Lane's Cut-off Grade Model
Also known as: Lane Model, Cut-off Grade Optimization, Lane's Optimization Model
Lane's Cut-off Grade Model, developed by Kenneth F. Lane and formalized in his 1988 book, provides a rigorous economic framework for determining the minimum grade at which ore should be mined and processed. It accounts for variable mining costs, metallurgical recovery, and commodity prices to optimize profit per unit processed. The model is foundational in mining economics and underpins daily operational decisions at thousands of mines worldwide.
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When to use it
Apply Lane's model whenever making strategic or tactical ore classification decisions: ultimate pit design, phase planning, stockpile management, or mill feed optimization. Use when commodity prices, costs, or metallurgical parameters are subject to change. Assume ore grades in the block model are accurate and that recovery relationships are known. Use parametric sensitivities to generate a series of pit designs for different price scenarios. Prefer alternatives like discrete linear programming for very complex multi-commodity or multi-constraint problems.
Strengths & limitations
- Simple, analytically solvable framework that mining engineers can understand and apply without software
- Incorporates all relevant economic variables in a single decision criterion
- Naturally handles price volatility by re-calculating cut-off grades under different price scenarios
- Computationally efficient; can be solved in spreadsheets for quick feasibility studies
- Provides economic justification for mining decisions that can be presented to regulators and investors
- Assumes linear relationships between grade and recovery, which oversimplifies nonlinear metallurgical processes
- Does not directly optimize pit geometry or production schedules; must be coupled with pit limit algorithms
- Ignores spatial relationships in the ore body; can lead to unrealistic ore extraction sequences
- Sensitive to cost and recovery function estimates; small errors compound in economic calculations
- Does not natively handle multiple commodities or competing process paths without extension
Frequently asked
How often should I recalculate the economic cut-off grade?
Recalculate whenever major costs change (labor, fuel, power) or when commodity prices move more than 10-15% from the assumed forecast. Many mines update quarterly or monthly. During volatile commodity markets (e.g., gold, copper), weekly or daily updates may be justified.
Can I use Lane's model for multiple ore types with different metallurgical recoveries?
Yes. For each ore type, calculate a separate marginal revenue curve R_i(g) and set a separate cutoff grade g*_i. This is practical when ore types are spatially distinct (e.g., fresh vs. oxide ore). When ore types are mixed in the same block, a more complex optimization is needed.
What if mining costs increase as the pit gets deeper?
Incorporate depth-dependent costs into the marginal cost function: C(g, depth). This makes cutoff grades depth-dependent as well. Deeper, lower-grade material may not be worth mining even if shallow ore above cutoff is being extracted.
How do I handle ore that I mine today but process later?
Ore mined for immediate processing uses the current cutoff grade. Ore stockpiled for future processing should use a lower cutoff (adjusted for storage losses) if you expect commodity prices to rise or costs to fall. This requires scenario analysis and probabilistic forecasting.
Is Lane's model compatible with the Lerchs-Grossmann algorithm?
Yes. Lane's model sets the cutoff grade; Lerchs-Grossmann then optimizes the pit boundary given that cutoff. Alternatively, the pit can be optimized for multiple cutoff scenarios, generating nested pit shells. Some software integrates both methods seamlessly.
Sources
How to cite this page
ScholarGate. (2026, June 3). Lane's Cut-off Grade Model. ScholarGate. https://scholargate.app/en/mining-engineering/cut-off-grade
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Bond Work IndexMining Engineering↔ compare
- Lerchs-Grossmann AlgorithmMining Engineering↔ compare
- PseudoflowMining Engineering↔ compare