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assigned to those blocks; the dumps (crushers, process plants, stockpiles, waste dumps) to
which the material should be sent; and the amount, priority and/or order of each such material movement target. Plans (or a process to determine) ‘disruptions’ to load and haul operations are also often known at this time-scale, including equipment maintenance, availability
of equipment and operators, blasting, road maintenance, etc.
A haulage allocation plan specifies the flow rate of material from dig-units to dumps, and
is generated as a guide for operations to achieve the planned production targets.
Existing methods optimise instantaneous material flow rates for the current state of the
mine. Our proposed system, the ‘Flow Planner’, extends this planning methodology by generating an optimal haulage allocation plan for a specified time horizon (e.g. shift, day or
similar rolling window). The Flow Planner optimises time-varying flows across this longer
time horizon, in order to best achieve the overall production targets. This is made possible by
incorporating the planned/known events that will disrupt future operations in the short term
(maintenance, operator schedules, blasting, etc).
The objective used in existing commercial solutions is to maximise the instantaneous productivity of the mine. Taking a longer-term view of optimisation, our Flow Planner is able to consider more specific objectives, that is, achieving the production targets while minimising operating
costs. The truck operating costs are simply modelled as a cost per unit time of operation per
truck. The process plant feed cost is incurred when a process plant operates below a minimum
desired throughput. The plan failure cost component models the revenue lost due to not meeting
the production targets. Combinations of material blocks and target destinations can have different plan failure costs, enabling prioritisation, or speculative ‘stretch goals’ to be included.
3.1 MIP model
The units of the variables and parameters used in the MIP do not matter as long as they
are consistent. While material flows are specified in terms of volume of material, this can
be interchanged with material mass without consequence. The indices used in the developed
MIP are as follows:
t ∈ T
time periods
θ ∈ Θ truck types
s ∈ S
shovels
i, j ∈ L locations
b ∈ B blocks
i, j ∈ D all dumps (process plants, stockpiles, waste dumps)
i, j ∈ C process plants
A given shift is divided into a set of time periods
{
}
t max
…
.
}
t max L is the set of locations. The set of blocks is a subset of locations, B L. Similarly, D L indicates the set of
dumps, C D indicates the set of process plants.
The flow rates in this model represent both the loaded truck flows (from blocks to dumps)
and the empty truck flows (from dumps to blocks). For example, suppose that the flow rate
from block b to process plant c is 100 kg/s at time period t. This requires an equivalent of
100 kg/s of empty trucking capacity to be arriving (empty) at block b in time period t, in
order for it to also be departing (loaded). Therefore the flow of empty trucks (from dumps to
blocks) is also calculated. Apart from ensuring this logical consistency, this also allows complementary flows to be discovered; it may be advantageous for trucks to alternate between
two cycles that move material in opposing directions (i.e. where the empty haul routes for
trucks alternating between the cycles is shorter than the empty haul of trucks remaining on
the same cycle).
The following sets are defined in order to aid the description of MIP decision variables.
Let N i be the set of possible destinations for material from a location i L. If i B, then
N D
i
N N
meaning that loaded trucks leaving a block cannot travel to another block, only
dumps. Similarly, if i D, then N B
i
N N
, which indicates that empty trucks leaving any dumps
can only travel to blocks to be loaded.
assigned to those blocks; the dumps (crushers, process plants, stockpiles, waste dumps) to
which the material should be sent; and the amount, priority and/or order of each such material movement target. Plans (or a process to determine) ‘disruptions’ to load and haul operations are also often known at this time-scale, including equipment maintenance, availability
of equipment and operators, blasting, road maintenance, etc.
A haulage allocation plan specifies the flow rate of material from dig-units to dumps, and
is generated as a guide for operations to achieve the planned production targets.
Existing methods optimise instantaneous material flow rates for the current state of the
mine. Our proposed system, the ‘Flow Planner’, extends this planning methodology by generating an optimal haulage allocation plan for a specified time horizon (e.g. shift, day or
similar rolling window). The Flow Planner optimises time-varying flows across this longer
time horizon, in order to best achieve the overall production targets. This is made possible by
incorporating the planned/known events that will disrupt future operations in the short term
(maintenance, operator schedules, blasting, etc).
The objective used in existing commercial solutions is to maximise the instantaneous productivity of the mine. Taking a longer-term view of optimisation, our Flow Planner is able to consider more specific objectives, that is, achieving the production targets while minimising operating
costs. The truck operating costs are simply modelled as a cost per unit time of operation per
truck. The process plant feed cost is incurred when a process plant operates below a minimum
desired throughput. The plan failure cost component models the revenue lost due to not meeting
the production targets. Combinations of material blocks and target destinations can have different plan failure costs, enabling prioritisation, or speculative ‘stretch goals’ to be included.
3.1 MIP model
The units of the variables and parameters used in the MIP do not matter as long as they
are consistent. While material flows are specified in terms of volume of material, this can
be interchanged with material mass without consequence. The indices used in the developed
MIP are as follows:
t ∈ T
time periods
θ ∈ Θ truck types
s ∈ S
shovels
i, j ∈ L locations
b ∈ B blocks
i, j ∈ D all dumps (process plants, stockpiles, waste dumps)
i, j ∈ C process plants
A given shift is divided into a set of time periods
{
}
t max
…
.
}
t max L is the set of locations. The set of blocks is a subset of locations, B L. Similarly, D L indicates the set of
dumps, C D indicates the set of process plants.
The flow rates in this model represent both the loaded truck flows (from blocks to dumps)
and the empty truck flows (from dumps to blocks). For example, suppose that the flow rate
from block b to process plant c is 100 kg/s at time period t. This requires an equivalent of
100 kg/s of empty trucking capacity to be arriving (empty) at block b in time period t, in
order for it to also be departing (loaded). Therefore the flow of empty trucks (from dumps to
blocks) is also calculated. Apart from ensuring this logical consistency, this also allows complementary flows to be discovered; it may be advantageous for trucks to alternate between
two cycles that move material in opposing directions (i.e. where the empty haul routes for
trucks alternating between the cycles is shorter than the empty haul of trucks remaining on
the same cycle).
The following sets are defined in order to aid the description of MIP decision variables.
Let N i be the set of possible destinations for material from a location i L. If i B, then
N D
i
N N
meaning that loaded trucks leaving a block cannot travel to another block, only
dumps. Similarly, if i D, then N B
i
N N
, which indicates that empty trucks leaving any dumps
can only travel to blocks to be loaded.