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the outcrop portion of the deposit is optimized for OP mining and during the OP mining
operation, the deep-seated portion below the bottom of the open pit is evaluated for UG
mining. This approach leads to missed financial and sustainability opportunities because it
often leads to sub-optimal solutions.
A mathematical programming framework for determining the extraction strategy for any
deposit that has the potential to be exploited with several variations of mining options in the
presence of a suitable crown pillar, capital development (shaft/decline) and operational developments (level, ore drives and crosscuts) has been developed. Integrating three-dimensional
(3D) crown pillar positioning into the optimization process allows the OP and UG mining
options the fair opportunity to economically compete for selection.
This paper presents a Mixed Integer Linear Programming (MILP) framework for solving the
open pit and underground mining transition problems. The model determines a suitable optimized mining option and strategy for extracting a deposit that is potentially amenable to either
or both open pit and underground mining option. A synthetic copper dataset is used as a case
study to implement the model for evaluation. Sensitivity analysis is further conducted to assess
the influence of selected technical and economic parameters to changes in the mining options.
The next section of this research paper covers a summarized literature review on open
pit to underground mining transition with highlights on research gaps. Section 3 discusses
the assumptions and notations used in the proposed MILP model. Section 4 introduces and
explains the proposed integrated MILP model for the open pit to underground mining transition complex. Section 5 documents the implementation of the MILP model for a synthetic
copper deposit while Section 6 outlines the research conclusions and recommendations.
2 SUMMARY OF LITERATURE REVIEW
Strategic open pit and underground mining interface optimization models have been developed
based on determining the transition depth between open pit and underground mining.
These existing models focus on investigating how an underground mining operation can be
exploited after the open pit mine life and/or finding the transition depth. Acknowledging
notable challenges and shortfalls, several researchers have employed techniques, algorithms
and/or models to determine the transition depth (Bakhtavar et al., 2009, Dagdelen and
Traore, 2014, De Carli and de Lemos, 2015, King et al., 2016, Opoku and Musingwini, 2013,
Ordin and Vasil’ev, 2014, Roberts et al., 2013, MacNeil and Dimitrakopoulos, 2017) and the
ore block extraction strategy (Ben-Awuah et al., 2016, De Carli and de Lemos, 2015, King
et al., 2016, MacNeil and Dimitrakopoulos, 2017, Whittle et al., 2018).
Optimizing the location of a crown pillar is a key factor in the optimal resource extraction
evaluation process for deposits amenable by both open pit and underground mining. Finding
the most suitable location of the crown pillar in a combined OPUG mining operations is one
of the most interesting problems for mining engineers today (Bakhtavar et al., 2012). The
transition from open pit to underground (OPUG) mining involves a complicated geomechanical
process. Recent formulations of the OPUG mining transition complexes produces near optimal solutions at minimal level of confidence, and do not integrate the positioning of a 3D
crown pillar, capital and operational developments into the optimization process.
Kurppa and Erkkilä (1967) assessed the simultaneous extraction between open pit and
underground (OPUG) mining during the operations of the Pyhasalmi mine. They indicated
that, simultaneous mining was possible due to the geometry of the orebody being worked.
Luxford (1997) argued that, cost usually drives the decision to make the transition because
as the open pit waste stripping cost keeps increasing with depth, there comes a time when
the underground mining cost will be less than the open pit mining cost. Ben-Awuah et al.
(2016) investigated the strategy of mining options for an orebody using a mathematical programming model. The research evaluated the financial impacts of applying different mining
options separately or concurrently to extract a given orebody. The formulation maximizes the
NPV of the reserve when extracted with: (1) open pit mining, (2) underground mining, and
(3) concurrent open pit and underground mining (Ben-Awuah et al., 2015). The positioning
the outcrop portion of the deposit is optimized for OP mining and during the OP mining
operation, the deep-seated portion below the bottom of the open pit is evaluated for UG
mining. This approach leads to missed financial and sustainability opportunities because it
often leads to sub-optimal solutions.
A mathematical programming framework for determining the extraction strategy for any
deposit that has the potential to be exploited with several variations of mining options in the
presence of a suitable crown pillar, capital development (shaft/decline) and operational developments (level, ore drives and crosscuts) has been developed. Integrating three-dimensional
(3D) crown pillar positioning into the optimization process allows the OP and UG mining
options the fair opportunity to economically compete for selection.
This paper presents a Mixed Integer Linear Programming (MILP) framework for solving the
open pit and underground mining transition problems. The model determines a suitable optimized mining option and strategy for extracting a deposit that is potentially amenable to either
or both open pit and underground mining option. A synthetic copper dataset is used as a case
study to implement the model for evaluation. Sensitivity analysis is further conducted to assess
the influence of selected technical and economic parameters to changes in the mining options.
The next section of this research paper covers a summarized literature review on open
pit to underground mining transition with highlights on research gaps. Section 3 discusses
the assumptions and notations used in the proposed MILP model. Section 4 introduces and
explains the proposed integrated MILP model for the open pit to underground mining transition complex. Section 5 documents the implementation of the MILP model for a synthetic
copper deposit while Section 6 outlines the research conclusions and recommendations.
2 SUMMARY OF LITERATURE REVIEW
Strategic open pit and underground mining interface optimization models have been developed
based on determining the transition depth between open pit and underground mining.
These existing models focus on investigating how an underground mining operation can be
exploited after the open pit mine life and/or finding the transition depth. Acknowledging
notable challenges and shortfalls, several researchers have employed techniques, algorithms
and/or models to determine the transition depth (Bakhtavar et al., 2009, Dagdelen and
Traore, 2014, De Carli and de Lemos, 2015, King et al., 2016, Opoku and Musingwini, 2013,
Ordin and Vasil’ev, 2014, Roberts et al., 2013, MacNeil and Dimitrakopoulos, 2017) and the
ore block extraction strategy (Ben-Awuah et al., 2016, De Carli and de Lemos, 2015, King
et al., 2016, MacNeil and Dimitrakopoulos, 2017, Whittle et al., 2018).
Optimizing the location of a crown pillar is a key factor in the optimal resource extraction
evaluation process for deposits amenable by both open pit and underground mining. Finding
the most suitable location of the crown pillar in a combined OPUG mining operations is one
of the most interesting problems for mining engineers today (Bakhtavar et al., 2012). The
transition from open pit to underground (OPUG) mining involves a complicated geomechanical
process. Recent formulations of the OPUG mining transition complexes produces near optimal solutions at minimal level of confidence, and do not integrate the positioning of a 3D
crown pillar, capital and operational developments into the optimization process.
Kurppa and Erkkilä (1967) assessed the simultaneous extraction between open pit and
underground (OPUG) mining during the operations of the Pyhasalmi mine. They indicated
that, simultaneous mining was possible due to the geometry of the orebody being worked.
Luxford (1997) argued that, cost usually drives the decision to make the transition because
as the open pit waste stripping cost keeps increasing with depth, there comes a time when
the underground mining cost will be less than the open pit mining cost. Ben-Awuah et al.
(2016) investigated the strategy of mining options for an orebody using a mathematical programming model. The research evaluated the financial impacts of applying different mining
options separately or concurrently to extract a given orebody. The formulation maximizes the
NPV of the reserve when extracted with: (1) open pit mining, (2) underground mining, and
(3) concurrent open pit and underground mining (Ben-Awuah et al., 2015). The positioning