Choosing the Optimum Underground Mine Layout with Regard to Metal Price Uncertainty Using Expected Utility Theory

Document Type : Original Article

Authors

Department of Mining and Metallurgical Engineering, Amirkabir University of Technology, Tehran, Iran

Abstract

Metal price is one of the most important parameters in the calculation of cut- off grade. The cut- off grade has the main role in determination of mine layout. Mine layout actuates mineable reserve, mine life and economic profitability. Not considering the uncertainty in metal prices can lead to a non-optimal layout. In this paper optimum underground mine layout is determined by expected utility theory with regard to metal price uncertainty. With the proposed approach metal price uncertainty is modeled by Monte Carlo simulation technique and decision maker will be gained probability of underground mine layouts. The utility function of underground mine layouts is defined and by the probability of them, expected utility is determined. Underground mine layout with the maximum expected utility is the optimum layout. Application of this approach in a hypothetical gold mine, in addition to considering metal price uncertainty, leads to 14% more mineable reserve and 18% higher net present value than normal design.

Keywords


1. Rendu, J. M., “Reporting Mineral Resources and Mineral
Reserves in the United States of America”, Technical and 
Regulatory Issues, In Proceedings, Sixth International Mining
Geology Conference: Australasian Institute of Mining and
Metallurgy, (2006), 11–20.  
2. Riddle, J. M., “A dynamic programming solution of a blockcaving
mine layout”, In Proceedings The 14th APCOM
Symposium, Society of Mining Engineers-American Institute
of Mining, Metallurgy, and Petroleum Engineers, New York,
(1977), 767–780.  
3. Alford, C., Brazil, M. and Lee, D.H., “Optimisation in
underground mining”, In Handbook of operations research in
natural resources, Springer, (2007). 
4. Ataee-Pour, M., “A heuristic algorithm to optimise stope
boundaries”, PhD Thesis, University of Wollongong,
Australia, (2000). 
5. Jalali, S.E. and Ataee-pour, M., “A 2D dynamic programming
algorithm to optimize stope boundaries”, In 2004 Proceedings
of the 13th symposium on Mine Planning and Equipment
Selection, Poland, (2004), 45–52.  
6. Dimitrakopoulos, R. and Grieco, N., “Stope design and
geological uncertainty: quantification of risk in conventional
designs and a probabilistic alternative”, Journal of Mining
Science, Vol. 45, No. 2, (2009), 152–163.  
7. Topal, E. and Sens, J., “A new algorithm for stope boundary
optimization”, Journal of Coal Science and Engineering,
Vol. 16, No. 2, (2010), 113–119.  
8. Little, J., “Simultaneous optimisation of stope layouts and 
production schedules for long-term underground mine
planning”, PhD Thesis, University of Queensland, Australia,
(2012). 
9. Bai, X., “Optimization of underground stope with network
flow method”, PhD Thesis, University of Montreal, Canada,
(2013). 
10. Sandanayake, D.S.S., Topal, E. and Asad, M. W. A., “A
heuristic approach to optimal design of an underground mine
stope layout”, Applied Soft Computing, Vol. 30, (2015), 595–
603.  
11. Ataee-Pour, M., “A critical survey of the existing stope layout
optimization techniques”, Journal of Mining Science, Vol.
41, No. 5, (2015), 447–466.  
12. Nhleko, A.S., Tholana, T. and Neingo, P. N., “A review of
underground stope boundary optimization algorithms”,
Resources Policy, Vol. 56, (2018), 59–69.  
13. Castillo, F.D. and Dimitrakopoulos, R., “Joint effect of
commodity price and geological uncertainty over the life of
mine and ultimate pit limit”, Mining Technology, Vol. 123,
No. 4, (2014), 207–219.  
14. Baek, J., Choi, Y. and Park, H. S., “Uncertainty representation
method for open pit optimization results due to variation in
mineral prices”, Minerals, Vol. 6, No. 17, (2016), 1–15.  
15. Sabour, S.A. and Dimitrakopoulos, R., “Incorporating
geological and market uncertainties and operational flexibility
into open pit mine design”, Journal of Mining Science, Vol.
47, No. 2, (2011), 191–201.  
16. Wellmer, F.W. and Hagelüken, C., “The feedback control
cycle of mineral supply, increase of raw material efficiency,
and sustainable development”, Minerals, Vol. 5, No. 4,
(2015), 815–836. 
17. McIsaac, G. and Pelley, C., “Strategic design of an
underground mine under conditions of metal price
uncertainty”, PhD Thesis, Queen’s University, Canada, (2008). 
18. Alonso-Ayuso, A., Carvallo, F., Escudero, L.F., Guignard, M.,
Pi, J., Puranmalka, R. and Weintraub, A., “Medium range
optimization of copper extraction planning under uncertainty
in future copper prices”, European Journal of Operational
Research, Vol. 233, No. 3, (2014), 711–726.  
19. Salama, A., Nehring, M. and Greberg, J., “Evaluation of the
impact of commodity price change on mine plan of
underground mining”, International Journal of Mining
Science and Technology, Vol. 25, No. 3, (2015), 375–382.  
20. Winston, W.L. and Goldberg, J.B., Operations research:
applications and algorithms (Vol. 3), Belmont, CA: Duxbury
Press, (2004). 
21. Rendu, J.M., An introduction to cut-off grade estimation,
Society for Mining, Metallurgy and Exploration, (2014). 
22. Computer Aided Engineering (CAE), Datamine Studio 3,
User’s Manual, MRO help. 
23. Von Neumann, J. and Morgenstern, O., “Theory of games and
economic behavior”, Princeton University, United States, (1947). 
24. Adam, F., Encyclopedia of decision making and decision
support technologies (Vol. 2), IGI Global, (2008). 
25. Gold price, Available online: https://goldprice.org/.