Mining Goes Digital – Mueller et al. (Eds)
© 2019 Taylor & Francis Group, London, ISBN 978-0-367-33604-2
144
MILP framework for open pit and underground mining
transitions evaluation
B.O. Afum
Mining Optimization Laboratory, Laurentian University, Sudbury, Canada
University of Mines and Technology (UMaT), Tarkwa, Ghana
E. Ben-Awuah
Mining Optimization Laboratory, Laurentian University, Sudbury, Canada
ABSTRACT: The strategic decisions to exploit a mineral deposit extending from the
surface to great depth are essential to the financial and sustainability benefits of any mining
project. Mining option strategies for resource extraction include: (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 (c) and (d). This research investigates the extraction
strategy that maximizes the Net Present Value (NPV) of a resource using a Mixed Integer
Linear Programming (MILP) optimization framework. The MILP model determines the best
extraction strategy for a given ore body and further determines the mining and processing
schedule, positioning of the required crown pillar, and the schedule for underground capital
and operational developments. The model is implemented for a synthetic copper case study.
1 INTRODUCTION
Decisions made at the prefeasibility stage of a mining project are essential to the
commencement and sustainability of the project. Important decisions including the selection
of a suitable mining option(s) for exploiting the deposit improves the confidence of mine
management and investors when their correctness and accuracy are done right from the onset
of the mining project. The decision on the choice of mining option(s) becomes complicated
when the deposit is deep-seated and exhibits significant outcrops. The potential of such a
deposit to be exploited by open pit (OP) or underground (UG) mining or both (OPUG)
could lead to several variations of mining options. To generate early revenue, the portion of
the deposit closer to the surface is often exploited by open pit mining option while the deeper
portions are exploited with underground mining option. In OP mining, the incremental stripping ratio and overall mining cost with depth makes UG mining profitable beyond a certain
depth. This depth has been referred to by several authors as the transition depth or point
(Bakhtavar et al., 2009, Dagdelen and Traore, 2014, De Carli and de Lemos, 2015, King
et al., 2016, MacNeil and Dimitrakopoulos, 2017, Opoku and Musingwini, 2013, Ordin and
Vasil’ev, 2014, Roberts et al., 2013, Ben-Awuah et al., 2016, Ben-Awuah et al., 2015).
The choice of the most economic mining option(s) can be implemented through an
optimization approach. The optimization process becomes complicated when the transition
point acts as the unmined crown pillar together with the integration of both capital and
operational developments. This leads to several variations of the optimal mining option(s):
(a) independent OP mining; (b) independent UG mining with crown pillar; (c) simultaneous
OPUG mining with crown pillar; (d) sequential OPUG mining with crown pillar; and
e) combinations of (c) and (d). The decision to adopt any mining option strategy will
primarily depend on the project economics and the geology of the mining area. Traditionally,
© 2019 Taylor & Francis Group, London, ISBN 978-0-367-33604-2
144
MILP framework for open pit and underground mining
transitions evaluation
B.O. Afum
Mining Optimization Laboratory, Laurentian University, Sudbury, Canada
University of Mines and Technology (UMaT), Tarkwa, Ghana
E. Ben-Awuah
Mining Optimization Laboratory, Laurentian University, Sudbury, Canada
ABSTRACT: The strategic decisions to exploit a mineral deposit extending from the
surface to great depth are essential to the financial and sustainability benefits of any mining
project. Mining option strategies for resource extraction include: (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 (c) and (d). This research investigates the extraction
strategy that maximizes the Net Present Value (NPV) of a resource using a Mixed Integer
Linear Programming (MILP) optimization framework. The MILP model determines the best
extraction strategy for a given ore body and further determines the mining and processing
schedule, positioning of the required crown pillar, and the schedule for underground capital
and operational developments. The model is implemented for a synthetic copper case study.
1 INTRODUCTION
Decisions made at the prefeasibility stage of a mining project are essential to the
commencement and sustainability of the project. Important decisions including the selection
of a suitable mining option(s) for exploiting the deposit improves the confidence of mine
management and investors when their correctness and accuracy are done right from the onset
of the mining project. The decision on the choice of mining option(s) becomes complicated
when the deposit is deep-seated and exhibits significant outcrops. The potential of such a
deposit to be exploited by open pit (OP) or underground (UG) mining or both (OPUG)
could lead to several variations of mining options. To generate early revenue, the portion of
the deposit closer to the surface is often exploited by open pit mining option while the deeper
portions are exploited with underground mining option. In OP mining, the incremental stripping ratio and overall mining cost with depth makes UG mining profitable beyond a certain
depth. This depth has been referred to by several authors as the transition depth or point
(Bakhtavar et al., 2009, Dagdelen and Traore, 2014, De Carli and de Lemos, 2015, King
et al., 2016, MacNeil and Dimitrakopoulos, 2017, Opoku and Musingwini, 2013, Ordin and
Vasil’ev, 2014, Roberts et al., 2013, Ben-Awuah et al., 2016, Ben-Awuah et al., 2015).
The choice of the most economic mining option(s) can be implemented through an
optimization approach. The optimization process becomes complicated when the transition
point acts as the unmined crown pillar together with the integration of both capital and
operational developments. This leads to several variations of the optimal mining option(s):
(a) independent OP mining; (b) independent UG mining with crown pillar; (c) simultaneous
OPUG mining with crown pillar; (d) sequential OPUG mining with crown pillar; and
e) combinations of (c) and (d). The decision to adopt any mining option strategy will
primarily depend on the project economics and the geology of the mining area. Traditionally,