413
previous attempts. After 200 hours of computation time, the program had not converged on
an optimal solution; however, the solution did result in a 24% increase in NPV over the current mine schedule after only 1.6 hours of computation.
Surface mine optimization has been researched and applied to the industry since the 1960s,
(Lerchs and Grossmann, 1964; Johnson, 1968). Today, there are numerous commercially
available tools utilizing optimization techniques to improve surface operations, e.g., Geovia
Whittle Dassault Systèmes (2018), Pit Optimizer Maptek Pty Ltd (2016), MineSight Economic Planner Hexagon AB (2019), to name a few. Over the last two decades, researchers
and industry have worked to develop similar tools for underground mine planning. Today,
underground mine planners utilize SOT+ (MIRARCO Mining Innovations, 2018), often in
conjunction with a 3-dimensional mine design package. SOT+ uses heuristics to develop feasible schedules, iteratively improving over the previously best known solution, that may or
may not provide an optimal solution.
Recent research has focused on using deterministic (Brickey, 2015; O’Sullivan, 2014;
Little et al., 2008; Topal, 2008; Newman et al., 2003) and stochastic optimization (Carpentier
et al., 2016) to produce robust and optimal underground mine schedules. This paper focuses
on modeling techniques, existing and new, that can improve the solution quality of deterministic optimization applications to underground production scheduling. A substantive review
of underground mine optimization applications can be found in Alford et al. (2007) and
Newman et al. (2010).
2 UNDERGROUND MINE PRODUCTION SCHEDULING
Production scheduling is an integral part of the mine planning process. Scheduling underground operations differs from open pit scheduling and is generally considered more challenging and complex (O’Sullivan et al., 2015) to accomplish. Optimizing underground schedules,
consequently, also differs significantly from open pit scheduling. Underground excavations
are represented as activities, with varying associated tonnages and production rates. Activities can be broadly delineated into (i) production, i.e., stopes, top-cuts, under-cuts, (ii) development, i.e., ramps, shafts, raises, and (iii) auxiliary, i.e., sumps, electric stations.
The traditional production scheduling process endeavors to determine a feasible
sequence of these activities such that operational objectives are met (Newman et al.,
2010). When optimizing the schedule, the operational goal(s), e.g. maximizing net present
value or minimizing costs, is represented by the objective function, while sequencing and
resource limitations constrain the model. Operational objectives are often based on corporate goals. Sequencing constraints (or activity precedence) are derived from geotechnical
limitations, and physical or operational sequencing. Lastly, resource constraints enforce
operational limitations such as equipment capacity, milling capacity and even ventilation
requirements.
Production schedules can be categorized on the basis of time horizon as either strategic
(long-term) or tactical (short-term). As the names suggest, a strategic schedule is used to provide a big-picture view of the operation, while the tactical schedule aims to inform activity
sequencing at a weekly, daily or shift fidelity.
2.1 The UG-RCPSP model
An underground production schedule optimization model is used to determine the start
dates for a set of activities in order to maximize the operation’s value (Net Present Value),
while adhering to precedence and resource constraints (King et al., 2017). The Underground
Resource Constrained Production Scheduling Problem (UG-RCPSP) model builds on the
work of Brickey (2015), a particular case of the resource constrained project scheduling
problem (RCPSP). The RCPSP is a known NP-hard problem (Artigues et al., 2013) that
consists of scheduling activities over time, subject to precedence and resource availability
constraints. The following generalized formulation illustrates the UG-RCPSP.
previous attempts. After 200 hours of computation time, the program had not converged on
an optimal solution; however, the solution did result in a 24% increase in NPV over the current mine schedule after only 1.6 hours of computation.
Surface mine optimization has been researched and applied to the industry since the 1960s,
(Lerchs and Grossmann, 1964; Johnson, 1968). Today, there are numerous commercially
available tools utilizing optimization techniques to improve surface operations, e.g., Geovia
Whittle Dassault Systèmes (2018), Pit Optimizer Maptek Pty Ltd (2016), MineSight Economic Planner Hexagon AB (2019), to name a few. Over the last two decades, researchers
and industry have worked to develop similar tools for underground mine planning. Today,
underground mine planners utilize SOT+ (MIRARCO Mining Innovations, 2018), often in
conjunction with a 3-dimensional mine design package. SOT+ uses heuristics to develop feasible schedules, iteratively improving over the previously best known solution, that may or
may not provide an optimal solution.
Recent research has focused on using deterministic (Brickey, 2015; O’Sullivan, 2014;
Little et al., 2008; Topal, 2008; Newman et al., 2003) and stochastic optimization (Carpentier
et al., 2016) to produce robust and optimal underground mine schedules. This paper focuses
on modeling techniques, existing and new, that can improve the solution quality of deterministic optimization applications to underground production scheduling. A substantive review
of underground mine optimization applications can be found in Alford et al. (2007) and
Newman et al. (2010).
2 UNDERGROUND MINE PRODUCTION SCHEDULING
Production scheduling is an integral part of the mine planning process. Scheduling underground operations differs from open pit scheduling and is generally considered more challenging and complex (O’Sullivan et al., 2015) to accomplish. Optimizing underground schedules,
consequently, also differs significantly from open pit scheduling. Underground excavations
are represented as activities, with varying associated tonnages and production rates. Activities can be broadly delineated into (i) production, i.e., stopes, top-cuts, under-cuts, (ii) development, i.e., ramps, shafts, raises, and (iii) auxiliary, i.e., sumps, electric stations.
The traditional production scheduling process endeavors to determine a feasible
sequence of these activities such that operational objectives are met (Newman et al.,
2010). When optimizing the schedule, the operational goal(s), e.g. maximizing net present
value or minimizing costs, is represented by the objective function, while sequencing and
resource limitations constrain the model. Operational objectives are often based on corporate goals. Sequencing constraints (or activity precedence) are derived from geotechnical
limitations, and physical or operational sequencing. Lastly, resource constraints enforce
operational limitations such as equipment capacity, milling capacity and even ventilation
requirements.
Production schedules can be categorized on the basis of time horizon as either strategic
(long-term) or tactical (short-term). As the names suggest, a strategic schedule is used to provide a big-picture view of the operation, while the tactical schedule aims to inform activity
sequencing at a weekly, daily or shift fidelity.
2.1 The UG-RCPSP model
An underground production schedule optimization model is used to determine the start
dates for a set of activities in order to maximize the operation’s value (Net Present Value),
while adhering to precedence and resource constraints (King et al., 2017). The Underground
Resource Constrained Production Scheduling Problem (UG-RCPSP) model builds on the
work of Brickey (2015), a particular case of the resource constrained project scheduling
problem (RCPSP). The RCPSP is a known NP-hard problem (Artigues et al., 2013) that
consists of scheduling activities over time, subject to precedence and resource availability
constraints. The following generalized formulation illustrates the UG-RCPSP.