TRANSACTION PAPER

A new mathematical programming model for production schedule optimization in underground mining operations

M. Nehring^I; E. Topal^II; J. Little^III

^ISchool of Mechanical and Mining Engineering, CRC Mining, The University of Queensland, Brisbane
^IIWestern Australia School of Mines, Curtin University of Technology, Kalgoorlie
^IIISchool of Mechanical and Mining Engineering, The University of Queensland, Mining Engineering, Anglo Coal Australia Pty Ltd, Drayton Mine

SYNOPSIS

Mixed integer programming (MIP) has been used for optimizing production schedules of mines since the 1960s and is recognized as having significant potential for optimizing production scheduling problems for both surface and underground mining. The major problem in long-term production scheduling for underground orebodies generally relate to the large number of variables needed to formulate a MIP model, which makes it too complex to solve. As the number of variables in the model increase, solution times are known to increase at an exponential rate. In many instances the more extensive use of MIP models has been limited due to excessive solution times.
This paper reviews production schedule optimization studies for underground mining operations. It also presents a classical MIP model for optimized production scheduling of a sublevel stoping operation and proposes a new model formulation to significantly reduce solution times without altering results while maintaining all constraints. A case study is summarized investigating solution times as five stopes are added incrementally to an initial ten stope operation, working up to a fifty stope operation. It shows substantial improvement in the solution time required when using the new formulation technique. This increased efficiency in the solution time of the MIP model allows it to solve much larger underground mine scheduling problems within a reasonable time frame with the potential to substantially increase the net present value (NPV) of these projects. Finally, results from the two models are also compared to that of a manually generated schedule which show the clear advantages of mathematical programming in obtaining optimal solutions.

Keywords: Underground mine optimization, mixed integer programming, longterm scheduling, mathematical programming application

“Full text available only in PDF format”

References

CARLYLE, M. and EAVES, B. C. Underground planning at Stillwater Mining Company, Interfaces, 2001. pp. 50-60.         [ Links ]

ILOG Corporation, CPLEX, AMPL, Version 10.0, 2006.         [ Links ]

LAWRENCE, B W. Considerations for sublevel stoping in techniques in underground mining, Littleton, Society for Mining, Metallurgy and Exploration Inc. 1998.         [ Links ]

LITTLE, J., NEHRING, M., and TOPAL, E. A new mixed-integer programming model for mine production scheduling optimisation in sublevel stope mining. Proceedings-Australian Mining Technology Conference, Twin Waters. The Australasian Institute of Mining and Metallurgy, 2008. pp. 157-172.         [ Links ]

LITTLE, J. A new approach to using mixed-integer programming for scheduling optimisation in sublevel stope mining, Bachelor thesis, The University of Queensland, Brisbane. 2007.         [ Links ]

MCISSAC, G. Long-term planning of an underground mine using mixed-integer linear programming, Canadian Institute of Mining, vol. 98, 2005. pp. 1-6.         [ Links ]

NEHRING, M and TOPAL, E. Production schedule optimisation in underground hard rock mining using mixed integer programming. Proceedings-Project Evaluation, Melbourne. The Australasian Institute of Mining and Metallurgy, 2007. pp 169-175.         [ Links ]

NEHRING, M. Stope Sequencing and Optimisation in Underground Hardrock Mining, Bachelor thesis, The University of Queensland, Brisbane, 2006.         [ Links ]

TOPAL, E. Advanced underground mine scheduling using mixed integer programming, PhD thesis, Colorado School of Mines, Colorado. 2003.         [ Links ]

TOPAL, E. Conceptual conversations and discussion sessions, The University of Queensland, Brisbane. 2006.         [ Links ]

Topal, E. Optimised production scheduling in sublevel stope mining. Unpublished Interim Report, The University of Queensland, Brisbane. 2007.         [ Links ]

TOPAL, E. Early start and late start algorithms to improve the solution time for long-term underground mine scheduling. South African Institute of Mining and Metallurgy Journal, 2008. pp. 99-107.         [ Links ]

TROUT, L P. Underground mine production scheduling using mixed integer programming. Proceedings-The 25th International APCOM Symposium, Melbourne. The Australasian Institute of Mining and Metallurgy, 1995. pp. 395-400.         [ Links ]

Paper received Mar. 2009
Revised paper received Mar. 2010