Whittle Modules

Gemcom Software International Four-X Analyser Modules The Four-X Analyser product suite consists of the following modules: Foundation Multi-element Mining Width Milawa Algorithm Multi Analysis Advanced Analysis Stockpile and Cut Off Optimisation Buffer Stockpiles Blending

Foundation: Data Importation The Four-X Analyser Foundation will accept data in the industry standard Whittle format. Resource model files and Pit design/Reserve files can be imported, with or without a Parameters File. Four-X imports and exports data through specialized interfaces, most of which are built into generalized mining packages for convenience. Gemcom, Micromine, Medsystem, Surpac and others include such an interface in its block modelling software. On completion of importation, a brief summary is presented to enable reconciliation with the original data.

Model Manipulation This function analyses an existing Block Model, performs transformations on it, and creates a new (re-blocked) Block Model. The transformations that can be performed include: • • • • •

Adding expensive blocks for the purpose of biasing the pit optimisation (Add blocks tab). This can be used for example, to stop pits encroaching on lease boundaries etc. Adjusting the model framework (Adjust framework tab). This is usually performed to allow pits to expand to areas outside the model framework. Calculating positional cost adjustment factors for mining and processing costs with user-defined expressions. Adjusting the shape and size of the blocks (Adjust blocks tab). Combining mineralised parcels, to improve mining selectivity modelling. Additional functions are included under the Tools Menu for advanced data manipulation.

Pit Slope Modeling This is the most comprehensive and flexible slope modelling system available for pit optimisation. Pit slope definitions can be defined for the whole model in a variety of flexible ways. Up to fifty slope profiles are defined. Each profile consists of up to eight bearing / slope pairs. Profiles can then be assigned to different parts of the block model in the following ways: • • • •

Rectangular slope regions. Rock-types in the Model file. Zone Numbers in the Model file. Profile Numbers in a Profile Number file.

The slope model can also include user-defined “additional arcs” which are used to define complex relationships between different parts of the model, and link together blocks, which must be mined together. The slope model is used to control the manner in which pit shells are generated in the pit optimization process.

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Gemcom Software International Pit Optimisation Pit optimisation is carried out by a Whittle implementation of the well-known Lerchs Grossmann algorithm. It is able to respond to: • • • •

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Very simple or very complex pit slope modelling, including the application of user-defined “additional arcs”. “Expensive” blocks, defined by the user in the reblocking node. Expensive blocks can be used to represent lease boundaries or immovable objects such as processing plants, which cannot be under-mined. Price, cost and processing models can be based on very simple inputs or very complex user-defined expressions. Cost and prices can be expressed simply as “dollars per tonne” or “dollars per gram”, or they can be modelled using user-defined expressions. User-defined expressions can include a range of variables and functions. For example, it is possible to build an expression to vary the cost of processing depending on the grade and position in the model from which the ore came. Recoveries can be represented as a simple percentage, or the expression builder can be used to build a complex variable recovery function.

The pit optimization is controlled by a range of user-controlled setting, which affects the precise manner in which the optimization proceeds. Up to 100 optimal pit outlines are produced in a single run of the Pit Shells node.

Economic Scenario The economic scenario sets the base case for scheduling and analysis, including costs, prices, throughput limits, recoveries etc. Users can apply the same settings that were used in the pit optimization or they can change them in order to apply special analysis techniques. The vast majority of the settings in the Economic Scenario can be changed over time, adding to the sophistication of the model.

Analysis and Graphs The user can specify the use of three different life-of-mine scheduling techniques, and view graphs of the results, or export data for analysis in a spreadsheet. The options include: • • • •

Schedule Graph – shows tonnes mined and tonnes processed for each period in the mine life. Pit-by-Pit Graph – shows tonnage and NPV values for a range of different pits using three different scheduling methods. It is possible to have as many as 300 life-of-mine schedules represented in a single graph. Size v. Value Graph – A variation on the Pit-by-Pit Graph showing the total mine tonnage and NPVs for three different scheduling methods. Custom Period Graph – A user-defined analysis for a single life-of-mine schedule. The user can choose from hundreds of variables to display in the graph. All data that is displayed in graphs can be exported for further analysis in a spreadsheet program. Each analysis generates a comprehensive report, outlining all the assumptions and settings, and the details of all the life of mine schedules produced.

Data Export Four-X Analyser Foundation allows a large range of data and reports to be exported or printed. They include: • • • • •

Audit reports for each model import; pit slope modelling; pit optimization and analysis/life-of-mine scheduling. Block models. Schedules. Pit outlines. Analysis data.

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Gemcom Software International Data Visualisation Four-X Analyser Foundation includes an interactive 3D visualiser, which allows pit contours to be viewed instantly. This viewer is very fast, so pits can be moved and spun around in real time. Viewing one pit to another is instantaneous. As well as the pit contours, data planes show grades, or other model file information. Users have control over how the contours look and can switch data planes on or off and set up custom grade colour schemes. This same visualiser can be used to: • • •

View model files – examine the model in three dimensions. Examine all the variables in the model. View pit shells – examine the pits overlayed on the block model if you wish. View mining schedule – watch the pit grow from period to period.

Multi-element The Multi-element module allows up to ten elements to be defined in the model. Individual elements and reported separately and the grades and quantities of each element are available for use in user-defined expressions, graphs and reports. Multi-element capabilities are very useful for analysing multi-product mines. The capability can also be used for: • •

Applying grade-dependent costs, prices and recoveries. It could be that the recovery of one element is dependent on the grade of another. Allowing for deleterious elements by applying stochastic liberation estimation to the recovery function.

Mining Width Users are able to very rapidly adjust their pushbacks to allow for mining width constraints. The speed and repeatability of the process means that users can experiment with different mining widths to see what impact they have. Because the process is contained within Four-X Analyser, the results can be quickly analysed and compared to other scenarios. The mining width module allows users to modify a selection of shells from the pit shells node, allowing for mining width constraints. It is achieved in a fraction of the time it would take to adjust the shells manually in a GMP, and unlike manual methods, it can be strictly controlled and repeated at will. Eleven different settings control the manner in which the adjustments proceed.

Milawa Algorithm The Milawa Algorithm ® adds a new dimension to life-of-mine scheduling. It optimises the schedule, taking into account all your production and economic constraints, while seeking to maximise the utilization of available mining and processing capacity. The Milawa Algorithm® is a proprietary algorithm which schedules phases in order to maximise NPV. It responds to all production constraints, price and cost models within Four-X Analyser and also provides additional controls over the schedule. How does it work? The Milawa Algorithm® consists of three parts: •

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The first part takes a set of variables and generates a feasible schedule from them. A full set of the variables describes the life of mine schedule. The number of variables required depends on the number of benches in the ultimate pit, pushbacks, and time periods in the life of the mine. The possible values for these variables are constrained by what is technically feasible in terms of the pit shell precedence rules and any constraints imposed by the user (mining, processing, selling constraints, maximum and minimum lead, maximum vertical advance per period). The second part is an evaluation routine, which calculates the NPV for an individual schedule. The third part searches the domain of feasible schedules for the one, which has the highest NPV. This routine also has logic built in to decide when to stop searching.

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Milawa does not generate and evaluate all feasible schedules as the number of feasible schedules can be extremely large. Rather it strategically samples the feasible domain and gradually focuses the search (without necessarily narrowing it) until it converges on its solution. The number of evaluations required to converge on a solution varies, but 5000 is typical, and this usually takes less than a minute. The feasible domain can be viewed as a multi-dimensional volume (one dimension for each variable used to describe the life of mine schedule), where each point in the volume has a corresponding NPV. The optimum solution is the point which has the highest NPV, but it is possible for there to be more than one point with the maximum NPV. It is also possible for there to be a range of other solutions, which have NPVs, which are very close to the maximum. Milawa cannot guarantee to find a schedule with the absolute maximum NPV, particularly if the highest happens to occur on a very sharp peak. However, experience has shown that it will find a solution with a very high NPV. The Milawa Algorithm™ can also be run in 'balancing mode'. In balancing mode, the Milawa Algorithm substitutes an evaluation routine, which returns higher, values when production facilities are fully used early in the life of the mine. How good are the results produced by Milawa? The best way to evaluate the results is to compare them to the best case and worst case schedules, which provide very convenient internal high and low benchmarks for the NPV of the project for the configuration and constraints under examination.

Multi Analysis This module significantly extends the capabilities of Four-X Analyser by allowing multiple imported models per project, and branching of the analysis trees thereafter. You can, for example attach several pit slope nodes to an imported model node, each representing a different set of assumptions. Four-X Analyser keeps track of all the data dependencies for you. You can build hugely complex analysis models, which can be viewed, accessed and managed simply. Scenario branching allows you to build up an analysis tree, with all the data dependencies managed by Four-X Analyser, and all the relationships clearly represented on the screen. Features include: • • •

Nodes can have multiple child nodes attached to them. In turn, those child nodes can have their own children, leading to an expanding tree of analysis. Nodes and branches can be cut, copied and pasted. Branches can be collapsed or expanded to hide or reveal the detail.

Advanced Analysis This module allows Four-X Analyser to perform very complex analysis. This is extremely useful to designers who are interested in extensively testing sensitivities, and performing risk analysis. Features include: •

Custom Grand Total Graph. The user can define any one of hundreds of variables (such as mining costs, dilutions, recoveries) to vary over a range, and Four-X will produce a life of mine schedule for each case. The user can display any number of results (e.g. NPV, strip ratio, IRR, ore tonnes) in a graph or export the results to a spreadsheet.

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Custom Schedule Graph - The user can display any number of results (e.g. NPV, strip ratio, IRR, ore tonnes) in a graph or export the results to a spreadsheet. Advanced Grand Total Analysis - The user can define one or more of hundreds of variables (such as mining costs, dilutions, recoveries) to vary over a range, and Four-X will produce a life of mine schedule for each case. For example, varying 3 parameters each over ten steps would lead to the generation of 1000 life of mine schedules. The user can write any number of results (e.g. NPV, strip ratio, IRR, ore tonnes) into a table and either view it, or export the results to a spreadsheet. Spider Diagram - This is a special type of multivariate sensitivity analysis, which is represented in a spider graph. The user chooses several parameters to vary and a percentage to vary them by. The user also chooses which result should be shown in the graph.

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Stockpile and Cut-off Optimisation This module provides comprehensive grade-stockpile and cut off optimisation with the objective of maximizing NPV. The model re-schedules the mining sequence, taking in to account all the constraints and setting in Four-X Analyser and optimising the stockpile utilisation and cut off strategy. It can be used for: •

Determine the optimum usages of grade stockpiles in order to maximise NPV. Gemcom América Latina Fidel Oteíza 1953, Of. 502, Providencia, Santiago. Chile Fono: 562 3412074 Fax: 562 3418569

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Determine the optimum cut-off strategy for maximisation of NPV. The Stockpile And Cut-Off Module includes a whole value chain model, extending its use beyond optimisation, to a vast range of ‘what-if’ analysis and advanced design techniques. Professional mine designers can experiment with different stockpile, processing and mining configurations and rapidly analyse the impact on different parts of value change and the total economic impact.

Buffer Stockpiles Use the Buffer stockpiles module to store material for future periods to avoid future stripping hurdles or to balance mining and processing rates. Users can control whether the stockpile movement is independent of the mining limit. If stockpile movement is independent of the mining tonnage then top-ups can be made at the end of period otherwise the stockpile is only used up at the end of mine life. Users can control whether to use stockpile to balance mining and processing. If they select this option then mining can proceed after the mill is full or production targets have been met with the remainder of the ore being fed to the stockpile.

Blending For bulk commodity applications, the new Blending Module now makes bulk blending, to meet product specifications, and extractive blending much easier than before. This module optimises the blend, and the stockpile usage and when combined with Four-X’s Milawa Algorithm®, also optimizes the scheduling of the mine. All this is driven by the overall objective of maximising the NPV of the whole operation. Whittle have integrated the industry standard LindoTM Linear Programming (LP) engine into Four-X, where it is used to optimize the blend and the stockpile utilisation. Four-X reduces the problem to an LP formulation and passes it to the Lindo optimization engine. Lindo then calculates the solution and feeds the results back to Four-X, which completes the calculations and formats the results for the user. When used in conjunction with the Milawa Algorithm, blend optimizations occur within each Milawa iterative loop, so blend considerations influence the schedule optimization. Combining both the algorithms of Milawa and Lindo leads to an unprecedented ability to handle tremendous complexity. The result is a schedule that meets all your technical requirements, and maximises project NPV.

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