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24-058
MILP Production Scheduling Models for
Evaluating Continuous Improvement Projects
Steven Hoerger
Peak View Mine Planning, Englewood, CO
SUMMARY
Mixed integer linear programming (MILP) production
scheduling models can be used to evaluate if tonnage
improvement projects will deliver value over all time periods
and whether new bottlenecks will be created. These MILP
models can evaluate the interconnected effects of mine and
process capacities, mining locations, cutoff grades, stock-
piles, and orebody grade/tonnage distributions.
A case study compares potential value creation from a
mine capacity increase, a mill capacity increase, or a simul-
taneous increase in all capacities. For perspective, proj-
ect valuations for capacity increases are compared against
valuations for cost reduction projects, mine planning
improvements such as phase design, dynamic cutoff grades
and stockpiling, and the impact of geostatistics improve-
ments in the areas of block model accuracy and ore control
selectivity.
INTRODUCTION
Mine planners seek to create production schedules to
maximize the value generated from an orebody subject to
mining and processing constraints and defined cost struc-
tures. Continuous improvement (CI) leaders often focus
on increasing value by expanding constraints and improv-
ing cost structures. Accurate prediction of the value to be
created by constraint expansions requires understanding
how production schedules will change as mine and pro-
cess capacity changes interact with orebody grade-tonnage
distributions. Accurate estimates of value creation allow
CI investments to be prioritized against each other and
against available capital budgets and organizational change
bandwidth.
An open pit production schedule defines which loca-
tions are mined when—the mining sequence—and which
mined material is sent to which destination at which time—
the processing sequence (Clark and Dagdelen, 2023). The
destinations could be a waste dump, stockpile or one or
more processing facilities that generate a saleable product.
At an operation with a single processing facility, the pro-
cessing sequence is often expressed as a cutoff grade sched-
ule: material above a time period’s operating cutoff grade is
sent to the processing facility material below the operating
cutoff is sent to the waste dump. A breakeven cutoff ensures
that material above cutoff generates sufficient revenue to
cover the costs of processing the material vs the alterna-
tive of sending the material to the waste dump. An oper-
ating cutoff should cover these costs plus the opportunity
cost of delaying the processing of future material (Rendu,
2014). At many mines, a stockpile cutoff is also used to
define material to be saved for processing at the end of the
mine life or during periods of insufficient ore availabil-
ity. The optimum mining and processing sequences often
result in “balanced” operating cutoff grades where yearly
tons mined equals the mining capacity constraint and
yearly tons mined above the operating cutoff grade matches
the processing constraint (Lane, 1988). In this situation,
where both mining and processing are bottlenecks, translat-
ing constraint expansions into expected metal production
increases becomes challenging because the capacity changes
lead to cutoff changes in each time period.
24-058
MILP Production Scheduling Models for
Evaluating Continuous Improvement Projects
Steven Hoerger
Peak View Mine Planning, Englewood, CO
SUMMARY
Mixed integer linear programming (MILP) production
scheduling models can be used to evaluate if tonnage
improvement projects will deliver value over all time periods
and whether new bottlenecks will be created. These MILP
models can evaluate the interconnected effects of mine and
process capacities, mining locations, cutoff grades, stock-
piles, and orebody grade/tonnage distributions.
A case study compares potential value creation from a
mine capacity increase, a mill capacity increase, or a simul-
taneous increase in all capacities. For perspective, proj-
ect valuations for capacity increases are compared against
valuations for cost reduction projects, mine planning
improvements such as phase design, dynamic cutoff grades
and stockpiling, and the impact of geostatistics improve-
ments in the areas of block model accuracy and ore control
selectivity.
INTRODUCTION
Mine planners seek to create production schedules to
maximize the value generated from an orebody subject to
mining and processing constraints and defined cost struc-
tures. Continuous improvement (CI) leaders often focus
on increasing value by expanding constraints and improv-
ing cost structures. Accurate prediction of the value to be
created by constraint expansions requires understanding
how production schedules will change as mine and pro-
cess capacity changes interact with orebody grade-tonnage
distributions. Accurate estimates of value creation allow
CI investments to be prioritized against each other and
against available capital budgets and organizational change
bandwidth.
An open pit production schedule defines which loca-
tions are mined when—the mining sequence—and which
mined material is sent to which destination at which time—
the processing sequence (Clark and Dagdelen, 2023). The
destinations could be a waste dump, stockpile or one or
more processing facilities that generate a saleable product.
At an operation with a single processing facility, the pro-
cessing sequence is often expressed as a cutoff grade sched-
ule: material above a time period’s operating cutoff grade is
sent to the processing facility material below the operating
cutoff is sent to the waste dump. A breakeven cutoff ensures
that material above cutoff generates sufficient revenue to
cover the costs of processing the material vs the alterna-
tive of sending the material to the waste dump. An oper-
ating cutoff should cover these costs plus the opportunity
cost of delaying the processing of future material (Rendu,
2014). At many mines, a stockpile cutoff is also used to
define material to be saved for processing at the end of the
mine life or during periods of insufficient ore availabil-
ity. The optimum mining and processing sequences often
result in “balanced” operating cutoff grades where yearly
tons mined equals the mining capacity constraint and
yearly tons mined above the operating cutoff grade matches
the processing constraint (Lane, 1988). In this situation,
where both mining and processing are bottlenecks, translat-
ing constraint expansions into expected metal production
increases becomes challenging because the capacity changes
lead to cutoff changes in each time period.