444
2 RELATED WORK
Researchers have mainly applied mathematical optimization to generate short-term production schedules in open-pit mines considering the optimization of multiples objectives. An
excellent review of works related to short-term production scheduling in open-pit mines can
be found in Blom et al. (2018). Smith (1998) describe a model to maximize ore production subject to ore quality constraints. Huang et al. (2009) describe a production scheduling tool based on MILP to solve short- and medium-term schedule problems for open-pit
mines that involves multiple models, multiple processes, multiple destinations, and blending requirements. Eivazy & Askari-Nasab (2012) develop a MILP model for minimizing the
overall cost of open-pit mines, considering multiple destinations. The model incorporates
buffer and blending stockpiles, horizontal directional mining and decisions on ramps while
controlling operational constraints such as head grade, mining and processing capacities,
and mining precedence. L’Heureux et al. (2013) propose an optimization model based on
MILP to determine the blocks to extract and their order, considering precedence among
operational tasks, drilling, blasting, transportation, processing, movement of shovels, drills
among others. Blom et al. (2014, 2016) propose an optimization problem based on MILP to
address the short-term scheduling problem in open-pits networks. The authors also present
a rolling-horizon-based algorithm for solving this model. Blom et al. (2017) presents a novel
variation of the rolling horizon-based algorithm presented in Blom et al. (2014, 2016), in
which multiple distinct schedules are generated, concurrently, each optimized concerning an
ordered sequence of objectives. Matamoros & Dimitrakopoulos (2016) propose a formulation based on stochastic mixed integer programming. The objective function considers terms
associated with operating fleet cost, mining cost, and penalty cost to penalize deviation from
production target, expected fleet utilization and mining width. Fioroni et al. (2008) presented
a MILP model to allocate shovels to mine faces and the number of trips that each type of
truck fleet have to carry out to these faces, subject to production and blending constraints.
The models are called by an open-pit truck-shovel simulation model, whenever a change in
the mine operation system occurs, in order to update the allocation of shovels to the new
operation state. Upadhyay & Askari-Nasab (2016, 2017, 2018) described a MILP model to
allocate shovels to mine faces in order to: maximize production, meet desired head grade and
tonnage at crushers and minimize shovel movements. This model is called by an open-pit
truck-shovel simulation model, similarly than the work of Fioroni et al. (2008).
3 MATERIALS AND METHODS
In this section, we present the optimization model and describe the methodology to generate
short-term mine production schedules optimizing various objective optimizations using the
hierarchical and weighted sum methods.
3.1 Optimization model
The optimization model proposed is a shovel allocation problem based on MILP. The objective of the model is to provide shovel allocations to phases and benches over a one year scheduling horizon. We present the sets & indexes, variables and parameters of the optimization
model in Tables 1, 2, and 3, respectively.
Here we describe the constraints of the proposed optimization model. The material
extracted by the fleet of shovels of the bench b of the phase f along the planning horizon
must be equal to the total material available (Equation 1). The total ore sent to the ore
processing plant must be lower than the ore processing capacity (Equation 2). The shovel’s
operative time plus the shovel’s movement time between the phases are lower or equal to the
availability of the shovel (Equation 3). In order to assign operative time, a shovel p must be
assigned to the bench b of the phase f (Equation 4). When a bench is finished, it cannot be
assigned with any shovels (Equation 5). To assign a shovel p in a bench b of a phase f, that
2 RELATED WORK
Researchers have mainly applied mathematical optimization to generate short-term production schedules in open-pit mines considering the optimization of multiples objectives. An
excellent review of works related to short-term production scheduling in open-pit mines can
be found in Blom et al. (2018). Smith (1998) describe a model to maximize ore production subject to ore quality constraints. Huang et al. (2009) describe a production scheduling tool based on MILP to solve short- and medium-term schedule problems for open-pit
mines that involves multiple models, multiple processes, multiple destinations, and blending requirements. Eivazy & Askari-Nasab (2012) develop a MILP model for minimizing the
overall cost of open-pit mines, considering multiple destinations. The model incorporates
buffer and blending stockpiles, horizontal directional mining and decisions on ramps while
controlling operational constraints such as head grade, mining and processing capacities,
and mining precedence. L’Heureux et al. (2013) propose an optimization model based on
MILP to determine the blocks to extract and their order, considering precedence among
operational tasks, drilling, blasting, transportation, processing, movement of shovels, drills
among others. Blom et al. (2014, 2016) propose an optimization problem based on MILP to
address the short-term scheduling problem in open-pits networks. The authors also present
a rolling-horizon-based algorithm for solving this model. Blom et al. (2017) presents a novel
variation of the rolling horizon-based algorithm presented in Blom et al. (2014, 2016), in
which multiple distinct schedules are generated, concurrently, each optimized concerning an
ordered sequence of objectives. Matamoros & Dimitrakopoulos (2016) propose a formulation based on stochastic mixed integer programming. The objective function considers terms
associated with operating fleet cost, mining cost, and penalty cost to penalize deviation from
production target, expected fleet utilization and mining width. Fioroni et al. (2008) presented
a MILP model to allocate shovels to mine faces and the number of trips that each type of
truck fleet have to carry out to these faces, subject to production and blending constraints.
The models are called by an open-pit truck-shovel simulation model, whenever a change in
the mine operation system occurs, in order to update the allocation of shovels to the new
operation state. Upadhyay & Askari-Nasab (2016, 2017, 2018) described a MILP model to
allocate shovels to mine faces in order to: maximize production, meet desired head grade and
tonnage at crushers and minimize shovel movements. This model is called by an open-pit
truck-shovel simulation model, similarly than the work of Fioroni et al. (2008).
3 MATERIALS AND METHODS
In this section, we present the optimization model and describe the methodology to generate
short-term mine production schedules optimizing various objective optimizations using the
hierarchical and weighted sum methods.
3.1 Optimization model
The optimization model proposed is a shovel allocation problem based on MILP. The objective of the model is to provide shovel allocations to phases and benches over a one year scheduling horizon. We present the sets & indexes, variables and parameters of the optimization
model in Tables 1, 2, and 3, respectively.
Here we describe the constraints of the proposed optimization model. The material
extracted by the fleet of shovels of the bench b of the phase f along the planning horizon
must be equal to the total material available (Equation 1). The total ore sent to the ore
processing plant must be lower than the ore processing capacity (Equation 2). The shovel’s
operative time plus the shovel’s movement time between the phases are lower or equal to the
availability of the shovel (Equation 3). In order to assign operative time, a shovel p must be
assigned to the bench b of the phase f (Equation 4). When a bench is finished, it cannot be
assigned with any shovels (Equation 5). To assign a shovel p in a bench b of a phase f, that