327
5 DISCUSSION AND CONCLUSIONS
Although many approaches to decrease the grade uncertainty in surface mine planning and
scheduling, the subject is not as well studied in the problem of stope sequencing. Conventional stope sequencing MILP models contain mathematical, production requirement and
mine stability constraints. In this paper, an approach that incorporates grade uncertainty into
stope sequencing has been studied. This approach is composed of two stages; producing the
stope layout plan and the sequence with grade uncertainty considerations. Grade uncertainty
is incorporated by assessing the variation among different sequential Gaussian simulations and
using chance constrained programming. Chance constrained programming modifies the objective function to maximize the average NPV and minimize the variation. The net present value
maximization objective of the conventional solution approach is revised with a multi-objective
optimization of maximization of the net present value and the minimization of the grade uncertainty. The emphasis on the variation minimization changes with the risk intolerance factor.
The case study has shown that the prioritization of stope extraction was made according
to the average stope grades and their variations. In cases where the risk intolerance is higher,
in other words, in the more conservative strategies, the objective was lower whereas the risk
was lower. On the contrary, in higher risk strategies the objective was higher but the risk of
not obtaining the target gains was higher. The sequence selection must be made by comparing the outcomes and taking into account of the company risk taking strategies. Other
sources of uncertainty will be considered in the future work.
ACKNOWLEDGEMENTS
The authors thank the Natural Sciences and Engineering Research Council of Canada
(#488262-15) and Promine for supporting this research.
REFERENCES
Chanda, E.C.K. 1990. “An application of integer programming and simulation to production planning
for a stratiform ore body.” Mining Science and Technology 11 (2):165–72.
Manchuk, John. 2008. “A Framework for Stope Sequence Optimization.”
Musingwini, C. 2016. “Optimization in underground mine planning-developments and opportunities.”
Journal of the Southern African Institute of Mining and Metallurgy 116 (9):809–20.
Nehring, M., Erkan Topal, and J. Little. 2010. “A new mathematical programming model for production
schedule optimization in underground mining operations.” Journal of the Southern African Institute
of Mining and Metallurgy 110 (8):437–46.
Sari, Yuksel Asli, and Mustafa Kumral. 2018a. “Risk-based stope sequencing optimization for underground mines through chance-constrained programming.” In Manuscript submitted for publication.
Sari, Yuksel Asli, and Mustafa Kumral. 2018b. “Sublevel stope layout planning through a greedy heuristic approach based on dynamic programming.” In Manuscript submitted for publication.
Terblanche, S.E., and A. Bley. 2015. “An improved formulation of the underground mine scheduling
optimisation problem when considering selective mining.” ORiON 31 (1):1–16.
Trout, L.P. 1995. Underground mine production scheduling using mixed integer programming. Paper
presented at the 25th International APCOM Symposium Proceedings.
Villalba Matamoros, Martha E., and Mustafa Kumral. 2017. “Heuristic stope layout optimisation
accounting for variable stope dimensions and dilution management.” International Journal of Mining and Mineral Engineering 8 (1):1–18.
Villalba Matamoros, Martha E., and Mustafa Kumral. 2018. “Underground mine planning: stope layout optimisation under grade uncertainty using genetic algorithms.” International Journal of Mining,
Reclamation and Environment:1–18.
5 DISCUSSION AND CONCLUSIONS
Although many approaches to decrease the grade uncertainty in surface mine planning and
scheduling, the subject is not as well studied in the problem of stope sequencing. Conventional stope sequencing MILP models contain mathematical, production requirement and
mine stability constraints. In this paper, an approach that incorporates grade uncertainty into
stope sequencing has been studied. This approach is composed of two stages; producing the
stope layout plan and the sequence with grade uncertainty considerations. Grade uncertainty
is incorporated by assessing the variation among different sequential Gaussian simulations and
using chance constrained programming. Chance constrained programming modifies the objective function to maximize the average NPV and minimize the variation. The net present value
maximization objective of the conventional solution approach is revised with a multi-objective
optimization of maximization of the net present value and the minimization of the grade uncertainty. The emphasis on the variation minimization changes with the risk intolerance factor.
The case study has shown that the prioritization of stope extraction was made according
to the average stope grades and their variations. In cases where the risk intolerance is higher,
in other words, in the more conservative strategies, the objective was lower whereas the risk
was lower. On the contrary, in higher risk strategies the objective was higher but the risk of
not obtaining the target gains was higher. The sequence selection must be made by comparing the outcomes and taking into account of the company risk taking strategies. Other
sources of uncertainty will be considered in the future work.
ACKNOWLEDGEMENTS
The authors thank the Natural Sciences and Engineering Research Council of Canada
(#488262-15) and Promine for supporting this research.
REFERENCES
Chanda, E.C.K. 1990. “An application of integer programming and simulation to production planning
for a stratiform ore body.” Mining Science and Technology 11 (2):165–72.
Manchuk, John. 2008. “A Framework for Stope Sequence Optimization.”
Musingwini, C. 2016. “Optimization in underground mine planning-developments and opportunities.”
Journal of the Southern African Institute of Mining and Metallurgy 116 (9):809–20.
Nehring, M., Erkan Topal, and J. Little. 2010. “A new mathematical programming model for production
schedule optimization in underground mining operations.” Journal of the Southern African Institute
of Mining and Metallurgy 110 (8):437–46.
Sari, Yuksel Asli, and Mustafa Kumral. 2018a. “Risk-based stope sequencing optimization for underground mines through chance-constrained programming.” In Manuscript submitted for publication.
Sari, Yuksel Asli, and Mustafa Kumral. 2018b. “Sublevel stope layout planning through a greedy heuristic approach based on dynamic programming.” In Manuscript submitted for publication.
Terblanche, S.E., and A. Bley. 2015. “An improved formulation of the underground mine scheduling
optimisation problem when considering selective mining.” ORiON 31 (1):1–16.
Trout, L.P. 1995. Underground mine production scheduling using mixed integer programming. Paper
presented at the 25th International APCOM Symposium Proceedings.
Villalba Matamoros, Martha E., and Mustafa Kumral. 2017. “Heuristic stope layout optimisation
accounting for variable stope dimensions and dilution management.” International Journal of Mining and Mineral Engineering 8 (1):1–18.
Villalba Matamoros, Martha E., and Mustafa Kumral. 2018. “Underground mine planning: stope layout optimisation under grade uncertainty using genetic algorithms.” International Journal of Mining,
Reclamation and Environment:1–18.