Authors: Nezhadshahmohammad, F; Khodayari, F; Pourrahimian, Y |

Nezhadshahmohammad, F, Khodayari, F & Pourrahimian, Y 2017, 'Draw rate optimisation in block cave production scheduling using mathematical programming', in M Hudyma & Y Potvin (eds),

Among the underground mining methods available, caving methods are favoured because of their low cost and high production rates. Block caving operations offer a much smaller environmental footprint compared to equivalent open pit operations due to the much smaller volume of waste to be moved and handled. In general, draw control is fundamental to success or failure of any block cave operation. Establishing relationships among draw columns to consider depletion rates of other draw columns is complex but essential to provide a reasonable solution for real block caving mines. This paper presents a mixed-integer linear programming (MILP) model to optimise the extraction sequence of drawpoints over multiple time horizons of block cave mines with respect to draw control systems. A mathematical draw rate strategy is formulated in this paper to guarantee exact solutions. Draw control management provides optimal operating strategies while meeting practical, technical and environmental constraints. Furthermore, dilution and caving are improved indirectly, because the method considers the draw rate strategy according to geotechnical properties of the rock mass. Surface displacements are controlled by using the draw rate in all drawpoints during the life of the mine. Application and verification of the presented model for production scheduling based on the draw control system are presented using a case study. Keywords: block caving, draw rate, optimisation, mixed-integer linear programming

Alonso-Ayuso, A, Carvallo, F, Escudero, LF, Guignard, M, Pi, J, Puranmalka, R & Weintraub, A 2014, ‘Medium range optimisation of copper extraction planning under uncertainty in future copper prices’, European Journal of Operational Research, vol. 233, no. 3, pp. 711–726.

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.

Charles, AB, Gordon, KC & Timothy, PC 2011, Block Caving, Society for Mining, Metallurgy & Exploration, Englewood.

Deiring, T 2004a, ‘Combining long term scheduling and daily draw control for block cave mines’, in A Karzulovic & MA Alfaro (eds), Proceedings of MassMin 2004, Instituto de Ingenieros de Chile, Santiago, pp. 486–490.

Diering, T 2004b, ‘Computational considerations for production scheduling of block cave mines’, in A Karzulovic & MA Alfaro (eds), Proceedings of MassMin 2004, Instituto de Ingenieros de Chile, Santiago, pp. 135–140.

Epstein, R, Goic, M, Weintraub, A, Catalán, J, Santibáñez, P, Rodolfo Urrutia, R, Cancino, R, Sergio 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.

Flores, G 2014, ‘Future challenges and why cave mining must change’, in R Castro (ed.), Proceedings of the 3rd International Symposium on Block and Sublevel Caving, Universidad de Chile Santiago, Chile, pp. 23-52.

Guest, AR, Van Hout, GJ & Von Johannides, A, 2000, ‘An application of linear programming for block cave draw control’,

in G Chitombo (ed.), Proceedings of MassMin 2000, The Australasian Institute of Mining and Metallurgy, Melbourne,

pp. 461–468.

Heslop, TG & Laubscher, DH 1981, ‘Draw control in caving operations on Southern African Chrysotile asbestos mines’, in DR Stewart (ed.), Proceedings of the International Conference on Caving and Sublevel Stoping: Design and Operation of Caving and Sublevel Stoping Mines, Society of Mining Engineers of the American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc., New York, pp. 755–774.

IBM 2015, CPLEX/IBM, IBM, Sunnyvale.

Khodayari, F & Pourrahimian, Y 2015a ‘Determination of development precedence for drawpoints in block-cave mining’,

in HP Martens (ed.), Proceedings of the Fifth International Symposium, Mineral Resources and Mine Development, Aachen University, Aachen, 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, no. 3, pp. 234–257.

Parkinson, AF 2012, Essay on Sequence Optimisation in Block Cave Mining and Inventory Policies with Two Delivery Sizes,

PhD thesis, University of British Columbia, Vancouver.

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

Pourrahimian, Y, Askari-Nasab, H & Tannant, D 2012, ‘Mixed-integer linear programming formulation for block-cave sequence optimisation’, International Journal of Mining and Mineral Engineering, vol. 4, no. 1, pp. 26–48.

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, pp. 739–750.

Preece, CA & Liebenberg, B 2007, ‘Cave management at Finsch Mine’, The Journal of The Southern African Institute of Mining and Metallurgy, vol. 107, pp. 775–781.

Queyranne, M, Parkinson, A, McCormick, ST, Diering, T, Malkin, P & Wolsey, L 2008, ‘The drawpoint scheduling approach to production planning in a block cave mine’, Operation Research in Mining Workshop, Viña del Mar.

Rahal, D 2008, Draw Control in Block Caving Using Mixed Integer Linear Programming, PhD thesis, The University of Queensland, Brisbane.

Rahal, D, Smith, M, Van Hout, GJ & Von Johannides, A 2003, ‘The use of mixed integer linear programming for long-term scheduling in block caving mines’, in FA Camisani-Calzolari (ed.), Proceedings of the 31st International Symposium on the Application of Computers and operations Research in the Minerals Industry, The South African Institute of Mining and Metallurgy, Johannesburg, pp. 123–132.

Riddle, J 1976, ‘A dynamic programming solution of a block - caving mine layout’, Proceedings of APCOM 1976: International Symposium on the Application of Computers and Operations Research in the Minerals Industries, pp. 767–780.

Rubio, E 2006, Block Cave Mine Infrastructure Reliability Applied to Production Planning, PhD thesis, University of British Columbia, Vancouver.

Rubio, E & Diering, T 2004, ‘Block cave production planning using operations research tools’, in A Karzulovic & MA Alfaro (eds), Proceedings of MassMin 2004, Instituto de Ingenieros de Chile, Santiago, pp. 141–149.

Smith, ML & Rahal, D 2001, ‘Draw control optimisation in the context of production scheduling’, in E Unal, B Unver & E Tercan (eds), Proceedings of the 17th International Mining Congress and Exhibition of Turkey, Chamber Mining Engineers Turkey, Ankara, pp. 831–838.

Smoljanovic, M, Rubio, E & Morales, N 2011, ‘Panel caving scheduling under precedence constraints considering mining system’,

in EY Baffi (ed.), 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. 2016, MATLAB (R2016a) 2016, version 9.0.0.341360, The MathWorks, Inc., Natick.

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 2018, 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