Open-pit design starts with two questions: which part of the deposit can be mined profitably, and in what sequence mining creates the most value. The answers come from geostatistical modelling, pit optimisation and production scheduling.
Block model and economic block value
The deposit is divided into regular blocks, and the grade of each block is estimated by geostatistical methods such as kriging, based on drill-hole data and variography. An economic value is then calculated for each block:
Block value = revenue from recoverable metal − processing cost − mining cost
Blocks with negative value that must be removed to access profitable blocks are treated as waste.
Pit optimisation algorithms
- Lerchs–Grossmann (1965): a graph-theory algorithm that finds the closure of blocks with maximum total value while honouring slope constraints.
- Pseudoflow: a faster method giving equivalent results, used in modern software.
- Nested pits: applying a range of revenue factors produces a series of pits used to define pushbacks and to test price sensitivity.
Overall slope constraints are derived from geotechnical studies and set separately for each structural domain.
Cut-off grade
The breakeven cut-off grade is the lowest grade whose revenue covers its processing cost:
Cut-off = (processing cost + G&A) ÷ [(price − refining & selling cost) × recovery]
Lane's theory (1964) showed that when mine, mill and market capacities and the time value of money are considered, the optimal cut-off varies over mine life and is usually higher in the early years.
Production scheduling
With the final pit and pushbacks defined, long- and short-term schedules are developed to maximise NPV while respecting mining and processing capacities, balancing stripping ratio and keeping plant feed grade consistent. Software such as NPV Scheduler, Datamine and Vulcan is used at this stage.
Conclusion
Pit optimisation is iterative and should be revisited as the geological model, prices and costs are updated. AriaHangard's mining engineering group provides resource evaluation, 3D modelling, pit optimisation and production scheduling for open-pit and underground mines.