Abstract
High production rates and low operating costs highlight block caving as one of the favorable underground mining methods. However, the uncertainties involved in the material flow make it complicated to optimize the production schedule for such operations. In this paper, a stochastic mixed-integer linear optimization model is proposed in order to capture horizontal mixing that occurs among the draw columns within the production scheduling optimization. The goal is to not only consider the material above each drawpoint for extraction from the same drawpoint, as traditional production scheduling does, but also to capture the horizontal movements among the adjacent draw columns. In this approach, different scenarios are generated to simulate the horizontal mixing among adjacent slices within a neighborhood radius. The best height of draw for draw columns is also calculated as part of the optimization. The model is tested for a block-cave mine with 640 drawpoints to feed a processing plant for 15 years. The resulting NPV is 473M$ while the deviations from the targets in all scenarios during the life of the mine are minimized. Using the proposed model will result in more reliable mine plans as it takes the horizontal mixing into account in addition to achieving the production goals. Using different penalties for grade deviations shows that the model is a flexible tool in which the mine planners can achieve their goals based on their priorities.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Khodayari, F. and Pourrahimian, Y., Mathematical Programming Applications in Block-Caving Scheduling: A Review of Models and Algorithms, Int. J. Min. and Min. Eng., 2015, vol. 6, pp. 234–257.
Song, X., Caving Process Simulation and Optimal Mining Sequence at Tong Kuang Yu mine, China, Proc. of the 21st Int. Symposium on Application of Computers and Operations Research in the Mineral Industry, Las Vegas, USA, 1989.
Guest, A.R., Van Hout, G.J., and Von Johannides, A., An Application of Linear Programming for Block Cave Draw Control, Mass Min., 2000, Brisbane, Australia, 2000.
Rubio, E., Long Term Planning of Block Caving Operations using Mathematical Programming Tools, Master of Applied Science, The University of British Columbia, 2002.
Rahal, D., Smith, M., Van Hout, G., and Von Johannides, A., The Use of Mixed Integer Linear Programming for Long-Term Scheduling in Block Caving Mines, Proc. of the 31st Int. Symposium on Application of Computers and Operations Research in the Minerals Industries, Cape Town, South Africa, 2003.
Rahal, D., Draw Control in Block Caving Using Mixed Integer Linear Programming, PhD, The University of Queensland, 2008.
Rahal, D., Dudley, J., and Hout, G.V., Developing an Optimised Production Forecast at Northparkes E48 Mine Using MILP, Proc. of the 5th Int. Conf. and Exhibition on Mass Min., Luleå, Sweden, 2008.
Weintraub, A., Pereira, M., and Schultz, X., A Priori and a Posteriori Aggregation Procedures to Reduce Model Size in Mip Mine Planning Models, Electronic Notes in Discrete Mathematics, 2008, vol. 30, pp. 297–302.
Smoljanovic, M., Rubio, E., and Morales, N., Panel Caving Scheduling under Precedence Constraints Considering Mining System, Proc. of the 35th APCOM Symposium, Wollongong, NSW, Australia, 2011.
Parkinson, A., Essays on Sequence Optimization in Block Cave Mining and Inventory Policies with Two Delivery Sizes, PhD, The University of British Columbia, 2012.
Pourrahimian Y., Askari-Nasab H., and Tannant D. Mixed-Integer linear programming formulation for block-cave sequence optimisation, Int. J. Min. and Min. Eng., 2012, Vol. 4, No. 1. — P. 26–49.
Pourrahimian, Y., Askari-Nasab, H., and Tannant, D., A Multi-Step Approach for Block-Cave Production Scheduling Optimization, Int. J. Min. Sci. and Tech., 2013, vol. 23, pp. 739–750.
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 J. Operational Research, 2014, vol. 233, pp. 711–726.
Khodayari, F. and Pourrahimian, Y., Determination of the Best Height of Draw in Block Cave Sequence Optimization, Proc. of the 3rd Int. Symposium on Block and Sublevel caving (CAVING 2014), Santiago, Chile, 2014.
Nezhadshahmohammad, F., Khodayari, F., and Pourrahimian, Y., Draw Rate Optimization in Block Cave Production Scheduling Using Mathematical Programming, Proc. of the 1st Int. Conf. on Underground Min. Tech. (UMT 2017), Sudbury, Ontario, Canada, 2017.
Nezhadshahmohammad, F., Pourrahimian, Y., and Aghababaei, H., Presentation and Application of a Multi-Index Clustering Technique for the Mathematical Programming of Block-Cave Production Scheduling, J. Min. Sci. and Tech., 2017.
Nezhadshahmohammad, F., Aghababaei, H., and Pourrahimian, Y., Conditional Draw Control System in Block-Cave Production Scheduling Using Mathematical Programming, J. Min., Reclamation and Environment, 2017, pp. 1–24.
Malaki, S., Khodayari, F., Pourrahimian, Y., and Liu, W.V., An Application of Mathematical Programming and Sequencial Gaussian Simulation for Block-Cave Production Scheduling, Proc. of the 1st Int. Conf. on Underground Min. Tech. (UMT 2017), Sudbury, Ontario, Canada, 2017.
Diering, T., Computational Considerations for Production Scheduling of Block Cave Mines, Mass Min., 2004, Santiago, Chile, 2004.
Diering, T., Quadratic Programming Applications to Block Cave Scheduling and Cave Management, Massmin 2012, Sudbury, Ontario, Canada, 2012.
Khodayari, F. and Pourrahimian, Y., Quadratic Programming Application in Block-Cave Mining, Proc. of the 1st Int. Conf. of Underground Min. (U-Mining 2016), Santiago, Chile, 2016.
Castro, R., Gonzalez, F., and Arancibia, E., Development of a Gravity Flow Numerical Model for the Evaluation of Drawpoint Spacing for Block/Panel Caving, J. of the Southern African Institute of Min. and Metallurgy 109, 2009, pp. 393–400.
Pierce, M.E., A Model for Gravity Flow of Fragmented Rock in Block Caving Mines. PhD, The University of Queensland, 2010.
Gibson, W., Stochastic Models for Gravity Flow: Numerical Considerations, Conf. Caving 2014, Santiago, Chile, 2014.
Castro, R.L., Fuenzalida, M.A., and Lund, F., Experimental Study of Gravity Flow under Confined Conditions, Int. J. Rock Mech. and Min. Sci., 2014, vol. 67, pp. 164–169.
Jin, A., Sun, H., Wu, S., and Gao, Y., Confirmation of the Upside-Down Drop Shape Theory in Gravity Flow and Development of a New Empirical Equation to Calculate the Shape, Int. J. Rock Mech. and Min. Sci., 2017, vol. 92, pp. 91–98.
Brunton, I., Lett, J., Sharrock, G., Thornhill, T., and Mobilio, B., Full Scale Flow Marker Experiments at the Ridgeway Deeps and Cadia East Block Cave Operations, Massmin 2016, Sydney, Australia, 2016.
Garcés, D., Viera, E, Castro, R., and Meléndez, M., Gravity Flow Full Scale Tests at Esmeralda Mine’s Block 2, El Teniente, Massmin 2016, Sydney, Australia, 2016.
Laubscher, D.H., Cave Mining—The State of the Art, J. the Southern African Institute of Min. and Metallurgy, 1994, vol. 94, pp. 279–293.
Khodayari, F. and Pourrahimian, Y., Determination of Development Precedence for Drawpoints in Block-Cave Mining, Proc. of the 5th Int. Symp. Min. Resources and Mine Development (AIMS 2015), Aachen, Germany, 2015.
The Math Works Inc., MATLAB. Massachusetts, United States.
IBM, IBM ILOG CPLEX Optimization Studio V12.6.3 Documentation, IBM Corporation, N. Y., 2015.
Author information
Authors and Affiliations
Corresponding author
Additional information
Published in Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, 2019, No. 5, pp. 105–120.
Rights and permissions
About this article
Cite this article
Khodayari, F., Pourrahimian, Y. & Liu, W.V. Production Scheduling with Horizontal Mixing Simulation in Block Cave Mining. J Min Sci 55, 789–803 (2019). https://doi.org/10.1134/S1062739119056161
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1062739119056161