Skip to main content

Optimizing Infill Drilling Decisions Using Multi-armed Bandits: Application in a Long-Term, Multi-element Stockpile

  • Chapter
  • First Online:
  • 1688 Accesses

Part of the book series: Quantitative Geology and Geostatistics ((QGAG,volume 19))

Abstract

Every mining operation faces a decision regarding additional drilling at some point during its lifetime. The two questions that always arise upon making this decision are whether more drilling is required and, if so, where the additional drill holes should be located. The method presented in this paper addresses both of these questions through an optimization in a multi-armed bandit (MAB) framework. The MAB optimizes for the best infill drilling pattern while taking geological uncertainty into account by using multiple conditional simulations for the deposit under consideration. MAB formulations are commonly used in many applications where decisions have to be made between different alternatives with stochastic outcomes, such as Internet advertising, clinical trials and others. The application of the proposed method to a long-term, multi-element stockpile, which is a part of a gold mining complex in Nevada, USA, demonstrates its practical aspects.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • Agrawal S, Goyal N (2012) Analysis of Thompson sampling for the multi-armed bandit problem. Proceedings of the 25th Annual Conference on Learning Theory (COLT)

    Google Scholar 

  • Barnes RJ (1989) Sample design for geological site characterization. In: Armstrong M (ed) Geostatistics 1988, vol 4. Springer Netherlands, Avignon, pp 809–822

    Chapter  Google Scholar 

  • Benndorf J (2015) Making use of online production data: sequential updating of mineral resource models. Math Geosci 47(5):547–563

    Article  Google Scholar 

  • Boucher A, Dimitrakopoulos R (2009) Block simulation of multiple correlated variables. Math Geosci 41(2):215–237

    Article  Google Scholar 

  • Boucher A, Dimitrakopoulos R, Vargas-Guzman JA (2005) Joint simulations, optimal drillhole spacing and the role of the stockpile. In: Leuangthong O, Deutsch C (eds) Geostatistics 2004, vol 14. Springer Netherlands, Banff, pp 35–44

    Chapter  Google Scholar 

  • Chorn LG, Carr PP (1997) The value of purchasing information to reduce risk in capital investments. SPE hydrocarbon economics and evaluation symposium. Society of Petroleum Engineers

    Google Scholar 

  • Desbarats AJ, Dimitrakopoulos R (2000) Geostatistical simulation of regionalized pore-size distributions using min/max autocorrelation factors. Math Geol 32(8):919–942

    Article  Google Scholar 

  • Diehl P, David M (1982) Classification of ore reserves/resources based on geostatistical methods. CIM Bull 75(838):127–136

    Google Scholar 

  • Gershon M, Allen LE, Manley G (1988) Application of a new approach for drillholes location optimization. Int J Surf Min Reclam Environ 2:27–31

    Article  Google Scholar 

  • Goovaerts P (1997) Geostatistics for natural resources evaluation. Oxford University Press, New York

    Google Scholar 

  • Goria S, Armstrong M, Galli A (2001) Quantifying the impact of additional drilling on an openpit gold project. 2001 annual conference of the IAMG. Cancun

    Google Scholar 

  • Jewbali A, Dimitrakopoulos R (2011) Implementation of conditional simulation by successive residuals. Comput Geosci 37(2):129–142

    Article  Google Scholar 

  • Mahajan A, Teneketzis D (2008) Multi-armed bandit problems. In: Hero A III, Castanon D, Cochran D, Kastella K (eds) Foundations and applications of sensor management. Springer, New York, pp 121–151

    Chapter  Google Scholar 

  • May BC, Korda N, Lee A, Leslie DS (2012) Optimistic Bayesian sampling in contextual-bandit problems. J Mach Learn Res 13(1):2069–2106

    Google Scholar 

  • Menabde M, Froyland G, Stone P, Yeates G (2007) Mining schedule optimisation for conditionally simulated orebodies. In Orebody modelling and strategic mine planning. p 379–384

    Google Scholar 

  • Prange M, Bailey WJ, Couet B, Djikpesse H, Armstrong M, Galli A, Wilkinson D (2008) Valuing future information under uncertainty using polynomial chaos. Decis Anal 5(3):140–156

    Article  Google Scholar 

  • Ravenscroft PJ (1992) Risk analysis of mine scheduling by conditional simulation. Trans Inst Min Metall Sect A 101:A104–A108

    Google Scholar 

  • Schlee E (1991) The value of perfect information in nonlinear utility theory. Theory Decis 30(2):127–131

    Article  Google Scholar 

  • Scott SL (2010) A modern Bayesian look at the multi-armed bandit. Appl Stoch Model Bus Ind 26(6):639–658

    Article  Google Scholar 

  • Switzer P, Green AA (1984) Min/max autocorrelation factors for multivariate spatial imagery. Stanford University, Department of Statistics, Standford

    Google Scholar 

  • Thompson WR (1933) On the likelihood that one unknown probability exceeds another in view of the evidence of two samples. Biometrika 25(3/4):285–294

    Article  Google Scholar 

Download references

Acknowledgements

We thank Newmont Mining Corporation for providing us with the data necessary to conduct this research and the organizations that funded this research: the Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant 239019 and the COSMO Mining Industry Consortium (AngloGold Ashanti, Barrick Gold, BHP Billiton, De Beers Canada, Kinross Gold, Newmont Mining and Vale) supporting the COSMO laboratory.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Rein Dirkx .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

Dirkx, R., Dimitrakopoulos, R. (2017). Optimizing Infill Drilling Decisions Using Multi-armed Bandits: Application in a Long-Term, Multi-element Stockpile. In: Gómez-Hernández, J., Rodrigo-Ilarri, J., Rodrigo-Clavero, M., Cassiraga, E., Vargas-Guzmán, J. (eds) Geostatistics Valencia 2016. Quantitative Geology and Geostatistics, vol 19. Springer, Cham. https://doi.org/10.1007/978-3-319-46819-8_13

Download citation

Publish with us

Policies and ethics