341
potentially change the outcome: the hill could move up or down, left or right. The shape of
the hill can be different with the change of one input, or a combination of a set of changes.
This is an important exercise to validate the model, and also to test sensitivities of the major
inputs, such as mining methods, metal prices, etc.
Some observations from the HoV analysis:
• Changing the metal price will move the NPV hill up and down, but not left and right. This
indicates that the optimal cut-off grade is relatively stable when the metal price changes.
By contrast, the cut-off grade calculation with the traditional break-even cut-off grade
calculation is directly linked to metal price (linear relationship).
• The profile of the NPV hill is very sensitive to the discount rate. For major capital investment projects, it is important to set up the right discount rate to reduce the risk and generate acceptable rate of turns.
2.5 Schedule optimization
HoV provides strategic guidance to the detailed tactical and operational mine planning.
With modern commercial mine planning software, mining sequences with predecessors and
successors can be systematically set up with rules and logics, to make sure the mine plans
are practical, following the proper mining sequences and operational constrains. Resource
leveling is a useful scheduling tool and is available through commercial mine planning
packages. Resource leveling, by definition, is a technique in which start and finish dates are
adjusted based on resource constraints with the goal of balancing demand for resources with
the available supply
[9] . One of the limitations of resource leveling, as a smoothing tool, is
the lack of optimization algorithms, and that the leveled mine plan cannot always follow
objectives as identified by the HoV analysis.
A few schedule optimization tools have been applied for this project, named as SOT and
OMP
[10]
. SOT, is commercially available, uses the mine design and sequence as input, including
precedence links between development and stoping activities. Mining properties such as duration,
length, weight, product grades, activity types and mine area, can be imported into SOT for each
mining activity. Mining scenarios, consisting of operational resources and capacities, discount
rate, metal prices, operating costs, and capital costs, can be set up in SOT to test various options.
SOT uses the heuristics algorithm to optimize the NPV of long term mine schedules
[11]
. OMP
uses Bienstock-Zuckerberg (BZ) algorithm with focus on solving resource constrained project
scheduling problems
[12]
. We tested OMP to produce ‘seeds’ to speed up the SOT runs.
For this project the mine design has a number of parameters that need to be balanced to
determine a viable mine schedule by using SOT, which can be tailored to specific user inputs
such as production constraints, targets and mining resources. To avoid peaks and troughs of
resource demand and utilization, some of the critical constraints should be applied:
• Geotechnical constraints
• Ventilation constraints
• Equipment resource constraints
• Activity constraints by heading, level and zone
• Mill processing constraints
• Geochemistry value constraints for upper and lower bounds
• Multi-layer constraints to create a reasonable and executable mine plan
In addition to the above constraints, for this particular project, SOT was configured
to target high-value stopes in the early years (typically stopes with high gold grades and
favorable geochemistry), with lower value stopes in the later years of the mine life. A number
of different production rates were tested using SOT, ranging from 700ktpa to 1000ktpa in
increments of 100ktpa. For each of the scenarios, different mining and milling costs (and
subsequently cut-off grades) must be considered, in order to determine the relative NPV.
The mine planning cut-off grade for the project is dynamic. A “two pass” approach was
applied, with mining of high grade ore in the early years to maximize NPV followed by
mining of lower grade ore in the later years to improve free cash flow. This “two-pass”
potentially change the outcome: the hill could move up or down, left or right. The shape of
the hill can be different with the change of one input, or a combination of a set of changes.
This is an important exercise to validate the model, and also to test sensitivities of the major
inputs, such as mining methods, metal prices, etc.
Some observations from the HoV analysis:
• Changing the metal price will move the NPV hill up and down, but not left and right. This
indicates that the optimal cut-off grade is relatively stable when the metal price changes.
By contrast, the cut-off grade calculation with the traditional break-even cut-off grade
calculation is directly linked to metal price (linear relationship).
• The profile of the NPV hill is very sensitive to the discount rate. For major capital investment projects, it is important to set up the right discount rate to reduce the risk and generate acceptable rate of turns.
2.5 Schedule optimization
HoV provides strategic guidance to the detailed tactical and operational mine planning.
With modern commercial mine planning software, mining sequences with predecessors and
successors can be systematically set up with rules and logics, to make sure the mine plans
are practical, following the proper mining sequences and operational constrains. Resource
leveling is a useful scheduling tool and is available through commercial mine planning
packages. Resource leveling, by definition, is a technique in which start and finish dates are
adjusted based on resource constraints with the goal of balancing demand for resources with
the available supply
[9] . One of the limitations of resource leveling, as a smoothing tool, is
the lack of optimization algorithms, and that the leveled mine plan cannot always follow
objectives as identified by the HoV analysis.
A few schedule optimization tools have been applied for this project, named as SOT and
OMP
[10]
. SOT, is commercially available, uses the mine design and sequence as input, including
precedence links between development and stoping activities. Mining properties such as duration,
length, weight, product grades, activity types and mine area, can be imported into SOT for each
mining activity. Mining scenarios, consisting of operational resources and capacities, discount
rate, metal prices, operating costs, and capital costs, can be set up in SOT to test various options.
SOT uses the heuristics algorithm to optimize the NPV of long term mine schedules
[11]
. OMP
uses Bienstock-Zuckerberg (BZ) algorithm with focus on solving resource constrained project
scheduling problems
[12]
. We tested OMP to produce ‘seeds’ to speed up the SOT runs.
For this project the mine design has a number of parameters that need to be balanced to
determine a viable mine schedule by using SOT, which can be tailored to specific user inputs
such as production constraints, targets and mining resources. To avoid peaks and troughs of
resource demand and utilization, some of the critical constraints should be applied:
• Geotechnical constraints
• Ventilation constraints
• Equipment resource constraints
• Activity constraints by heading, level and zone
• Mill processing constraints
• Geochemistry value constraints for upper and lower bounds
• Multi-layer constraints to create a reasonable and executable mine plan
In addition to the above constraints, for this particular project, SOT was configured
to target high-value stopes in the early years (typically stopes with high gold grades and
favorable geochemistry), with lower value stopes in the later years of the mine life. A number
of different production rates were tested using SOT, ranging from 700ktpa to 1000ktpa in
increments of 100ktpa. For each of the scenarios, different mining and milling costs (and
subsequently cut-off grades) must be considered, in order to determine the relative NPV.
The mine planning cut-off grade for the project is dynamic. A “two pass” approach was
applied, with mining of high grade ore in the early years to maximize NPV followed by
mining of lower grade ore in the later years to improve free cash flow. This “two-pass”