MiningMath

MiningMath

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Unlimited scenarios and decision trees for your strategic evaluations

1. Install and activate

System Requirement

The only mandatory requirement for using MiningMath is a 64-bits system, due to its use of Direct Block Scheduling technology. Other minimum requirements are listed further:

  1. Windows 10

  2. 64-bits system (mandatory)

  3. 110 MB of space (installation) + additional space for your projects' files.

  4. Processor: processors above 2.4 GHz are recommended to improve your experience.

  5. Memory: at least 4 GB of RAM is required. 8 GB of RAM or higher is recommended to improve your experience.

  6. Microsoft Excel.

  7. OpenGL 3.2 or above. Discover yours by downloading and running the procedure available at here

  8. Visual C++ Redistributable: Installation of Visual C++ Redistributable is necessary to run this software.

Recommended hardware

Memory should be a higher priority when choosing the machine in which MiningMath will be run on. In addition, a list of priority upgrades to improve performance with large scale datasets is given below.

  1. Higher Ram

  2. Higher Ram frequency

  3. Higher processing clock

Installing

Installing MiningMath is quick and straightforward.. This guide will provide step-by-step instructions for installing the software on your computer.

Download the MiningMath Installer

  1. Visit the MiningMath website at https://miningmath.com.
  2. Click on the button located on the center of the homepage
  3. Save the installation file to your computer

Run the MiningMath Installer

  1. Locate the downloaded installation file and double-click to launch the installer.
  2. The installation wizard will start. Follow the simple instructions in the prompt until the installation has been completed.

Congratulations! You have successfully installed the MiningMath software on your computer.

Activating Your License

The free version of the MiningMath software is automatically activated upon installation and is valid for 60 days. After this period, it can be renewed for free by contacting MiningMath support.

To activate the full version of the software, follow these steps:

  1. Open the MiningMath software and click on the "License" option in the left column.

  2. Enter your activation code into the field provided and click on "Activate License". Make sure that your computer is connected to the internet. The software will contact the activation server and complete the activation process. 

If you encounter any issues during the activation process, please contact MiningMath support for assistance.

2. Quick testing

The software comes with a pre-installed project called Marvin_Strategy_Optimization, which uses the Marvin deposit, a widely used dataset in the literature. This project contains various pre-configured scenarios that will be useful in the future to learn how to use the software.

Follow these steps to quickly test the software:

  1. Select the Marvin_Strategy_Optimization project and save it to a folder on your machine where you have write permissions.
  2. Once saved, double-click on the project to open it. This project contains several pre-configured scenarios that can be run to test the software.

  3. Run some scenarios to familiarize yourself with the software's configuration, execution, and results process.

The Marvin deposit will also be used in the next steps of this guide.

3. Formatting stage

Note: the examples in this page are made with the Marvin dataset that comes pre-installed. Still, these steps would be the same if you were using your own data.

In order to use the software, you need to import your block model into the system. To do this, it is necessary to follow certain formatting specifications and assign the proper field types to each column of the block model.

Formatting Specifications

  1. Regularized block model: All blocks must be the same size.

  2. Air blocks must be removed prior to importation. This is the way MiningMath recognizes the topography.

  3. Coordinates of each block in the 3 dimensions.

  4. Header Names should not have special characters or have them exceed 13. Use this recommendation for folders and files also.

  5. The data format should be a CSV file (Comma Separated Value), which might be compatible with most mining packages. An example can be seen below.

Good practices

  • Configure Microsoft Windows number formatting to use dot as the decimal separator.
  • Use the metric system.
  • Set multiple fields that will consider different economic values, material types, contaminant limits, and any other variable you wish to analyze or control.

Field types

Field Types are the fields MiningMath can understand. Each column imported should be assigned to the proper field type so that the software treats each variable accordingly with its meaning.

Mandatory Field Types

To run any optimization scenario, you will need to at least one field for each of these variables types:

Coordinates X, Y, and Z Your geo-referenced information.

Average

Any variable that could be controlled by means of minimums and maximums considering its average: grades, haulage distance, and other variables.

Economic Value

Columns with the economic value when sent to the available destinations. It is possible to import multiple economic values at once, and they may be used simultaneously (ex.: multiple processing streams) or calculated in the internal calculator.

Optional Field Types

Density Block's density.

Slope

Slopes varying block-by-block, which gives the flexibility to define slopes by lithotype and sectors

Recovery

Recoveries varying block-by-block.

Sum

Any variable that could be controlled by means of minimums and maximums considering its sum

Other

Information that you wish to have in the exported outputs

Skip

Any variable that should be ignored. This field type might help improve the runtime since these variables will not be considered and will not be exported along with the optimization outputs.

Software conventions

The model’s origin must be placed at the bottom portion

It should start to count from the minimum coordinates at X, Y, and Z (in this order). To clarify, the Z-coordinate grows first, followed by the Y-coordinate, and then the X-coordinate. In the Marvin example you can see how Z grows first for the same values of X and Y.

Note: Each software uses its own conventions for data format, naming, numbering systems, etc. These differences should be observed to prevent conflicts when working with data from multiple software.

What you must know

MiningMath uses coordinates (X,Y,Z) for which Z represents the elevation starting upwards

Other mining software may use indexes with IZ starting downwards. MineSight is an example that uses this notation.

To invert downwards coordinates use the following formula to convert: new(Z)=max(Z)+1–current(Z)

Air blocks

MiningMath recognizes that all imported blocks of your model are underground. This means it is necessary to remove all the air blocks prior to importation. Unless your topography is totally flat, which is unlikely.

The non-removal of air blocks may lead to unsatisfactory results and long processing times, since it would be considering blocks that do not exist in reality. The following video shows how to remove air blocks using filters on MS Excel. These tips are also applicable to any mining software of your choice.

Common issues

If you are having issues formatting your CSV check some common problems here. You can also post questions in our forum so the community can quickly help you. 

4. Importing stage

Note: the examples in this page are made with the Marvin dataset that comes pre-installed. Still, these steps would be the same if you were using your own data.

To import the block model, select the option New Project on the left panel of MiningMath.

Afterwards, the file name input field is shown in red, indicating a mandatory field. Browse for and select the CSV formatted file. Press Next to advance.

After selecting the CSV file you should enter the Model Name. Optionally, the destination folder (Model Folder) can be changed as well as the Scenario Name, and a Scenario Description can be added.

Summary statistics

Upon clicking Next, the following window will provide a statistical summary of information for the block model that will be imported.

Coordinates

After importing the CSV file into MiningMath, you will need to specify the origin, and block dimensions. The number of blocks is automatically calculated based on this information. In this project, the origin was x=0, y=0, and z=0, and the block dimensions were 30 meters in each coordinate.

Column types

After clicking Next, a form appears, linking the imported CSV file headers to available field types in MiningMath. Each imported column must be associated with a corresponding field type, such as block coordinates with Coord. X, Y, and Z.

Other columns

Typically, MiningMath recognizes some columns automatically when their headers are similar to the field type name. Otherwise, MiningMath will automatically assign them to the field type Other.

Next buttom

To enable the Next button, you need to assign the coordinates and at least one other data column. MiningMath requires some mandatory fields to run a scenario, such as economic value for the processing plant and waste dump. If these are not defined now, you will be able to add them later using the internal calculator.

Grade units

After clicking Next, MiningMath will require grade units. In the Marvin example, the copper grade has been defined as a percentage (%), while gold grade was defined as PPM, which stands for parts per million and, in turn, is equivalent to g/ton.

View model

By clicking on View Model you will be able to visualize your data in the Viewer tab and do some preliminary evaluation. By clicking on Setup Scenario you will be redirected to the scenario tab to create your first scenario to be optimized.

You can have a quick look at your imported data in the Model tab. Don’t worry about checking every detail at this stage. You will have the chance to fully validate your data at the next steps.

5. Calculator stage

Note: Using the internal calculator is not a required step for creating scenarios and optimizing your model. It is only required if you don’t have economic values or if you need to derive new fields not present in the original data.

By using the calculator you can define new fields based on your imported values. Any calculation can be done in the Function tab.

Example

The most common use of the calculator is to create new economic values. You can learn more about destinations required in the explanation below.

MiningMath does not require pre-defined destinations ruled by an arbitrary cut-off grade. Instead, the software uses an economic value for each possible destination and for each block. The average grade that delineates whether blocks are classified as ore or waste will be a dynamic consequence of the optimization process.

Therefore, MiningMath requires at least two destinations: 1 processing stream and 1 waste dump. Therefore, each block must be associated with:

  • 1 Economic value for the processing plant
  • 1 Economic value for the waste dump

MiningMath can determine the best destination option during optimization without the user pre-setting it. If you don’t have economic values defined in your model, you can use the example below as a guide to calculate them.

Note: Even blocks of waste might have processing costs in the economic values of the plant. Therefore, non-profitable blocks would have higher costs when sent to process instead of waste.

Note: If you have any material that should be forbidden in the plant, you can use economic values to reduce the complexity and runtime, as mentioned here.

The definition of economic values involves considering factors such as the destination of the block, grades, recovery, mining cost, haul costs, treatment costs, blasting costs, and selling price.

An example of the calculation is provided with the calculation parameters listed below.

Description Cu (%) Au (PPM)
Recovery
0.88
0.6
Selling price (Cu: $/t, Au: $/gram)
2000
12
Selling cost (Cu: $/t, Au: $/gram)
720
0.2
Processing cost ($/t)

                  4

Mining cost ($/t)
                 0.9
Discount rate (%)
                 10
Dimensions of the blocks in X, Y, Z (m)
          30, 30, 30

Block Tonnes

  1. Block Tonnes = BlockVolume * BlockDensity

  2. Block Tonnes = 30*30*30*[Density]

Tonnes Cu

  1. Tonnes Cu = Block Tonnes x (Grade Cu/100)

  2. Tonnes Cu = [BlockTonnes]*([CU]/100)

Mass Au

  1. Mass Au = Block Tonnes x Grade Au

  2. Mass Au = [BlockTonnes]*[AU]

Economic Value Process

  1. Economic Value Process =
    [Tonnes Cu x Recovery Cu x (Selling Price Cu – Selling Cost Cu)] +
    [Mass Au x Recovery Au x (Selling Price Au – Selling Cost Au)] –
    [Block Tonnes x (Processing Cost + Mining Cost)]

  2. Economic Value Process = ([TonnesCu]* 0.88 * (2000–720)) + ([MassAu] * 0.60 * (12 – 0.2)) – ([BlockTonnes] * (4.00 + 0.90))

Economic Value Waste

  1. Economic Value Waste = –Block Tonnes x Mining Cost

  2. Economic Value Waste = –[BlockTonnes] * 0.9

The block in the example above would generate -299,880$ if sent to the process, and –55,080.1$ if discarded as waste. Therefore, this block might go to waste, since it would result in less loss than when it is processed. MiningMath defines the best destination regarding the set of constraints throughout the time, thus this decision is a lot more complex than the example above in most cases.

Tip: You can use the calculator to define multiple economic values. For example, what if the selling price or selling cost of Cu varies? These alternative scenarios can be evaluated later on with the help of our decision tree. To learn more about the calculator click here.

6. Validation stage

Complex projects with many constraints may demand hours to execute. Hence, it is important that imported data is validated before to avoid possible errors. This page provides an example with the Marvin Deposit and shows how you can set up and run a scenario to validate your data.

Set up

In order to validate your data and make sure there are no apparent errors in it, the following setup is recommended:

  1. Process and dumps set with respective recovery values.

  2. A bigger production capacity than the expected reserves. In this example, the expected life of mine vs production rate is 35-year producing 10 Mt per year. Hence, a value of 1,000 Mt would be big enough to cover the whole reserve.

  3. No discount rate.

  4. No stockpiling.

  5. Density and slope values.

  6. Timeframe: Years (1), since it would all be processed in 1 period.

You can create a new scenario by right clicking in a decision tree. If you don’t have any decision trees, you can create one by clicking on the + sign.

After creating a scenario, you will be prompted to enter general parameters, such as density and slope angles.

The Destinations tab should be enabled after entering the general parameters.

Here, you need to add at least one process and one waste dump.

Next, you will be required to add the Production limits. 

For the Validation scenario, you can use years in the Timeframe and an unbounded value for the process, for example 1,000,000,000.

The Overview tab will give you a general view of your setup. For the Marvin dataset, the validation will be as depicted below.

Lastly, you can run the scenario by using the Run button at the top.

Results

Once the execution has finished, you will be able to visualize the reports in the same tab, or open the respective csv and xlsx files in Excel. This execution will also generate the topography surface that you can as an example to create other surfaces, for instance force or restrict mining areas. After running the suggested scenario, you should evaluate the results in the Viewer tab and the respective reports in Excel.

Evaluation

Evaluating the results reported in the validation should help you identify any apparent problems that you can fix before running more complex scenarios. Some of the common questions that might help you in this analysis:

  1. Did the scenario run properly?

  2. Are most of the positive economic values from the process inside this surface?

  3. Is the mining happening in reasonable areas?

  4. Is the NPV reported reasonable for an unrestricted scenario?

If your validation does not seem correct, you might have to reevaluate your block model. For example, there might be wrong values in the data imported, errors with data formatting, or if you used the internal calculator, there might be something wrong with the formulas applied. Otherwise, if everything seems correct, you should proceed to the next page.

7. NPV upper bound

Before adding more complex constraints to your project, it is important to have some general idea of how high the NPV of your project can be. The NPV upper bound is an unrealistic limit, but it can help as a reference point as you progress through the project and add all its constraints at different steps.

At this stage, you can add some surface representing any restricted area in the project. Learn more about force or restrict mining areas. For the Marvin example there is no such restriction. However, if you are using your own data set, make sure that your surface files are well formatted as detailed here. You can use any previously generated surface, such as the topography, as an initial example to help you in this process.

You can run a scenario similar to the validation one including any force or restricted mining areas. The figure below shows an illustrative setup.

Super Best Case

The Super Best Case is the recommended approach to define the NPV upper bound. It aims to maximize the discounted cash flow of a project by exploring the entire solution space, with the only constraint being processing capacity. It is a global, multi-period optimization that seeks to uncover the full upside potential for the project’s net present value.

MiningMath allows you to control the entire production
without oscillations due to our global optimization.
MiningMath performs a global optimization, without previous steps
limiting the solution space at each change. Hence, a completely different
scenario can appear, increasing the variety of solutions.
The mathematical optimization is done in a single
step through the use of surfaces, not being bound to fixed benches.
MiningMath navigates through the solution space by using surfaces
that will never result in split benches, leading to a more precise optimization.
MiningMath defines surfaces that describe the group of blocks that
should be mined, or not, considering productions required, and
points that could be placed anywhere along the Z-axis. This flexibility
allows MiningMath's algorithm to control the overall slope angle precisely,
with no errors that could have a strong impact on transition zones.

Set up

For the Marvin dataset, you can setup the Super Best Case similarly to the validation stage, but including the limit for processing capacity, which in this case is 30Mt per year.

Results

After running the Super Best Case scenario evaluate the results. You can check if restrictions are respected and if results in the report are reasonable.

Tip: It is important to mention that if you have multiple destinations, extra processing, or dump routes, it could be added for proper destination optimization (note that MiningMath does not apply the concept of cut-off grades). Besides that, the surfaces obtained here could be used in further steps or imported back into any mining package for pushback design and scheduling

8. Refining the NPV upper bound

After having identified the NPV upper bound of your project, it is recommended that you start adding average constraints, sum constraints, and stockpiling. If there are any average and sum variables in your project, they will be already imported at this stage. Nonetheless, you can always define new variables in the calculator if necessary. Next, you can see some examples of average constraints, sum constraints, and stockpiling being employed in the Marvin dataset.

Average constraints

Average constraints are based on quantifiable parameters modeled block by block. To use this feature, the dataset must include an auxiliary field/column representing the desired limit for each block.

When to use?

Average constraints are usually employed for blending low-grade and high-grade blocks to enhance profitability. Nonetheless, they have a diverse range of applications, being applicable to any variable that can be modeled based on these assumptions.

Set up

The figures below depict two parameters imported as average variables.

The limits of average variables can be defined in the Scenario tab. As depicted below, it is possible to input limits (A), for each period range (B), weights (C) and each destination (D).

You in Overview tab you can see these limits as depicted below. 

Example

The scenario below exemplifies the impact of an Average constraint on the Super Best Case of the Marvin dataset. In this case, the NPV goes from 942 M$ NPV in the Super Best Case to 933 M$ in the new scenario with Average constraints. Hence, the new constraint has only a small impact on the NPV.

On the left, CU grade with average constraint (0.42 min and 0.46 max) , and on the right CU grade with no average constraint.

On the left, Cumulative NPV (933 M$) with CU grade constrained between 0.42 and 0.46. On the right, CU grade unconstrained (942 M$).

Sum constraints

Sum constraints are based on the sum of any quantifiable parameter modeled block by block. To use this feature, the dataset must include an auxiliary field/column representing the desired limit for each block.

When to use?

Sum constraints controls the total amount mined in a single period of the respective sum variable for each block. Basically, any variable which needs to have a total amount controlled could be employed. Some examples of variables that could be controlled with a Sum constraint are listed below:

  • Total amount of processing hours
  • Tonnages and proportions of rock type and metal production.
  • Consumption of inputs such as energy spent during comminution, and fleet hours spent to mobilize material.
  • Contaminants control on the processing plant during each period.

The user can define:

  • Different sum limits for each material.
  • Different sum limits for each interval.
  • Different sum limits for each destination.
  • Combine all the options above in order to achieve globally optimized results.

Set up

Sum variables can be constrained in a similar manner to average ones. The figures below depict one parameter imported as a sum variable and its respective limits in the Sum tab.

Example

Consider the scenario above with a maximum limit of 13.000 hours of processing equipment. This constraint can be inserted at the Sum tab previously depicted. The impact of this restriction can be evaluated when results are compared to a unrestricted scenario.

On the left, processing hours with sum constraint (13000 max). On the right, unconstrained processing hours.

On the left, cumulative NPV (931 M$) with the sum of Proc hours constrained at 13,000 max. On the right, Proc hours unconstrained (942 M$).

The resulting reports show the 13000 hours limit was respected for each period. However, the NPV decreased from 942 M$ NPV in the Super Best Case to 931 M$ in this new defined scenario. Such a fall demonstrates that in order to achieve the full value of the project, identified in the Super Best Case, the addition of more processing equipment would be necessary. This addition might not be feasible or reasonable, showing that, in this case, the new results are closer to a more realistic scenario.

Stockpilling

Stockpiles are optimized blocks that were initially designated for disposal. They are processed after the main optimization phase, where the algorithm analyzes their value (Revenue – Fixed Mining Cost – Rehandling Cost) compared to the cost of discarding them. If worthy, blocks will be reclaimed, complementing production shortfalls over time.

Set up

To enable the stockpiles on the interface the first step is on the General tab where two inputs are required:

  1. Fixed Mining Cost: value used to decompose the economic value while considering stockpiles;

  2. Rehandling Cost: represents the cost to reclaim blocks from the stockpile to the process

After that, on the Destinations tab, you can define stockpile limits for each processing plant added, remembering that this limit is based on the life of mine, not in a period time frame.

NoteSince stockpiles are a post-processing unit of the algorithm, total tonnage restrictions might be violated when the stockpiles are processed. Total tonnage restrictions are only considered during the processing unit of the algorithm.

9. Long-term planning

After having refined the NPV upper bound of your project, it is recommended that you start adding geometric constraints. MiningMath incorporates geometric parameters as constraints within the objective function, rather than applying them after pit optimization. This approach enables solutions that align with operational criteria while maximizing net present value (NPV), leading to improved data utilization and identification of opportunities that could be overlooked by manual processes and arbitrary assumptions.

Geometric constraints available

The Geometric tab is the place to set minimum mining & bottom widths, mining length and vertical rate of advance, whose values are applicable to every period.

These parameters are defined as follows:

Mining Width: Distance from a pit to another.

Bottom Width: Bottom minimum area.

Vertical rate of advance: vertical distance mined on each period

Minimum mining length: minimum distance that must exist between at least two points amidst the walls of surfaces among two consecutive mining periods.

Adding a single geometric constraint

When adding more restrictions to a project, it is common for the net present value (NPV) to decrease as the project becomes more restricted. However, since geometric constraints are non linear, it is possible that the results may not follow this trend as new values are tested. To analyze the impact of individual widths or lengths, start by evaluating flexible values to determine an upper bound for NPV under this new geometric constraint, even if the solution is not fully operational yet. Refine these initial results until they are feasible. Assessing geometric constraints is vital for optimizing fleet equipment configuration, maximizing productivity, and increasing project NPV.

For example, consider the base scenario for the Marvin dataset and subsequent decision tree built to explore different values of mining width.

Evaluation

The goal in this case is to understand the impact of different values of mining width (in green), which will be tested with a range of different values, from 0m up to 200m. 

Note that there is no linear relationship between mining width and NPV. In other words, a higher mining width does not necessarily imply a lower NPV. As previously mentioned, that is due to the non-linearity of the problem.

Considering the nature of global optimization employed in MiningMath, other variables might also be affected by different mining widths. For example, the production could be analysed for identification of possible issues when employing different mining widths.

This example illustrates the impact of using different mining widths. However, it could also be reproduced for the other geometric constraints.

Adding multiple geometric constraints

Once you have gained some knowledge on the impact of single geometric constraints, it is important to gain a comprehensive view of the impact of overall geometric limitations on the project’s performance. You can do that by creating scenarios that include each geometric constraint sequentially and gradually increasing or decreasing their values from the least selective until the desirable requirement.

Consider the following base scenario and decision tree built to investigate the use of bottom width, mining width and vertical rate of advance using the Marvin dataset.

Evaluation

The goal is to understand the impact of different values of geometric constraints. The geometric parameters (in green) will be tested with a range of different values: bottom width with values from 0m up to 200m; mining width with values from 0m up to 200m; and vertical rate of advance with values from 50m up to 300m. In this example, 26 different scenarios were evaluated. 

Note that there is no linear relationship between geometric constraints and NPV. In other words, a higher width or lower vertical rate of advance do not necessarily imply a lower NPV. As previously mentioned, that is due to the non-linearity of the problem. The cumulative NPV of the scenarios is compared in the graph below.

There are usually two outcomes when performing such an analysis:

  1. Contrasting geometrics parameters with small NPV variations; or

  2. Similar geometric parameters with larger NPV variations.

In conclusion, it is important to create several scenarios to perform your long term planning. As exemplified above, results can be quite similar or quite different due to the non-linearity of the problem. Considering the nature of global optimization employed in MiningMath, it is also important to evaluate other indicators. The figures below depict the tonnage achieved for the production, demonstrating the possible impacts for different geometric constraints.

Conclusion

At this stage you should be familiar with the most basic concepts in MiningMath. This will give you the skills to start working on your own data. Each project is different, and might require different analysis and adjustments. You can see other type of common analyses performed with MiningMath here. Also, you can check a suggestion of pages for more advanced concepts here.

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