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A unique approach to maximizing NPV
A unique approach to maximizing NPV
This case study is based on the MSc research of Alexey Tsoy at the Camborne School of Mines, University of Exeter. The study explored how value generation in mining can be enhanced when constraints are considered directly in the optimization process, rather than handled sequentially after geometric design.
While the stepwise structure of traditional methods of mining planning provides clarity for geometric analysis, it also breaks the link between geometry and economics, often leading to suboptimal financial performance. This research examined the limitations of such traditional frameworks and tested how MiningMath’s Single-step Mine Optimization can unify all planning parameters (mining rate, processing capacity, blending, time value, and multiple destinations) within a single optimisation model.
Using a copper deposit in Zambia as a reference, the study findings highlight how traditional methods ensure geometric feasibility but fail to maximise Net Present Value (NPV), while MiningMath achieves both economic optimisation and operational consistency under real constraints indicates the transition from Lerchs–Grossmann geometry-based optimization to MiningMath’s Single-step Mine Optimization represents a breakthrough in strategic mine planning.
Traditional open-pit planning follows a stage-wise optimisation workflow that defines pits and cut-offs independently of operational constraints. These methods produce consistent geometries but disregard time value, processing alternatives, and throughput limitations, leading to an underestimation of a project’s full economic potential.
MiningMath’s Single-step MIning Optimization eliminates this gap by solving the mine scheduling problem in a single step. It integrates all relevant constraints simultaneously and optimises directly for N
When applied to the same block models used in Alexey Tsoy’s MSc research, MiningMath’s approach achieved up to 50% higher NPV than traditional methods while maintaining operational feasibility. The case illustrates how integrating constraints into the optimisation process transforms theoretical potential into tangible value for mining companies.
The tests were conducted on a copper deposit in Zambia containing sulphide and oxide ores. Processing involved flotation (to produce concentrate) and tank leaching (to produce copper cement). Some blocks required sequential processing through both methods.
The Lerchs–Grossmann algorithm remains the standard for open-pit optimisation, defining the ultimate pit and pushbacks based on block values calculated from fixed cut-off grades.
A typical workflow involves:
Building a block model.
Running pit optimization (LG algorithm).
Designing pushbacks.
Scheduling and sequencing.
Reporting production and stockpiling.
This structure provides reliable geometric outputs but is unconstrained and fails to represent the complex interactions between mining, processing, and economics. It excludes fundamental strategic elements such as:
Throughput or plant capacity limitations.
Discount rate and time value of money.
Stockpile rehandling and feed variability.
Interdependencies between ore types and processing routes.
Dependence on subjective decisions in phase definition.
Results that do not directly account for the time value of money.
Risk of inconsistency between mine-plant capacity and sequencing.
Problems such as the Gap Problem, which require the creation of artificial sub-phases.
The outcome is geometrically valid but economically incomplete, producing stable pit geometries. However, they cannot capture the dynamic trade-offs between mining and processing. Main limitations include:
Absence of system constraints during optimisation.
Static cut-off grades detached from market and process realities.
Sequential decision-making across pit, pushbacks, and scheduling.
Optimisation focused on geometry, not on total economic value.
Consequently, even well-designed pits can produce suboptimal NPVs when real constraints are applied later in the process.
Mining operations are value chains with interdependent bottlenecks. Constraints such as blasting, hauling, milling, or leaching capacity determine overall system performance.
Following Goldratt’s Theory of Constraints, system optimisation requires:
Identifying the constraint.
Exploiting it efficiently.
Subordinating other operations to it.
Elevating it when justified.
Reassessing as the constraint evolves.
MiningMath operationalises these principles by embedding them within a mathematical optimisation model that maximises discounted cash flow under all constraints.
MiningMath’s Single-step Mine Optimization solves the mine scheduling problem holistically. It uses mixed-integer linear programming (MILP) to find the optimal set of extraction, processing, and destination decisions that maximise NPV.
Additionally, in MiningMath, the cut-off grade is not predefined. Instead, it becomes a dynamic variable determined within the optimisation process, allowing value-based routing between multiple destinations.
The system simultaneously considers:
Mining, processing, and stockpiling capacity.
Ore type blending and grade distribution.
Economic factors such as recovery, cost, and discounting.
This approach ensures that each tonne mined follows the most profitable path throughout the value chain, without relying on static thresholds or manual iteration.
Key advantages include:
Integration of all constraints into one model.
Simultaneous evaluation of geometry and time-discounted value.
Automatic handling of multiple processing routes and blending targets.
Rapid generation of optimised, feasible schedules.
This unified structure removes the need for iterative cycles between pit optimization and scheduling, producing one integrated plan that reflects both economic and operational reality.
Produced standard ultimate pits and pushbacks.
Ignored throughput and processing constraints.
Generated a sequence focused on tonnage, not NPV.
Served as a valid geometric reference, but not an economic optimum.
Produced a constrained, time-discounted schedule integrating all process and capacity limits.
Dynamically assigned blocks to flotation, leaching, stockpiling, or waste, based on their NPV contribution.
Reordered phases to prioritise higher-value material earlier in the schedule.
Delivered an NPV approximately 50% higher than the Lerchs–Grossmann–based plan, under identical input data.
The improvement was due to MiningMath’s capacity to jointly optimize extraction sequence, processing route, and scheduling—decisions that are handled separately in traditional methods
| Early-Stage Sb Project | Cu Deposit with Defined Resources | Producing Au Company | |
|---|---|---|---|
Traditional Method Results | Generated indicative pits but no throughput integration. | Delivered a consistent reserve estimate. | Required multiple independent pit and stockpile models merged manually. |
MiningMath Results | Produced realistic throughput-constrained scenarios, offering early insights into scale and value trade-offs. | Maintained similar tonnages but achieved 50% higher NPV through integrated sequencing and destination control. | Completed full-system scheduling in two weeks, integrating variable ore hardness (Bond Work Index) and multiple pits in one optimization, revealing new operational priorities and higher economic efficiency. |
Whereas traditional approaches deliver feasible geometry and standard reporting, MiningMath provides an integrated, constraint-aware solution that directly maximises NPV and ensures operational consistency.
Direct NPV maximisation under discounting.
Unified constraint management across mining, processing, and blending.
Rapid generation of multiple “what-if” scenarios.
Automatic derivation of cut-off values within the optimisation.
Better risk control through system-based modelling.
Improved capital allocation and bottleneck identification.
Strategic long-term scheduling aligned with business goals.
Scalability for multi-deposit or corporate optimisation.
Reliable scientific basis to justify investments.
Traditional methods remain useful for preliminary geometric evaluation but lack the analytical depth and financial insight required for integrated decision-making in modern mining operations.
In all applications derived from Alexey Tsoy’s study, MiningMath achieved superior economic results compared to traditional methods, demonstrating how a unified optimisation model can convert theoretical potential into measurable financial gains.
Discover how Single-step Mine Optimization can turn constraints into value. Contact us to maximize NPV and ensure realistic, profitable mine plans.
Windows 64-Bit (x86_64) - 121 MB
Windows 64-Bit (x86_64) - 121 MB
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