroft, P.J. 1992. Risk analysis for mine scheduling by conditional simulation. Transactions of the Institution of Mining and Metallurgy Section A: Mining Industry 101, A104–A108.
Sarin, R., & West-Hansen, J. 2005. The long-term mine production scheduling problem. IIE Transactions, 37(2), 109–121.
Stacey, T.R., & Terbrugge,P.J. 2000. Open pit to underground–transition and interaction. Proceedings of the MassMin 2000 Conference, Brisbane, Queensland, Australia, 29 October–2 November 2000, 97–104
Topuz, E., & Duan, C. 1989. A survey of operations research applications in the mining industry. CIM Bulletin, 82(925), 48–50.
Visser, W.F., & Ding, B.2007. Optimization of the transition from open pit to underground mining. Proceedings of the International Mining Symposia 2007, Aachen University, Aachen, Germany, 30–31 May 2007, 131–148
Yen, J.Y. 1971. Finding the k shortest loopless paths in a network. Management Science, 17(11), 712–716.
Acknowledgement
This research was undertaken while the first author was a graduate student at the University of California, Berkeley. The first author gratefully acknowledges support from a fellowship from the National Sciences and Engineering Research Council of Canada.
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Yano, C., McFadden, C. (2014). Mine Planning Above and Below Ground: Generating a Set of Pareto-Optimal Schedules Considering Risk and Return. In: Pulat, P., Sarin, S., Uzsoy, R. (eds) Essays in Production, Project Planning and Scheduling. International Series in Operations Research & Management Science, vol 200. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-9056-2_14
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