TRANSACTION PAPER

Early start and late start algorithms to improve the solution time for long-term underground mine production scheduling

E. Topal

Senior Lecturer, School of Engineering and Senior Researcher, CRC Mining, The University of Queensland Brisbane, Australia

SYNOPSIS

Mixed integer programming (MIP) has been used for optimizing production schedules of mines since the 1960s. The major problem in the long-term production scheduling for an entire orebody is that the number of integer variables needed to formulate an MIP model is too large to solve the formulation. This number may reach well over one hundred thousand. To overcome this difficulty, this paper presents two new algorithms to reduce the size of the problem. These algorithms assign an earliest and latest possible start date for each machine placement, eliminating the integer variables that correspond to machine placement before its early start date and after its late start date. A case study based on Kiruna Mine, the second largest underground mine in the world, is summarized in the paper. It shows substantial improvement in the solution time required using the new algorithms. This increased efficiency in the solution time of the MIP model allows it to be applied to Kiruna Mine, with the potential to increase substantially the net present value (NPV) of the project.

“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 ]

KUCHTA, M., NEWMAN, A., and TOPAL, E. Implementing a Production Schedule at LKAB's Kiruna Mine, Interface, 2004. vol. 34, no. 2, pp. 124-134.         [ Links ]

LERCHS, H. and GROSSMANN, I.F. Optimum Design of open-pitmine, Transaction on CIM LXVII, 1965. pp. 47-54.         [ Links ]

MCISSAC, G. Long-term Planning of an Underground Mine Using Mixed-integer Linear Programming, CIM Bulletin, 2005. vol. 98.         [ Links ]

RAMAZAN, S. The new fundamental tree algorithm for production scheduling of open pit mines. European Journal of Operations Research, 2007. vol. 177, issue 2, pp. 1153-1166.         [ Links ]

RAMAZAN, S. and DIMITRAKOPOULOS, R. Recent applications of operations research and efficient MIP formulations in open pit mining. SME, transaction, 2004, vol. 316, pp. 73-78.         [ Links ]

TOLWINKI, B. Scheduling Production for Open Pit Mines. 27th Applications of Computers and Operations Research in Minerals Industries, 1998, pp. 168-175.         [ Links ]

TOPAL, E. Advanced Underground Mine Scheduling Using Mixed Integer Programming, PhD dissertation, Colorado School of Mines, Golden , Colorado, 2003.         [ Links ]

TOPAL, E., NEWMAN, A., and KUCHTA, M. Extensions to an Efficient Optimization Model for Long-Term Production Planning at LKAB's Kiruna Mine. Applications of Computers and Operations Research in Minerals Industries, South African Institute of Mining and Metallurgy, 2003.         [ Links ]

TROUT, L.P. Underground Mine Production Scheduling Using Mixed Integer Programming', 25th International APCOM Symposium Proceedings, Brisbane, Australia, 1995, pp. 395-400.         [ Links ]

Paper received Apr. 2007
Revised paper received Oct. 2007