Article 4: Step 4 ­– Risk assessment of your Strategic Mine Plan

So far in this series of articles, we have looked at how to:

• assess directional pit shell strategies
• identify the right level of investment through optimisation of production scales, and
• apply simultaneous optimisation to attain a higher value strategy within a pushback sequence and mining and processing limits.

With all of these calculations and trade-offs decided, it’s now time to assess the risks associated with the draft plan using multiple design scenarios. “Multiple” is the key word here. One or two scenarios are simply not enough to account for the fact that KPI responses are non-linear: increasing the throughput and cut-off grade, either jointly or separately, for example, will not necessarily lead to a proportional increase in value.

Traditionally, mine planners run multiple design scenarios using some form of strategic mine planning software, such as GEOVIA Whittle. But using Whittle alone only allows for tens of scenarios; using GEOVIA’s Strategic Mine Planning workflow – created using GEOVIA Whittle strategic mine planning software and SIMULIA process-automation tools – allows for thousands.

Furthermore, GEOVIA’s Strategic Mine Planning workflow allows the mine planner to build risk assessment into each step of the workflow by including additional sets of uncontrolled variables, such as noise or small variabilities around a traditionally fixed value.

Uncertainty sources and analysis

Uncertainty analysis is a method for quantitatively evaluating uncertainty in scenario components, such as input variables and parameters, and deducing an uncertainty distribution for each output variable rather than a single value.

A novel way to perform uncertainty analysis is by taking advantage of the current computational power through the Monte Carlo method, which is used to sample a random output, based on many deterministic simulations of an specific algorithm or routine, using random inputs that are governed by a probability density function.

Through GEOVIA’s Strategic Mine Planning workflow, the mine planner can link together Design of Experiments routines, to identify high-performance design configurations, with Monte Carlo simulations, to provide a stochastic value for the variables in each scenario.

(However, because executing Monte Carlo simulations while performing a full-size Design of Experiments could easily amount to 100,000 or more iterations, we recommend running the Monte Carlo methods described below against a small subset of identified high-performance designs.)

GEOVIA’s Strategic Mine Planning workflow allows the mine planner to include some sources of uncertainty through the use uncertainty analysis to determine the accuracy of the definition of the final pit and pushbacks as well as the production scale and schedule. Monkhouse and Yeates, in Beyond Naïve Optimisation (2007), identified the sources of uncertainty as:

• Orebody uncertainty, which includes uncertainty in grade variability and the resulting effect of it on various aspects of open pit design and planning.
• Processing uncertainty, which includes both block-to-block attributes for estimating geo-metallurgical performance (such as hardness or element recovery) and overall parameters which are usually common for all blocks (such as costs and throughput).
• Market uncertainty, which includes price uncertainty and, for some commodities, volume uncertainty regarding the demand for certain product specifications.
• Discount rate uncertainty, which includes political risk, country risk, and other capital-related considerations that may alter the NPV.  (In mining, NPV is often calculated using a fixed interest rate to discount the yearly cash flows estimated from mine planning and scheduling, so different rates will affect the trade-off between the actual versus future benefits.)
• Changing technologies uncertainty. Accounting for a major technology upgrade that could affect the mine plan is challenging because it is difficult to know for certain that the upgrade will happen and when, and whether it will actually increase quality, decrease costs, lead to higher recovery rates, etc.  

Risk measurements

There are a number of different methods for measuring and comparing the performance of the design configurations against the variability introduced by the uncertainty sources. However, each method has a drawback. For example:

• Average, standard deviation and coefficient of variation – traditional statistics used to assess results dispersion around the mean – do not consider any lop-sidedness in the results distribution.
• Value at Risk (VaR), which is the maximum loss possible over a target, usually the average, at a given level of confidence, usually 1% to 5%, may give a false sense of security since it ignores what happens in the tails of the output’s probability distribution.
• Expected Shortfall (ES) or Conditional Value at Risk (CVaR), which is the expected amount of loss for the fraction of cases where the VaR is exceeded, estimates risk in a conservative way but also fails to consider the most catastrophic outcome (known “white swan” or unknown “black swan”).
• Probability of success, which is calculated as a simple ratio of the number of cases (simulations) with a favourable outcome (defined by who performs the simulation) divided by the total number of simulations performed, is useful only when addressing Boolean choices – for example, defining if blocks are or are not inside a pit shell envelope.Difference between ES (or CVaR) and VaR from Transfer and Generalisation of Financial Risk Metrics to Discrete Event Simulation by Koors and Page (2012).

These drawbacks make it important for the mine planner to use a combination of these methods to arrive at the most accurate and reliable assessment of risk.

Assessing orebody uncertainty

How

There are many different methods for including orebody uncertainty in open pit optimisation, but the majority of experts rely on the use of conditional simulations – a version of a Monte Carlo simulation performed over the block-model estimation that creates several realisations of the block model.

When

Where experts differ is when to perform pit optimisation:

• Some prefer to perform pit optimisation for every realisation of the block model, and then find a way to join all of the generated shells, either through intersection or flagging the block model and selecting blocks according to a statistic criterion, such as a specific percentile.
• Others prefer to process the results of every realisation of the block model before performing the pit optimisation, an approach that also calculates the expected economic value of all realisations rather than the economic value of the expected grades (average grade of all realisations).

Assessing processing, market and discount rate uncertainty

Addressing processing, market and discount rate uncertainty in pit optimisation is simpler than addressing orebody uncertainty because it does not involve the use of conditional simulations and multiple realisations of the block model (a very large input to vary).

Instead, we have discovered, it can be done easily by including variability through Monte Carlo simulations governing the to-be-assessed input variables of the pit optimisation routine, and then performing the optimisation routine for each scenario.

The primary result of this assessment is a set of final pit shells, each produced through optimisation using stochastic input parameters. This information can then be stored within the block model, making it easier to identify blocks within an envelope that most likely will be included, and/or the envelope that represents a specific VaR or CVaR between all the generated pit shells.

Probability of the blocks of belonging to the final envelope, from Optimising Project Value and Robustness by Whittle, Stange and Hanson (2007).

Assessing risk in the schedule

There are two widely accepted approaches to assessing risk in scheduling:

• A flexible approach responds to different uncertainty scenarios by changing some of its parameters dynamically, usually based on Real Options (ROs), such as expand, wait, abandon, etc. This approach involves identifying which ROs can be taken in each mining period and evaluating each path based on several uncertainty scenarios before selecting a high-value design and RO path.
• A robust approach uses a fixed system that can withstand a wide spectrum of uncertainty scenarios without changing its parameters. This approach measures performance by comparing the KPIs of a large number of designs against a large number of uncertainty scenarios and defining risk measurement statistics to identify a robust design configuration (best average, VaR, probability of success, etc.)

While there is wide consensus that the flexible approach will produce higher theoretical performance (usually expected NPV) than the robust approach, many mining operations simply do not have the required flexibility, especially if ROs are considered at intervals of a year or less. Furthermore, as the probabilities within each uncertainty scenario govern the valuation of each decision path, identifying which events should trigger choosing/not choosing an option in a specific mining period is not a simple task.

With GEOVIA’s Strategic Mine Planning workflow, we believe a robust approach is better, because it enables the mine planner – using tools readily available in our portfolio – to identify a production scheduling sequence that adheres to both the company’s objectives and its commitments to different stakeholders.

Think of it as a multi-Hill-of-Value analysis, in which a Hill-of-Value surface is created for each uncertainty scenario. User-defined statistics, selected to measure robustness or other desired behaviours oriented toward strategic objectives, are then employed to summarise the results and make sense of the multiple surfaces.

In addition, we have identified some anti-fragile design configurations that can lower or stabilise the variance of output KPIs, given an increase in the volatility of the stochastic uncertainty scenarios (inputs). This allows the mine planner to trade-off between robust scenarios with higher expected NPV for a given level of uncertainty, and anti-fragile scenarios that can behave better when the level of uncertainty varies.

Conclusion

Our objective through this series of articles has been to share methods for making strategic mine planning work for you through automated workflows, that maximise the value of increasingly scarce resources and help future-proof mine planning decisions. This can be set-up and run to map the best possible solutions through thousands of scenarios, while considering the behaviour of different design configurations against a set of uncertain scenarios.

All the methods we have discussed form part of Dassault Systèmes’ Strategic Mine Planning Industry Process Experience (IPE), which combines SIMULIA automation and analysis software with GEOVIA mine-planning solutions, including:

• GEOVIA Whittle for open pit mining
• GEOVIA Caving PCBC and PCSLC for underground cave mining, and
• GEOVIA Surpac’s Stope Shape Optimizer for underground stope mining.

Within the world of open-pit mining specifically, this IPE has helped customers:

• identify design set-ups that result in high-performance sequences that improved their NPV from 10% up to 50%, and
• develop directional pushback strategies that reduced the stripping ratio by 16% to 20%, resulting in lower mining costs.

In addition:

• panel caving customers found a 30% improvement in the accuracy of grade forecasting through advanced scheduling and calibration of mixing algorithms using both GEOVIA Caving PCBC and SIMULIA software, and were able to identify a scenario that will result in a 10% reduction in development cost, while
• for a sub-level open stoping project, an automated workflow using GEOVIA Surpac’s Stope Shape Optimizer to define economically feasible stopes and Python code to perform a preliminary stability assessment based on empirical methods resulted in significant time savings: from a manual process of about one month to a semi-automatic process of about three days.

In summary, Dassault Systèmes’ Strategic Mine Planning IPE allows mine planners to:

• thoroughly explore all solutions by calculating thousands of scenarios that consider both design parameters and uncontrolled variables to reveal the best possible performance scenarios in line with the company’s strategic objectives
• create a collaborative environment, using SIMULIA software not only to simulate but also to process and analyse results using tables and charts that can then be stored and shared with decision makers and stakeholders on Dassault Systèmes’ 3DEXPERIENCE Platform, and
• save time by using automatic workflows that need only a single setup to assess thousands of scenarios so they can concentrate on what is most important: analysing results and making decisions.

Joaquín ROMERO is a Mining Industry Process Consultant at Dassault Systèmes GEOVIA with 5 years of experience in Industry and Consulting. Joaquin holds a BEng and MEng in Mining Engineering specialized in the use of simulation techniques for robust strategic planning (SMP) for open pit and panel caving mines. Joaquín´s experience began as an intern at Dassault Systèmes, playing a key role in the development of the SMP-OP methodology using GEOVIA Whittle and SIMULIA Isight. After his internship in 3DS, Joaquín extended his knowledge towards underground panel caving operations as an Extraction Process Chief at CODELCO’s El Teniente Mine. Joaquin returned to the 3DS GEOVIA Services team to help customers such as VALE, ARGOS and CHINALCO among others, with the implementation of SMP.

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