Authors: Malaki, S; Khodayari, F; Pourrahimian, Y; Liu, WV |

Malaki, S, Khodayari, F, Pourrahimian, Y & Liu, WV 2017, 'An application of mathematical programming and sequential Gaussian simulation for block cave production scheduling', in M Hudyma & Y Potvin (eds),

The current trend of deeper and lower-grade deposits makes open pit mining less profitable. Mass mining alternatives have to be developed if mining at a similar rate is to be continued. Block cave mining is becoming an increasingly popular mass mining method, especially for large copper deposits currently being mined with open pit methods. After finding the initial evaluation of a range of levels for starting the extraction of block cave mining, production scheduling plays a key role in the entire project’s profitability. Traditional long-term mine planning is based on deterministic orebody models, which can ignore the uncertainty in the geological resources. The purpose of this paper is to present a methodology to find the optimal extraction horizon and sequence of extraction for that horizon under grade uncertainty. The model does not explicitly take into account other potential project value drivers such as waste ingress into the draw column or the impact of primary or secondary fragmentation on either production or recovery. Maximum net present value (NPV) is determined using a mixed-integer linear programming (MILP) model after choosing the optimum horizon of extraction given some constraints such as mining capacity, production grade, extraction rate and precedence. Application of the method for block cave production scheduling using a case study over 15 periods is presented. Keywords: block caving, grade uncertainty, sequential Gaussian simulation, production scheduling

Albor Consuegra, FR & Dimitrakopoulos, R 2009, ‘Stochastic mine design optimisation based on simulated annealing: pit limits, production schedules, multiple orebody scebarios and sensitivity analysis’, Transactions of the Institution of Mining and Metallurgy, vol. 118, no. 2, pp. 80–91.

Asad, MWA & Dimitrakopoulos, R 2013, ‘Implementing a parametric maximum flow algorithm for optimal open pit mine design under uncertain supply and demand’, Journal of the Operational Research Society, vol. 64, no. 2, pp. 185–197.

Carpentier, S, Gamache, M & Dimitrakopoulos, R 2016, ‘Underground long-term mine production scheduling with integrated geological risk management’, Mining Technology: Transactions of the Institutions of Mining and Metallurgy: Section A, vol. 125, no. 2, pp. 93–102.

Chanda, ECK 1990, ‘An application of integer programming and simulation to production planning for a stratiform ore body’, Mining Science and Technology, vol. 11, no. 2, pp. 165–172.

Deutsch, CV & Journel, AG 1998, GSLIB: Geostatistical Software Library and User's Guide, Oxford University Press, New York.

Diering, T ‘Computational considerations for production scheduling of block cave mines’, in A Karzulovic & MA Alfaro (eds), Proceedings of the 4th International Conference and Exhibition on Mass Mining (MassMin 2004), Instituto de Ingenieros de Chile, Santiago, pp. 135–140.

Diering, T 2012, ‘Quadratic programming applications to block cave scheduling and cave management’, Proceedings of the 6th International Conference and Exhibition on Mass Mining (MassMin 2012), Canadian Institute of Mining, Metallurgy and Petroleum, Westmount, pp. 1–8.

Diering, T, Richter, O & Villa, D 2008, ‘Block cave production scheduling using PCBC’, in H Schunnesson & E Nordlund (eds), Proceedings of the 5th International Conference and Exhibition on Mass Mining (MassMin 2008), Luleå University of Technology, Luleå.

Dimitrakopoulos, R & Ramazan, S 2008, ‘Stochastic integer programming for optimising long term production schedules of open pit mines: methods, application and value of stochastic solutions’, Mining Technology: Transactions of the Institutions of Mining and Metallurgy: Section A, vol. 117, no. 4, pp. 155–160.

Dowd, PA 1994, ‘Risk assessment in reserve estimation and open-pit planning’, Transactions of the Institution of Mining and Metallurgy, vol. 103, pp. A148–A154.

Epstein, R, Goic, M, Weintraub, A, Catalán, J, Santibáñez, P, Urrutia, R, Cancino, R, Gaete, S, Aguayo, A & Caro, F 2012, ‘Optimising long-term production plans in underground and open-pit copper mines’, Operations Research, vol. 60, no. 1, pp. 4–17.

Grieco, N & Dimitrakopoulos, R 2007, ‘Managing grade risk stope design optimisation: Probabilistic mathematical programming model and application in sublevel stoping’, Mining Technology: Transactions of the Institutions of Mining and Metallurgy: Section A, vol. 116, no. 2, pp. 49–57.

Guest, AR, Van Hout, GJ & Von Johannides, A 2000, ‘An application of linear programming for block cave draw control’, Proceedings of MassMin 2000, The Australasian Institute of Mining and Metallurgy, Melbourne, pp. 461–468.

IBM 2015, IBM ILOG CPLEX, version 12.6.2, viewed 22 June 2017, http://www-01.ibm.com/support/docview.wss?uid=swg21959971

Khodayari, F & Pourrahimian, Y 2014, ‘Determination of the best height of draw in block cave sequence optimisation’, Proceedings of the 3rd International Symposium on Block and Sublevel Caving (Caving 2014), pp. 457–465.

Khodayari, F & Pourrahimian, Y 2015a, ‘Determination of development precedence for drawpoints in block-cave mining’, Proceedings of the 5th Aachen International Mining Symposia: Mineral Resources and Mine Development (AIMS 2015), pp. 383–391.

Khodayari, F & Pourrahimian, Y 2015b, ‘Mathematical programming applications in block-caving scheduling: A review of models and algorithms’, International Journal of Mining and Mineral Engineering, vol. 6, pp. 234–257.

Khodayari, F & Pourrahimian, Y 2016, ‘Quadratic programming application in block-cave mining’, Proceedings of the 1st International Conference of Underground Mining (U-Mining 2016), Universidad de Chile, Santiago, pp. 427–438.

Koushavand, B & Askari-Nasab, H 2009, ‘Transfer of geological uncertainty into mine planning’, in RK Singhal, A Mehrotra, K Fytas & H Ge (eds), Proceedings of the 18th International Symposium on Mine Planning and Equipment Selection (MPES 2009), Reading Matrix Inc., Calgary, pp. 462–476.

Lamghari, A & Dimitrakopoulos, R 2012, ‘A diversified Tabu search approach for open-pit mine production scheduling problem with metal uncertainty’, European Journal of Operational Research, vol. 222, no. 3, pp. 642–652.

Lamghari, A, Dimitrakopoulos, R & Ferland, J 2013, ‘A variable neighbourhood decent algorithm for the open-pit mine production scheduling problem with metal uncertainty’, Journal of the Operational Research Society, vol. 65, no. 9, pp. 1305–1314.

Leite, A & Dimitrakopoulos, R 2007, ‘Stochastic optimisation model for open-pit mine planning: application and risk analysis at a copper deposit’, Mining Technology: Transactions of the Institutions of Mining and Metallurgy: Section A, vol. 116, no. 3, pp. 109–118.

Lerchs, H & Grossmann, I 1965, ‘Optimum design of open-pit mines’, Canadian Mining Metallurgical Bulletin, vol. 58, pp. 17–24.

Maleki, M & Emery, X 2015, ‘Joint simulation of grade and rock type in a stratabound copper deposit’, Mathematical Geosciences, vol. 47, no. 4, pp. 471–495.

Montiel, L, Dimitrakopoulos, R & Kawahata, K 2015, ‘Globally optimising open-pit and underground mining operations under geological uncertainty’, Mining Technology: Transactions of the Institutions of Mining and Metallurgy: Section A, vol. 125, no. 1, pp. 2–14.

Osanloo, M, Gholamnejad, J & Karimi, B 2008, ‘Long-term open pit mine production planning: a review of models and algorithms’, International Journal of Mining, Reclamation and Environment, vol. 22, no. 1, pp. 3–35.

Parkinson, A 2012, Essays on Sequence Optimisation in Block Cave Mining and Inventory Policies with Two Delivery Sizes, PhD thesis, The University Of British Columbia, Vancouver.

Pourrahimian, Y 2013, Mathematical Programming for Sequence Optimisation in Block Cave Mining, PhD thesis, University of Alberta, Edmonton.

Pourrahimian, Y & Askari-Nasab, H 2014, ‘An application of mathematical programming to determine the best height of draw in blockcave sequence optimisation’, Mining Technology: Transactions of the Institution of Mining and Metallurgy Section A, vol. 123, no. 3, pp. 162–172.

Pourrahimian, Y, Askari-Nasab, H & Tannant, D 2013, ‘A multi-step approach for block-cave production scheduling optimisation’, International Journal of Mining Science and Technology, vol. 23, no. 5, pp. 739–750.

Rahal, D, Dudley, J & Hout, Gv 2008, ‘Developing an optimised production forecast at Northparkes E48 mine using MILP’, in H Schunnesson & E Nordlund (eds), Proceedings of the 5th International Conference and Exhibition on Mass Mining (MassMin 2008), Luleå University of Technology, Luleå, pp. 227–236.

Ramazan, S & Dimitrakopoulos, R 2004, ‘Traditional and new MIP models for production scheduling with in-situ grade variability’, International Journal of Surface Mining, Reclamation and Environment, vol. 18, no. 2, pp. 85–98.

Ramazan, S & Dimitrakopoulos, R 2013, ‘Production scheduling with uncertain supply: A new solution to the open-pit mining problem’, Optimisation and Engineering, vol. 14, no. 2, pp. 361–380.

Ravenscroft, P 1992, ‘Risk analysis for mine scheduling by conditional simulation’, Mining Technology: Transactions of the Institution of Mining and Metallurgy: Section A, vol. 101, pp. A104–A108.

Rubio, E 2002, Long Term Planning of Block Caving Operations Using Mathematical Programming Tools, Master’s thesis,

The University of British Columbia, Vancouver.

Rubio, E & Diering, T 2004, ‘Block cave production planning using operation research tool’, in A Karzulovic & MA Alfaro (eds), Proceedings of the 4th International Conference and Exhibition on Mass Mining (MassMin 2004), Instituto de Ingenieros de Chile, Santiago, pp. 141–149.

Sabour, SA & Dimitrakopoulos, R 2011, ‘Incorporating geological and market uncertainties and operational flexibility into open pit mine design’, Journal of Mining Science, vol. 47, no. 2, pp. 191–201.

Smoljanovic, M, Rubio, E & Morales, N 2011, ‘Panel caving scheduling under precedence constraints considering mining system’, Proceedings of the 35th International Symposium of Application of Computers and Operations Research in the Minerals Industry, The Australasian Institute of Mining and Metallurgy, Melbourne. pp. 407–417.

Song, X 1989, ‘Caving process simulation and optimal mining sequence at Tong Kuang Yu mine, China’, in A Weiss (ed.), Proceedings of the 21st Application of Computers and Operations Research in the Mineral Industry, Society of mining Engineering of the American Institute of Mining, Metallurgical, and Petroleum Engineers, Littleton, pp. 386–392.

The MathWorks, Inc. 2017, MATLAB, viewed 22 June 2017, https://au.mathworks.com/product/ltc/matlab.html

Vargas, E, Morales, N & Emery, X 2014, ‘Footprint and economic envelope calculation for block/panel caving mines under geological uncertainty’, Proceedings of the 3rd International Symposium on Block and Sublevel Caving (Caving 2014), pp. 449–456.

Weintraub, A, Pereira, M & Schultz, X 2008, ‘A priori and A posteriori aggregation procedures to reduce model size in MIP mine planning models’, Electronic Notes in Discrete Mathematics, vol. 30, pp. 297–302.

© Copyright 2019, Australian Centre for Geomechanics (ACG), The University of Western Australia. All rights reserved.

Please direct any queries to or error reports to repository-acg@uwa.edu.au

Please direct any queries to or error reports to repository-acg@uwa.edu.au