156
6 CONCLUSIONS AND RECOMMENDATIONS
An integrated Mixed Integer Linear Programming (MILP) model for evaluating the extraction of a mineral deposit has been developed, implemented, and tested on a synthetic copper dataset. The proposed MILP model interrogates a deposit and determines the optimal
extraction strategy for a combination or one of the mining options: (a) independent open pit
mining, (b) independent underground mining with crown pillar, (c) simultaneous open pit
and underground mining with crown pillar, (d) sequential open pit and underground mining
with crown pillar, and (e) combinations of simultaneous and sequential open pit and UG
mining with crown pillar. The location of the 3D crown pillar together with the required
capital and operational development schedules are decided by the optimization process. The
MILP model is applicable to all types of deposits and for any preferred direction of mineral extraction sequence. The capital development can either be a shaft, decline or both and
during optimization, depending on the optimal mining option, the capital development can
either commence from the surface, bottom of the open pit mine or both.
To implement the MILP model, the block model was organized by first selecting a preferred ore extraction method on a level (advancing or retreating) and siting the possible location of the underground capital and operational developments based on the philosophy and
geotechnical understanding of the mine. As in practice, the MILP model requires that an
incremental cost for open pit mining is defined per depth (m) for block extraction. Thus, the
cost of open pit mining increases with depth until underground mining becomes preferable
to open pit mining. This concept allows the optimizer to decide when to stop the open pit
mining operation, introduce a crown pillar and start the underground mining operation in
the presence of both capital and operational developments.
The results from the case study showed a combined sequential and simultaneous open
pit and underground mining option (OPUG) with crown pillar was selected as the optimal
mining option to exploit the deposit. The ore and rock extraction schedules for the open
pit and underground mining operations together with the operational and capital development schedules were determined for the synthetic copper project. The output of the model
in mapping-out the ore extraction per level in each period further provides more insight
into the mining sequence for selection of the appropriate underground mining method.
A sensitivity analysis conducted on selected technical and operational parameters indicate that the determination of the optimal mining option using the MILP model is very
sensitive to the selling price of copper, followed by the quantity of ore processed by the
underground mining operation and the completion rate of the underground capital development (shaft).
The authors recommend that stockpile management and geotechnical information be
incorporated into the MILP model to ensure the outputs of the model is exhaustive and
realistic. Similarly, it is necessary to extend the model from its current deterministic approach
to a stochastic framework to address the impact of grade uncertainty in the choice of mining
option and project evaluation.
REFERENCES
Bakhtavar, E., Shahriar, K. & Mirhassani, A. 2012. Optimization of the transition from open-pit to
underground operation in combined mining using (0–1) integer programming. J South Afr Inst Min
Metall 112, 1059–64.
Bakhtavar, E., Shahriar, K. & Oraee, K. 2009. Transition from open-pit to underground as a new optimization challenge in mining engineering. Journal of Mining Science, 45, 485–494.
Ben-Awuah, E., Otto, R., Tarrant, E. & Yashar, P. 2016. Strategic mining options optimization: Open
pit mining underground mining or both. International Journal of Mining Science and Technology, 26,
1065–1071.
Ben-Awuah, E., Richter, O. & Elkington, T. 2015. Mining options optimization: Concurrent open pit
and underground mining production scheduling. 37th International Symposium on the Application of
Computers and Operations Research in the Mineral Industry. Fairbanks, Alaska: SME.
6 CONCLUSIONS AND RECOMMENDATIONS
An integrated Mixed Integer Linear Programming (MILP) model for evaluating the extraction of a mineral deposit has been developed, implemented, and tested on a synthetic copper dataset. The proposed MILP model interrogates a deposit and determines the optimal
extraction strategy for a combination or one of the mining options: (a) independent open pit
mining, (b) independent underground mining with crown pillar, (c) simultaneous open pit
and underground mining with crown pillar, (d) sequential open pit and underground mining
with crown pillar, and (e) combinations of simultaneous and sequential open pit and UG
mining with crown pillar. The location of the 3D crown pillar together with the required
capital and operational development schedules are decided by the optimization process. The
MILP model is applicable to all types of deposits and for any preferred direction of mineral extraction sequence. The capital development can either be a shaft, decline or both and
during optimization, depending on the optimal mining option, the capital development can
either commence from the surface, bottom of the open pit mine or both.
To implement the MILP model, the block model was organized by first selecting a preferred ore extraction method on a level (advancing or retreating) and siting the possible location of the underground capital and operational developments based on the philosophy and
geotechnical understanding of the mine. As in practice, the MILP model requires that an
incremental cost for open pit mining is defined per depth (m) for block extraction. Thus, the
cost of open pit mining increases with depth until underground mining becomes preferable
to open pit mining. This concept allows the optimizer to decide when to stop the open pit
mining operation, introduce a crown pillar and start the underground mining operation in
the presence of both capital and operational developments.
The results from the case study showed a combined sequential and simultaneous open
pit and underground mining option (OPUG) with crown pillar was selected as the optimal
mining option to exploit the deposit. The ore and rock extraction schedules for the open
pit and underground mining operations together with the operational and capital development schedules were determined for the synthetic copper project. The output of the model
in mapping-out the ore extraction per level in each period further provides more insight
into the mining sequence for selection of the appropriate underground mining method.
A sensitivity analysis conducted on selected technical and operational parameters indicate that the determination of the optimal mining option using the MILP model is very
sensitive to the selling price of copper, followed by the quantity of ore processed by the
underground mining operation and the completion rate of the underground capital development (shaft).
The authors recommend that stockpile management and geotechnical information be
incorporated into the MILP model to ensure the outputs of the model is exhaustive and
realistic. Similarly, it is necessary to extend the model from its current deterministic approach
to a stochastic framework to address the impact of grade uncertainty in the choice of mining
option and project evaluation.
REFERENCES
Bakhtavar, E., Shahriar, K. & Mirhassani, A. 2012. Optimization of the transition from open-pit to
underground operation in combined mining using (0–1) integer programming. J South Afr Inst Min
Metall 112, 1059–64.
Bakhtavar, E., Shahriar, K. & Oraee, K. 2009. Transition from open-pit to underground as a new optimization challenge in mining engineering. Journal of Mining Science, 45, 485–494.
Ben-Awuah, E., Otto, R., Tarrant, E. & Yashar, P. 2016. Strategic mining options optimization: Open
pit mining underground mining or both. International Journal of Mining Science and Technology, 26,
1065–1071.
Ben-Awuah, E., Richter, O. & Elkington, T. 2015. Mining options optimization: Concurrent open pit
and underground mining production scheduling. 37th International Symposium on the Application of
Computers and Operations Research in the Mineral Industry. Fairbanks, Alaska: SME.