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With MiningMath there is no complex and slow learning curve!

Knowledge Base

Tutorials

Articles

Beginners guide

Run your first project

You can check a sequence of pages to learn how to run your first project with our Getting Started training. From installation process and formatting your model files up to the long-term planning of your project.

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Must-Read Articles

In order to take the maximum of MiningMath’s Optimization we recommend this flow through our Knowledge Base. It will guide you step-by-step in order to integrate multiple business’ areas and to improve your strategic analysis through risk assessments unconstrained by step-wise processes. 

Set up and first run

  1. Quick Check: Here you’ll have all the necessary instructions to install, activate and run MiningMath.

  2. How to run a scenario: Once everything is ready, it’s time to run your first scenario with MiningMath so you can familiarize with our technology!

Find new results

  1. Playing with pre-defined scenarios: Each change in a scenario opens a new world of possibilities, therefore, it’s time to understand a little more about and see it in practice, playing with pre-defined scenarios.

  2. Decision Trees: Decision Trees provide you a detailed broad view of your project, allowing you to plan your mining sequence by analyzing every possibility in light of constraints applied to each scenario, which options are more viable and profitable to the global project, as well as how these factors impact the final NPV.

Understand the technology in depth

  1. Current best practices: Here we go through the modern technology usually employed by other mining packages. It is important to understand these in order to comprehend MiningMath differentials.

  2. MiningMath uniqueness: Now that you’ve practiced the basics of MiningMath, and understand how other mining packages work, it’s time to get deep into the theory behind the MiningMath technology.

  3. Interface Overview: It’s time understand our interface overview with detailed information about every screen and constraints available in MiningMath. Home page, Model tab, Scenario tab, and Viewer for a better understanding of the possibilities.

Using and validating your data

  1. Formatting the Block Model: Learn how to format your block model data and use it in MiningMath.

  2. Importing the block model: Go through the importation process and to proper configure your data.

  3. Economic Values: 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. After your data is formatted and imported into MiningMath, you may build your Economic Value for each possible destination.

  4. Data Validation: Once your data is set, it’s time to validate it by running MiningMath with a bigger production capacity than the expected reserves. Thus, you will get and analyze results faster.

  5. Constraints Validation: Continuing the validation, start to add the first constraints related to your project so that you can understand its maximum potential.

Improve your results

  1. Integrated Workflow: Each project has its own characteristics and MiningMath allows you to choose which workflow fits best in your demand and to decide which one should be used.

  2. Super Best Case: In the search for the upside potential for the NPV of a given project, this setup explores the whole solution space without any other constraints but processing capacities, in a global multi-period optimization fully focused on maximizing the project’s discounted cash flow.

  3. Optimized Pushbacks: Identify timeframe intervals in your project, so that you can work with group periods before getting into a detailed insight. This strategy allows you to run the scenarios faster without losing flexibility or adding dilution on the optimization, which happens when you reblock.

  4. Optimized Schedules: Consider your real production and explore scenarios to the most value in terms of NPV.

  5. Short-term Planning: Now that you built the knowledge about your project based on the previous steps, it is time to start the integration between long and short-term planning in MiningMath. You may also optimize the short-term along with the long-term using different timeframes.

Export your results

  1. Exporting Data: After running your scenarios, you can export all data. Results are automatically exported to CSV files to integrate with your preferred mining package.

In-Depth MiningMath

This tutorial provides a detailed guidance to the pages in the knowledge base for new MiningMath users. A shorter tutorial can be found here with a set of must read articles. In this tutorial, a larger number of pages is contextualized and recommended for those with no previous experience using MiningMath but who wish to gain a more advanced knowledge.

Software requirements

  1. Quick check: Verify if your computer has all the minimum/recommended requirements for running the software.

  2. Put it to run: Here you’ll have all the necessary instructions to install, activate and run MiningMath.

Set up the block model

The next step after installation is to understand the home page interface and import your project data. The following pages go over these in detail.

  1. Home page: MiningMath automatically starts on this page. It depicts your decision trees, recent projects and model information.

  2. Import your block model: import your csv data, name your project, set fields and validation.

  3. Modify the block model: this window aims to help you to modify your block model accordingly with what is required for your project and also allows you to “Export” the block model to the CSV format to be used with any other software.

  4. Calculator: calculate and create new fields by manipulating your project inside MiningMath.

Handling unformatted data

If you don’t have a block model ready to be imported you might want to create a new one. The following pages can guide you through this process.

  1. Formating the block model

  2. Economic values

  3. Surfaces

  4. Surface validation

Define the scenario and run

Once you have started your block model defined, there are several options to set up your project’s parameters before running a scenario.

  1. Scenario tab: set densities, economic parameters, slope angles, stockpiles, add/remove processes and dumps, production inputs, geometric inputs and so on.

  2. Save as: save the scenario's configuration once it has been configured.

  3. Run: the Run tab is the last step before running your project’s optimization. Change the scenario name, set a time limit, and set up results files.

Results

After running your scenario it is important to analyze and understand the given results.

  1. Output files and 3D viewer: by default, MiningMath generates an Excel report summarizing the main results of the optimization. It also creates outputs of mining sequence, topography, and pit surfaces in csv format so that you can easily import them into other mining packages. The 3D viewer enables a view of your model from different angles. 

  2. Export model: export your model as a csv file. This can be used in new scenarios or imported in other mining packages.

Extensive set-up

MiningMath offers a lot of customization. You might use pre-defined scenarios to learn with standard parameters. Otherwise, the following pages of the knowledge base detail several important parameters that might need to be fine tuned in your project.

  1. NPV calculation

  2. Slope angles

  3. Stockpiles 

  4. Destinations

  5. Recovery

  6. Production constraints

  7. Geometric constraints

  8. Widths

  9. Vertical rate

  10. Surfaces

  11. Force mining

  12. Restrict mining

  13. Force+restrict mining

  14. Average constraints

  15. Sum constraints

  16. Time limit

Advanced content

Complex projects might need advanced configurations or advanced knowledge in certain topics. The following pages cover some subjects considered advanced in our knowledge base.

  1. Variable mining cost

  2. Multiple destinations

  3. Fixing destination

  4. Fake destinations

  5. Reclaim policy

  6. Material types

  7. Mining fronts

  8. Multi-mine

  9. Stochastic models

  10. Percent models

  11. Artificial stockpiles

Theory

In order to understand the theory behind MiningMath’s algorithm, a set of pages is provided to describe mathematical formulations, pseudo-code, and any rationale to justify the software design.

  1. Current best practice

  2. MiningMath Uniqueness

  3. Guaranteed Solutions

  4. Theory Validation

  5. In-depth Algorithm

Workflows

ManingMath acknowledges and supports different workflows. This knowledge base provides a set of articles aimed at showing how MiningMath can be integrated into other workflows or have its results used by different mining packages. 

  1. Decision trees

  2. Integration

  3. Integrated workflow

  4. Super best case

  5. Optimized pushbacks

  6. Optimized schedules

  7. Short-term planning

  8. Multi-mine

  9. Sustainable analysis

  10. Uncertainties at the beginning

Getting Started

Articles

Quick Check

System requirements

The only mandatory requirement for using MiningMath is a 64-bits system. 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 8 GB of RAM is required. 16 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 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. Here’s a list of priority upgrades to improve performance with large scale datasets: 

  1. Higher Ram

  2. Higher Ram frequency

  3. Higher processing clock

Common Issues

Insufficient memory

As previously presented, RAM should be one of the most important components to prioritize when selecting a computer to run MiningMath, especially because Windows alone consumes a significant amount of memory.

However, if you encounter an insufficient memory warning or a sudden crash while using MiningMath, there are some recommendations you can consider:

1. Memory Upgrade: If possible, this is the best solution to enhance efficiency. The characteristics to observe are listed in the previous item, “Recommended Hardware.” Based on our experience with more complex projects, 64 GB is usually sufficient for nearly all cases.

2. Free Up Memory: Consider closing other applications that are consuming the computer’s RAM while MiningMath is running.

3. Increase Windows Virtual Memory: This procedure involves allocating disk space to be used as RAM. To perform this procedure, we recommend this tutorial.

4. Reblock: If none of these options work, reblocking can be considered to reduce the size of the model. Check more details here.

Extra: In exceptional cases, when working with boxes, it may be viable to manipulate the block coordinates to bring them closer together, creating a smaller model box.

Put It to Run!

Installing, Activating and Running

Installing and activating MiningMath is quick and straightforward. All you need to do is follow the setup wizard and have an internet connection to activate your license. 

Video 1: MiningMath installation process.

Figure 1: MiningMath installation process from left to right.
Figure 1: MiningMath installation process from left to right.
Figure 2: MiningMath installation process from left to right.
Figure 2: MiningMath installation process from left to right.
Figure 3: MiningMath installation process from left to right.
Figure 3: MiningMath installation process from left to right.
Figure 4: MiningMath installation process from left to right.
Figure 4: MiningMath installation process from left to right.
Figure 5: MiningMath installation process from left to right.
Figure 5: MiningMath installation process from left to right.
Figure 6: MiningMath installation process from left to right.
Figure 6: MiningMath installation process from left to right.

Activating Your License

To activate your license, you will need to: 

  1. Open MiningMath (it will open automatically after the installation, but you can open it manually afterwards).

  2. On the left menu, click License.

  3. Select the field "I have an activation code" and paste the License Code provided by MiningMath.

  4. Click "Activate license".

Opening an old project

If you need to open an old project, just follow these steps:

  1. Open MiningMath (it will open automatically after the installation, but you can open it manually afterwards).

  2. On the left menu, click on Open Project.

  3. Search for the folder in which you saved your old project.

  4. Select the ".ssprj" file.

  5. Click on "Open" and it will show up on the "Recent Projects"

  6. Now you can open it!

The images below illustrate this process:

Figure 7: Click on "Open Project"
Figure 7: Click on "Open Project"
Figure 8: Search for your old project's folder
Figure 8: Search for your old project's folder
Figure 9: Select the ".ssprj" file of your old project
Figure 9: Select the ".ssprj" file of your old project
Figure 10: Open it and it will be available at "Recent Projects"
Figure 10: Open it and it will be available at "Recent Projects"

NOTE: 

MiningMath’s licensing method demands an internet connection. 

Optimizing Scenarios

Play with the predefined scenarios

MiningMath allows you to learn with each scenario by providing standard parameters which simulate some common constraints that a mining company may face. Standard scenarios are listed and described below so you can identify the main changes made within the “Overview” tab.

The ultimate goal of this practice is to prepare you to build Decision Trees, which allow you to organize scenarios in order to understand how variables influence one another and, consequently, how these variables determine the final NPV.

Figure 1: Scenarios on the Home Page

Market Conditions Decision Tree

1) BaseCase

The Base Case consists of the initial scenario, with a uniform production capacity and without sum, average or surface mining limits.

2) BaseCase-RampUp

While the base case considers a uniform production capacity, the BaseCase-RampUp scenario offers the possibility to vary the levels of production within the different timespans. We have an initial production capacity of 10Mton on the first 2 periods; 20 Mton on periods 3 and 4; and 30 Mton from period 5 until the end of the mine’s lifetime, with a total movement constraint of 30, 60, and 80 Mton, considering the increase of production within the time-frames mentioned.

Figure 3: BaseCase-RampUp

3) PriceUp and PriceDown

Scenarios “PriceUp” and “PriceDown” differ in relation to the basic scenario in the economic value used for the calculation of the P1 process, where there is an increase and a decrease of 10% at the copper selling price, respectively. In the destination tab, “P1 Cu +10” and “P1 Cu -10” were the values used for the process.

Figure 4: PriceUp
Figure 4: PriceUp
Figure 5: PriceDown
Figure 5: PriceDown

4) PriceUp-RampUp and PriceDown-RampUp

These scenarios consider a 10% copper selling price increase and decrease, and a ramp-up of the production capacity at the same time, as mentioned before.

Figure 6: PriceUp-RampUp
Figure 6: PriceUp-RampUp
Figure 7: PriceDown-RampUp
Figure 7: PriceDown-RampUp

5) PriceUp-RampUp-Protection300 and PriceUp-RampUp-Protection400

This scenario considers a 10% copper selling price increase and a ramp-up of the products at the same time, as mentioned in the previous scenario. In addition, a restrict mining surface (this constraint is used to prohibit access to this area in a specific timeframe) was included up to the fourth period, since it may represent some legal constraints on a project.

Figure 8: PriceUp-RumpUp-Protections

Other Decision Trees

Below you can see a description of some scenarios of other Decision Trees.

1) MW150 (Geometries Decision Trees)

The MW150 scenario considers different geometries from the base case at the geometric constraints. In this scenario, 150 meters was used as mining width (the horizontal distance between the walls of two surfaces that belonged to consecutive periods), and a vertical rate advance of 180 meters.

Figure 9: MW150

2) AvgCu (Average Decision Tree)

In the AvgCu scenario, blending constraints were added in the average tab to consider allowed at the process plant 0.5% as a minimum and 0.7% as a maximum average copper grade. The optimization will have to fulfill the P1 process capacity and, as an additional challenge, it has to meet this new set of parameters related to the Cu average content within the ore.

Figure 10: AvgCu

3) Proc13000h and Proc13000h-33Mt

(Process throughput Decision Tree)

Scenario Proc13000h considers 13.000 hours of processing equipment used as the maximum limit. This constraint was inserted at the sum tab and it controls variables such as rock type feeding, energy consumption, and any parameter controlled by its sum. Scenario Proc13000h-33Mt considers an increase of 10% in the production, inserted at the production tab beyond the parameters mentioned previously.

Figure 12: Processing hours

4) Yearly-TriannualProduction

(Short-Long Term Integration Decision Tree)

This considers a yearly production for period range 1-4 and triannual planning for range 5-end. This way is possible to integrate both short and long-term planning in a single run, facilitating the analysis and strategic definitions. 

Any kind of timeframe can be used according to your needs.

Yearly-Triannual Production Example
Figure 13: Short-Long Term Integration

Translations

MiningMath supports and encourages the translation of its knowledge base to multiple languages. If you would like to translate our knowledge base and have your profile advertised please contact us.

Portuguese

Ask GPT

You can use ChatGPT to help you with our knowledge base. First, you will need to have the Plugins options enabled on GPT-4.

GPT-4 plugins

After that, choose the AskYourPDF option:

GPT-4 AskYourPDF

Finally, you should enter the following prompt:

For the requests all along this chat, consider the following content: https://miningmath.com/Knowledge-Base.pdf
GPT-4 prompt example

Other prompts can help you with different requests. For example, you can ask GPT-4 to act as your own technical support agent that answers in the same language as your question:

Plugin AskYourPdf, consider the following content: https://miningmath.com/Knowledge-Base.pdf

Please answer the following question as a technical support agent, coming from a MiningMath user, in the same language as the question:

"QUESTION TEXT TO BE REPLACED"

Essential Topics

Articles

How to Run a Scenario

Video 1: Downloading MiningMath.

On MiningMath’s interface, you will find the Marvin block model and its scenarios (Figure 1). It is possible to preview the scenario and its parameters before opening it (Figure 2).

Choose and open Base Case, click the “Overview” tab (Figure 3) to check the parameters, and then click on “Run” to run the optimization (Figure 4).

After that, a short report with the results will be generated. To view it, check all the boxes on the “Load Options” window and click on “Load” (Figure 5).

Finally, whenever you feel ready to run your own scenarios, start by formatting your data here.

Figure 1: Marvin's scenarios
Figure 1: Marvin's scenarios
Figure 2: Open a scenario
Figure 2: Open a scenario
Figure 3: Check the project's overview tab
Figure 3: Check the project's overview tab
Figure 4: Click on the run button
Figure 4: Click on the run button
Figure 5: Loading the project
Figure 5: Loading the project

Common Issues: Setting your first scenario

When setting up your first scenario, you may come across some situations such as unavailable tabs and some fields marked in red. These situations are quite simple to resolve, as shown in the following video:

Play Video

Results of the Optimization

By default, MiningMath generates an Excel report summarizing the main results of the optimization. It also creates outputs of mining sequence, topography, and pit surfaces in .csv format so that you can easily import them into other mining packages.

Viewer

The 3D viewer enables a view of your model from different angles. The block colors are defined accordingly with each property displayed, varying from blue to red (smallest to largest), due to destinations, periods, or any other parameter. Therefore, it’s possible to filter the blocks by the period in which they were mined or processed, for instance. In addition, it also allows you to compare multiple scenarios by loading different cases and using the left bar to change from one to another.

Figure 1: Mine Periods 1-9
Figure 1: Mine Periods 1-9
Figure 2: Load executions
Figure 2: Load executions
Figure 3: Mine Period 1
Figure 3: Mine Period 1
Figure 4: Mine Periods 1-2
Figure 4: Mine Periods 1-2
Figure 5: Mine Periods 1-5
Figure 5: Mine Periods 1-5
Figure 6: Mine Period 4
Figure 6: Mine Period 4
Figure 7: Mine Periods 8-9
Figure 7: Mine Periods 8-9
Figure 8: Processing Periods 1-10
Figure 8: Processing Periods 1-10
Figure 9: Processing Periods 3-9
Figure 9: Processing Periods 3-9
Figure 10: Processing Periods 9-10
Figure 10: Processing Periods 9-10
Figure 11: Destinations
Figure 11: Destinations
Figure 12: Destination Process 1
Figure 12: Destination Process 1
Figure 13: Destination Waste
Figure 13: Destination Waste
Figure 14: Surface 1
Figure 14: Surface 1
Figure 15: Surface 3
Figure 15: Surface 3
Figure 16: Surface 7
Figure 16: Surface 7
Figure 17: Surface 9
Figure 17: Surface 9

Output Files

After optimizing your block model and running your scenario(s), MiningMath generates standard output files with detailed reports. The main files have a universal format (.csv), which allows you to easily import them onto other mining packages to start your mine design and further steps of your projects.

To open the project folder, click on the scenario’s name with the right button of your mouse and choose “Show in the Explorer“. The optimization’s main output files are:

  • Scenarioname.xlsx: Short report with the main results.

  • MinedBlocks.csv: Detailed report which presents all the blocks that have been mined.

  • Surface.csv: Grid of points generated through the pit each period.

Scenarioname.xlsx

Provides you with a short report with the main results of the optimization: several charts and sheets in which you can analyze the production on each period, the stockpiles by periods, the average grade of processes and dump, NPV per period, the cumulative NPV (Net Present Value), etc.

Figure 18: Graphic results

MinedBlocks.csv

This file offers a detailed report on all the mined blocks and their specificities: information on the mining sequence based on each block extracted, along with mined and processed periods, destinations, economic value, and all information used for the optimization. This file also allows you to identify blocks that were stocked and the algorithm decision-making process.

Figure 19: Mined blocks

Surface.csv

The surface scenario brings a grid of points generated through the pit of each period: each surface is named according to its mining periods and contains information about the topographic coordinates at that time. These files can be imported into the viewer separately, so that you can verify and validate your data before starting the optimization process. Note: The surfaces are exported/imported from/at MiningMath in Coordinates.

Figure 20: Surface's CSV

Video 1: Outputs and files hirearchy.

Play with Predefined Scenarios

MiningMath allows you to learn with each scenario by providing standard parameters which simulate some common constraints a mining company may face. Standard scenarios are listed and described below so you can identify the main changes made within the “Overview” tab.

The ultimate goal of this practice is to prepare you to build Decision Trees, which allow you to organize scenarios in order to understand how variables influence one another and, consequently, how these variables determine the final NPV.

Figure 1: Scenarios on the Home Page

Dataset

The examples in this page come preinstalled with every version of MiningMath. If you have deleted this project by any chance, please download the zip file below, extract the files and choose the “Open Project” option in MiningMath.

BaseCase

The Base Case consists of the initial scenario, with a uniform production capacity, and without sum, average, or surface mining limits.
Figure 2: BaseCase overview

BaseCase-RampUp

While the base case considers a uniform production capacity, the BaseCase-RampUp scenario offers the possibility to vary the levels of production within the various timespans. We have an initial production capacity of 10Mton on the first 2 periods; 20 Mton on periods 3 and 4; and 30 Mton from period 5 until the end of the mine’s lifetime, with a total movement constraint of 30, 60, and 80 Mton, considering the increase of production within the time-frames mentioned.

Figure 3: BaseCase-RampUp

PriceUp and PriceDown

Scenarios “PriceUp” and “PriceDown” differ in relation to the basic scenario in the economic value used for the calculation of the P1 process, where there is an increase and a decrease of 10% at the copper selling price, respectively. In the destination tab, “P1 Cu +10” and “P1 Cu -10” were the values used for the process.

Figure 4: PriceUp
Figure 4: PriceUp
Figure 5: PriceDown
Figure 5: PriceDown

PriceUp-RampUp and PriceDown-RampUp

These scenarios consider a 10% copper selling price increase and decrease, and a ramp-up of the production capacity at the same time, as mentioned before.

Figure 6: PriceUp-RampUp
Figure 6: PriceUp-RampUp
Figure 7: PriceDown-RampUp
Figure 7: PriceDown-RampUp

PriceUp-RampUp-Protection300 and PriceUp-RampUp-Protection400

This scenario considers a 10% copper selling price increase and a ramp-up of the products at the same time, as mentioned in the previous scenario. In addition, a restrict mining surface (this constraint is used to prohibit access to this area in a specific timeframe) was included up to the fourth period, since it may represent some legal constraints on a project.

Figure 8: PriceUp-RumpUp-Protections

Below you can see a description of some scenarios of other Decision Trees.

MW150

The MW150 scenario considers different geometries from the base case at the geometric constraints. In this scenario, 150 meters was used as mining width (the horizontal distance between the walls of two surfaces that belonged to consecutive periods), and a vertical rate advance of 180 meters.

Figure 9: MW150

AvgCu

In the AvgCu scenario, blending constraints were added in the average tab to consider allowed at the process plant 0.5% as a minimum and 0.7% as a maximum average copper grade. The optimization will have to fulfill the P1 process capacity and, as an additional challenge, it has to meet this new set of parameters related to the Cu average content within the ore.

Figure 10: AvgCu

AvgCu-Stock5Mt

Here, the same blending constraints of the previous scenario (AvgCu) were added, in addition to a stockpile limit of 5Mton for process 1, on the destination tab. This feature allows you to control the stock limit of your whole process, which increases the optimization flexibility to feed the plant, while respecting the blending constraints that were already implemented.

Figure 11: AvgCU-Stock5Mt

Proc13000h and Proc13000h-33Mt

Scenario Proc13000h considers 13.000 hours of processing equipment used as the maximum limit. This constraint was inserted at the sum tab and it controls variables such as rock type feeding, energy consumption, and any parameter controlled by its sum. Scenario Proc13000h-33Mt considers an increase of 10% in the production, inserted at the production tab beyond the parameters mentioned previously.

Figure 12: Processing hours

The Calculator

This feature allows the user to manipulate their project inside MiningMath, enabling adjustments and new field creation. Figure 1 shows a general view of the calculator. On the left side we have the block parameters and on the right the calculator itself, where the calculation can be done.

Figure 1: Calculator.

To manipulate the calculator just insert a name for the new field, select the type of field (to know more about field types, access this link), and build your expression. In case of a more complex expression, just mark the field “Logical Test” to enable conditional features. To manipulate the calculator just insert a name for the new field, select the type of field (to know more about field types, access this link), and build your expression. In case of a more complex expression, just mark the field “Logical Test” to enable conditional features.

  • + : Addition

  • - : Subtraction

  • * : Multiplication

  • / : Division

  • % : Modulus

  • ** : Exponential

  • // : Floor division

Practical approach

To facilitate the understanding, let’s work on some examples. You can see below a generic math expression (left), and its equivalent written on MiningMath’s calculator (right)

\((x^2)\times(\frac{y}{2}-1)\) ↔ x**2*((y/2)-1)

Adding a field without logical expression

Using an example of the Marvin’s Economic Value calculation, we are going to add a Block Tonnes field, as the figure 2:

Figure 2: Adding a new field

Adding a field with a logical expression

One more time using Marvin’s block model, let’s suppose we want a maximum slope angle of 45 degrees.

First, we name our Field, in this case, will be “SlopeMax45d”, select the field type as “Slope” and check the Logical Test box. Then a double click on the Slope field select it and already put it on the Expression. The next step is to select the operator, as we want a maximum of 45 degrees, we choose the operator “>” and insert the value 45 in the text box. If the value is true, that is, if this value is bigger than 45 it will now have the value of 45 assigned to it. If the value is false, i.e., lower than 45, then it will keep its value. Figure 3 shows this calculation:

Figure 3: Logical test expression

During the expression construction, green or red lines will underline it, highlighting the correct parts and the ones that need adjustments to become correct. When it is all set, just click on “Add field” and this new field will be available for use on the project on its correct field type assignments. In case the user needs to delete a field, just go to the parameters option, select and delete it.

Removing a field

To remove an existing field, go to the “Parameters” tab, select the desired field and click “Remove”.

Figure 4: Removing a field

NPV Calculation

MiningMath's internal math for NPV Calculation

The following video explains more about the NPV calculation made by MiningMath’s algorithm. The understand of these steps might be useful for users working on projects with variable mining costs, which are not yet smoothly implemented on the UI.

Video 1: NPV calculation.

Discount rate per period

The discount rate (%/year) is provided by the user in MiningMath’s interface, as depicted in the figure below.

Figure 1: Interface example to define discount rate (%/year)

Discounted cash flow for annual time frames

In a usual scenario period ranges are defined by annual time frames, as depicted in Fig-2.

Figure 2: Interface example with annual time frame

In this case, the annual discount rate multiplier (annual_multiplier) to return the discounted cash flow is performed as follows:

\(\text{annual_multiplier}(t) = \) \(\frac{1}{(1 + \text{input discount rate})^t}\)

The table below exemplifies one case for 10 periods.

Period Process 1 Dump 1 NPV (Discounted) M$ Annual multiplier Undiscounted NPV M$
1
P1
Waste
1.2
0.909
1.320
2
P1 +5%
Waste
137.9
0.826
166.859
3
P1 +5%
Waste
132.5
0.751
176.358
4
P1 +5%
Waste
105.4
0.683
154.316
5
P1 -5%
Waste
89
0.621
143.335
6
P1 -5%
Waste
92
0.564
162.984
7
P1 -5%
Waste
91.3
0.513
177.918
8
P1 -10%
Waste
52.3
0.467
112.110
9
P1 -10%
Waste
54.3
0.424
128.037
10
P1 -10%
Waste
12.1
0.386
31.384

Table 1: Example of annual multiplying factors and undiscounted cash-flows for a 10% discount rate per year. Process 1 exemplifies the use of different economic values per period.

In details, Table 1 lists:

  1. the NPV (discounted) resulting from a 10 yearly period with a 10% discount rate per year.

  2. the annual discount rate (annual_multiplier) for each period; and

  3. the undiscounted NPV as the result of the discounted NPV divided by the annual_multiplier.

Discounted cash flow for custom time frames

MiningMath allows the creation of scenarios in which period ranges are defined with custom time frames (months, trienniums, decades, etc.), as depicted in Figure 3.

Figure 3: Interface example with custom time frames

In this case, the discount rate is still provided in years on the interface. However, the discount rate per period follows a different set of calculations. To identity the correct multiplier (discount rate for a custom time frame) applied to each custom time frame, it is necessary to apply the formula below:

\( \text{mult}(t) = \frac{1}{(1 + \text{discount_rate}(t)) ^ {\text{tf_sum}(t)}}\)

where:

\(
\text{tf_sum}(t) = \sum_{i=1}^{t}\frac{TF(i)}{TF(t)}
\)

and

\(
\text{discount_rate}(t) = (1 + \text{annual_discount_rate})^{TF(t)} – 1
\)

and

\(
TF(t)=
\begin{cases}
1,& \text{if}\, t\, \text{is in years}\\
\frac{1}{12},& \text{if}\, t\, \text{is in months}\\ 3,& \text{if}\, t\, \text{is in trienniums}\\
etc.&
\end{cases}
\)

For example, to calculate the multiplier of the first period in figure 3, the equation would be:

\( TF(1) = \frac{1}{12} = 0.8333… \)

\( \text{tf_sum}(t) = \sum_{i=1}^{1}\frac{TF(1)}{TF(1)} = 1 \)

\( \text{discount_rate}(1) = (1 + \text{annual_discount_rate})^{TF(1)} – 1 = (1 + 0.1) ^ {1/12} – 1 = 0.007 \)

\( \text{mult}(1) = \frac{1}{(1 + \text{discount_rate}(1)) ^ {\text{tf_sum}(1)}} = \frac{1}{(1 + 0.007)^{1}} = 0.993 \)

Another example, to calculate the multiplier of period 15 in figure 3, the equation would be:

\( TF(15) = 3 \)

\( \text{tf_sum}(t) = \sum_{i=1}^{15}\frac{TF(i)}{TF(15)} = 2 \)

\( \text{discount_rate}(15) = (1 + \text{annual_discount_rate})^{TF(15)} – 1 = (1 + 0.1) ^ {3} – 1 = 0.331 \)

\( \text{mult}(15) = \frac{1}{(1 + \text{discount_rate}(15)) ^ {\text{tf_sum}(15)}} = \frac{1}{(1 + 0.331)^{2}} = 0.564 \)

Evaluate Project Potential

Certain constraints related to your project can be defined so that you can understand its maximum potential. The surface generated in this case could also be used as a restrict mining in the last period to reduce the complexity of your block model and the runtime of MiningMath, since it includes a set of constraints inputted.

Example

  • Set up a scenario with 1,000 Mt in the processing plants, which corresponds to a lot more mass than expected in the whole life of the mine.

  • Add the Minimum Bottom Width (100m). This constraint will allow you to have a suitable work-front for your equipment.

  • Restrict Mining surface, if you have this constraint in your project.

  • Grade constraint until 0.7%.

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

Figure 1: Sequencing
Figure 1: Sequencing
Figure 2: Restrict surface
Figure 2: Restrict surface
Figure 3: Surface
Figure 3: Surface

Note: Sum constraints can restrict the total amount of handling material (ore + waste) of the mine. Therefore, do not use them in the validation.

Figure 4: Production constraints
Figure 4: Production constraints
Figure 5: Geometric constraints
Figure 5: Geometric constraints
Figure 6: Average constraints
Figure 6: Average constraints

Using results

Now that Constraints Validation step is done, you are able to use this final surface as a guide for future optimizations. This approach reduces the runtime and the complexity of the algorithm because when you take it into account, the blocks below this final optimized surface won’t be considered and the heuristics inside the interface would be facilitated. Notice that we did not make any change in the discount rate, thus, this first NPV does not represent the reality. If you need an accurate result in this step, make sure to adjust it.

It’s important to remember that when we restrict the mining into this surface, the number of periods generated in future runs could be reduced because the average parameters of each one will have to meet the constraints of the overall package. Therefore, to achieve the same parameters in a lower timeframe, some blocks may be discarded due to the mining sequence and the optimization of destinations inside the whole mass.

Having this idea in mind, you should already have enough information to decide and structure the next step of the optimization. Based on the amount mined in the last item and in the processing capacity, define a good timeframe to identify the mining sequence. In this case, we had 231 Mt as the ore total mass to split in almost 23 years, since the processing capacity is 10Mt.

To improve efficiency in the optimization, before working on a yearly basis, we made the decision to consider the first 5 years. It is reasonable to generate a 10-year surface to consider the optimization inside this limit due to observations made before. Remember that each assumption here can be done accordingly with your project’s demands and that MiningMath can work with any timeframe to meet your needs.

Decision Trees

Comparing Scenarios

Decision Trees provide you with a detailed broad view of your project, allowing you to plan your mining sequence by analyzing every possibility in light of constraints applied to each scenario, which options are more viable and profitable to the global project, as well as how these factors impact the final NPV. Consider, for instance, the plant production per year as a variable factor. Using Decision Trees (Figure 1), you will be able to analyze how each constraint, e.g. the ore price, affects that year’s production and benefits or not the global project.

Figure 1: Essence of a Decision Tree, done in presentation software.

By running all the scenarios individually, just like what you did on Practice First, you will be able to identify how each change, within a set of constraints, impacts the NPV results and the mining sequence generated (Figure 2 and 3), which provides you a broader view of your project and enables you to decide which route you should take to generate value to your company.

Figure 2: BaseCase
Figure 2: BaseCase
Figure 3: PriceUp
Figure 3: PriceUp

How to Analyze Multiple Scenarios

Increase in the value of copper

Analyzing first the scenario in which there is a change in the economic value of the P1 process (“scn-PriceUp”), values such as NPV would naturally be different. In this case, analyzing the NPV and the total movement (Figure 3), it’s possible to understand that a different mining sequence was generated, which increased the mine’s lifetime by one period. This market change has also increased cumulative NPV (Figure 4) values based on its direct relation with the copper selling price. The charts below were made with the help of MiningMath’s results in simple spreadsheet software.

Figure 4: Total mass (Process+waste) handled on each scenario.
Figure 5: Cumulative NPV contrasts.

Adding an average grade limit

Now we can analyze the scenario in which a restriction in the average grade at P1 process was added, using a minimum and a maximum limit of copper (“scn41-AvgCu”). The blocks that would be processed would have to meet established targets, allowing a better selectivity of what should be processed or not. The ones which have higher or lower grades than required could be blended with others to generate an average grade that respects the constraints and improves the NPV.

Notice that there was a higher total production (Figure 5) in each period, caused by the increase of the stripping (ore/waste) ratio to meet the 30 Mtons of ore production at P1 Process and the average grade targets settled at the “scn41-AvgCu” scenario. A better stock pilling use is expected, in order to use all the blending capabilities and decision-making intelligence of the algorithm to decide which blocks could be mixed to fulfill the plant capacity. In addition, the cumulative NPV (Figure 6) shows that by inserting average grade constraints we consequently reduce the algorithm flexibility and lose some money to keep the operational stability frequently required at a processing plant.

In general, the main goal of MiningMath, considering the set of constraints provided, is to maximize the cumulative NPV in the shortest mine lifetime possible, which would reduce the project depreciation by interest rates. The charts below were made based on MiningMath results with the support of spreadsheet software.

Figure 6: Total mass handled on each scenario.
Figure 7: Cumulative NPV contrasts.

Building Decision Trees

You have been introduced to some of MiningMath’s functionalities. Now let’s take a closer look at how decision trees are built.

Mine project evaluation largely relies on technology from the 1960’s, in which a step-wise process is usually necessary along with time-consuming activities, like pit-design, in order to create only one single scenario. Evaluating projects through this approach could take from weeks to months of multidisciplinary work just to produce a couple of scenarios. This process is often guided by some arbitrary decisions that may constrain the mathematical solution space, confining solutions to engineering expertise and judgment.

A global optimization scheduling can speed up the process of generating multiple scenarios for project overview prior to detailed work. MiningMath integrates the business’ areas and allows managers to improve their decision-making process by structuring their strategic analysis through multiple decision trees with a broader and optimized view of their projects, comprising constraints from different areas of the company.

The following video shows a few possibilities recognized only when seeing the available paths to create value. The video is oriented to technical daily usage but also covers interesting subjects for the managerial perspective. For the last case, skip straight to minute 15:23.

Video 1: Video detailing the building of decision-trees.

Apply to your projects

Now that you have played with the sample data, it is time for a hands on approach and apply this optimized strategy to your own projects!

MiningMath already allows you to structure your Decision Trees layout at its home page, which facilitates and guides the decision-making and mining planning processes.

Take advantage of the possibility to add (+), rename, or delete Decision Trees (Figure 7), by clicking with the right button at their names and/or exchange scenarios (Figure 8) between trees to build different mining planning strategies. The icon is a shortcut, so you can easily open your scenario’s full report.

Compare everything in a single look and identify how each change impacts your results to build your own analysis by using presentations based on MiningMath charts as shown in Figure 1.

Figure 8: Decision Trees' table
Figure 8: Decision Trees' table
Figure 9: Decision Trees' organization
Figure 9: Decision Trees' organization

Interface Overview

Articles

Home Page

MiningMath automatically starts on the Home Page, as shown in Figure 1.

Overview of Recent Projects

Decision Trees feature enables you to create new tabs and ways to organize the mining planning strategies.

Open and View options for the current selected scenario under the Decision Trees tab.

Edit button shortcut, which will lead you to the Calculator functionality explored further ahead.

Model table discloses the main information regarding your block model and its parameters.

Figure 1: Interface example. Click to expand.

The following are three main information windows:

  • The Recent Projects window allows you to select a project and have an overview of the saved scenarios that will appear right away at the Decision Tree tab. It allows the user to quickly navigate through recent projects and scenarios without opening them from their original folders. Clicking with the right button on the project name, the user will have 4 options:

    1) New scenario: "Scenario config" window will open allowing you to decide in which decision tree to place the new scenario, its name, and a description for it. Afterward, is going to be directed to set it up in the scenario tab.

    2) Show in explorer: This option takes to the directory containing the folder with the project files and data.

    3) Remove from list: Excludes the referred project from the Recent Projects list.

    4) Delete project: Deletes the project and the scenarios from it.

  • The Decision Trees feature enables you to create new tabs and ways to organize the mining planning strategies by exchanging scenarios between them, if necessary. It allows access to all paths involved in the project, providing a broad view and enhancing the decision-making process. It shows decision trees’ scenarios with key information about them, such as name and description to easily identify its characteristics, NPV on M$, runtime, and a direct link to the sheet containing all the results of the scenarios, which are available after the scenario’s execution. It’s possible to:

    1) Add new trees by clicking on “+”

    2) Rename a tree by double-clicking its name

    3) Clicking with the right button, the user may add a new scenario, rename or delete this tree.

    Getting into more details, some hidden options are available to the user when clicking with the right button on the scenario’s name: open, view model, rename, show in explorer, delete, and the possibility to transfer it between decision trees. The scenario description can be easily edited with a double click.

    To open any scenario, click on one Recent Project first, and then choose the scenario you want to work with at the Decision Trees tab by clicking with the right button of your mouse, and choosing the option "Open", or just select the scenario and click on “Open” at the right bottom of this screen. The “View” button leads to the MiningMath’s Viewer.

  • The Model table discloses the main information regarding your block model and its parameters, so that you can easily review it at any time using the "Edit" button shortcut, which will lead you to the "Calculator" functionality.

Model Tab

This window aims to help you to modify your block model accordingly with what is required for your project and also allows you to “Export” the block model to the CSV format to be used with any other software.

This tab starts at the “Parameters” option, showing your previous set up at the importation, similar to Figure 2, and all the existing fields. It also allows you to remove any parameter at any time.

Figure 1: Parameters Model tab

The “Function” option discloses the “Validate your block parameters” table, so that you can choose a single block within your model to verify its values. It also enables MiningMath’s internal Calculator to make adjustments and changes to your dataset with the addition of new fields.

Figure 2: Internal Calculator at Function in Model tab

Scenario Tab

General Parameters

MiningMath automatically switches to the Scenario Tab in the General option once a scenario is opened, as shown in Figure 1. 

Figure 1: General tab and densities
Figure 1: General tab and densities
Figure 2: General tab and economic parameters
Figure 2: General tab and economic parameters
Figure 3: General tab and slope angles
Figure 3: General tab and slope angles
Figure 4: General tab and stockpiling
Figure 4: General tab and stockpiling

The General tab presents all the general inputs regarding densities (Figure 1), economic parameters (Figure 2), slope angles (Figure 3) and stockpiles (Figure 4), which are detailed next.

Densities

Densities, as shown in Figure 1, are used along with block size to calculate tonnages. The user has two options to define them:

  • "Field" shows the column(s) that has/have been assigned to the density during the importation. This option is intended to allow varying densities by block.

  • "Default value" is applicable to any block without density information, whether a density column is imported or not. It is also used when you choose the field as .

Economic Parameters

The Discount Rate is a field of Economic parameters, as seen in Figure 2. It is usually considered in an annual base, is responsible to define the impact of mining ore/waste over time, which influences the algorithm decision-making process.

While working with different time frames, the discount rate serves just a rough NPV approximation, and it doesn’t affect so much the quality of the solution, given that the best materials would be allocated first. Thus, by multiplying or splitting it by the number of periods, you might get reasonable results.

Slope Angles

Slope angles are one of the most important parameters when considering constraints hierarchy. The user, as seen in Figure 3, has two options here:

  • Field shows the column(s) that has/have been assigned to the slope during the importation. This option is intended to allow different slope angles by block.

  • Default value is used to any block without slope information, even if a column was assigned. It is also used when you choose the field as <none> .

Stockpiling

The stockpiling feature can be used by activating the checkbox. When this option is enabled, shown in Figure 4, the user can define:

  • Fixed mining cost (cost/t) refers to the average mining cost used for the economic function. This value is used to decompose the economic value while considering stockpiles.

  • Rehandling cost (cost/t) represents the cost to reclaim blocks from the stockpile to the process.

To illustrate the other tabs inside the Scenario tab, the parameters used in the Marvin case will be employed as summarized below:

Parameter Subparameter Value
Densities
Field
Density
Default value
2.75
Slope angles
Field
Slope
Default value
45 degrees
Stockpiling
Fixed mining cost
0.9$/t
Rehandling cost
0.2$/t
Discount rate

-

10%

Table 1: Parameters used in the Marvin cases.

Destinations: Process, Dump and Stockpile

Figure 5: Destinations tab, Recoveries for each element/mineral and destination, and Stockpile limit in tonnages.

On the Destinations tab (Figure 5), you will define destinations to where the blocks can be sent. Each destination must be mapped with their respective field containing the economic values. MiningMath requires at least one destination for the process and one destination for the dump. For each destination, you have an economic value and recoveries by elements.

Process & Dump

To add destinations, in the bottom corner of the window, click on:

  • Add Process

  • Add Dump

Each scenario must contain at least one process and one dump among the destinations imported. The destination of each block will be reported by assigning them with the numbers 1 or 2 (see the numbers beside the Name column), which depends on the order of addition.

Recovery

For each processing stream, the user must inform a process recovery, varying from 0 to 1, to any element/mineral whose column has been imported as a grade.

This value on the interface serves only for the purpose of generating reports, as it has been considered during the economic calculation. Use the following values for the processing stream:

  • Cu: 0.88

  • Au: 0.60

Stockpile

You can also define a tonnage limit for the stockpile if activated in the General tab (see Figure 4).

MiningMath considers the tonnage inputted as a cumulative upper limit that will be considered all over the life of mine.

In this example, a limit has not been defined, which implies an capacity to stock. Read more about stockpiles.

Economic Value

In the column of Economic value, you must assign each destination to its corresponding economic function. Therefore, use:

  • Destination 1 - Process 1 - Economic Value Process

  • Destination 2 - Dump 1 - Economic Value Waste

Figure 6 zooms in the destination fields, showing how they should look like for this example.

Figure 6: Economic values for each destination.

Production Inputs

Figure 7: Production tab and production limits for each destination based on an yearly timeframe.

After completing the previous fields, move to the Production tab (Figure 7). You can define limits (in tonnes) for each destination and the total amount of material moved per period and also add different timeframe ranges in the optimization. For this example, use the values as shown in Figure 7.

  • TimeFrame: Years (1)

  • Process 1: 30,000,000 t

  • Dump 1: 50,000,000 t

  • Total: 80,000,000 t

Read more about productions changing over time.

Geometric Inputs

Figure 8: Operational constraints.

On the Geometric tab (Figure 8), you can define parameters intending to find mathematical solutions that already consider basic requirements to be operationally feasible. Figure 8 highlights Operational Fields, which could differ for each period range and timeframe, such as minimum widths and vertical rate. Optional Fields are also allowed. These allow the definition of: 1) areas to be forced and/or restricted; and 2) periods to which surfaces are applied. In this example the values defined for all periods are:

  • Minimum width: Mining 100m, Bottom: 100 m

  • Vertical rate of advance: Maximum 150 m

In the Geometric tab you can also force mining and restrict mining using surfaces based on coordinates and defined as a 3D-grid of points in the CSV format. Surfaces are the most important constraints within MiningMath’s hierarchy, allowing you to impose one’s understanding and take control of prior results and operational aspects.

Using surfaces, you are able to play with geotechnical aspects, force certain regions to allocate waste material, restrict areas to protect the environment, and/or guide operational aspects by importing a designed pit.

Due to the complexity of this subject, surfaces will be treated in a specific section of our documentation.

Average

Figure 9: Blending constraints.

On the Average tab, you are able to define a minimum and/or maximum average grades for any element/mineral imported as grade (Figure 9 area 1).

Blending constraints can also be defined by period ranges (Figure 9 area 2) and/or destination (Figure 9 area 3).

It’s worth mentioning that this minimum limit does not represent cut-off values. Since it is based on average parameters, the algorithm can use lower values to respect this parameter and increase the NPV with higher ones. If you wish to input a cut-off, a good way to do it is by filtering these blocks and assigning the the mass as a sum field, as mentioned here.

Sum

Figure 10: Other constraints.

On the Sum tab, you are able to consider any summed parameter as a minimum and/or maximum limits for any data imported as other (Figure 10 area 1).

Other constraints can also be defined by period ranges (Figure 10 area 2) and/or destination (Figure 10 area 3).

This feature is available only at the full versions of MiningMath. Read more.

Overview

Figure 11: Overview screen for final verification of inputted parameters.
Figure 11: Overview screen for final verification of inputted parameters.
Figure 12: Save as information.
Figure 12: Save as information.
Figure 13: Execution options.
Figure 13: Execution options.

Click on Overview (Figure 11) for a single page summary of all parameters related to the direct block scheduling, as illustrated in the figure below.

The Save as option (Figure 12) can be used to redefine the name, description for an edited scenario, and its decision tree.

You can also decide which files MiningMath will produce as outputs by using the execution options (Figure 13) before clicking on “Run” your scenario.

Viewer

After running your scenario, the Mined Blocks file will disclose its results on the 3D viewer, enabling the view of your model from different angles. By selecting “Period Mined”, you are able to view the mining sequence period by period. By selecting a surface, it is possible to identify the topography changes of each period and also modify its opacity, facilitating the visualization.

MiningMath also allows you to import surfaces already created if you place them in the same folder as the other ones, so that you can validate their geometry if necessary.

Click on “Load Scenario” to import multiple scenarios and compare them, in order to extract the best results accordingly with your project constraints.

Figure 1: Viewer
Figure 1: Viewer
Figure 2: Viewer
Figure 2: Viewer

Overview

Last check before running

The Overview tab aims to let the user to give a last check on each parameter inputted. Every information available in this screen, as shown in Figure 1, is also present on the previous screens:

  1. General

  2. Destinations

  3. Production

  4. Geometric

  5. Average

  6. Sum

Note the user can even go straight to the overview tab to save time.

Figure 1: The Overview Tab.

Save As

Options to save a scenario

By clicking over Save As button, a window will pop-up, as shown in Figure 1. Then, the user will be able to set:

  • A scenario name

  • A scenario description

These fields intends to better identify a scenario among several ones by just taking a look at the Projects List.

Figure 1: Saving As.

Run

Running the optimization

The Run tab is the last step before running your project’s optimization. The Figure 1 below shows its interface.

Reports visualization

This screen allows you to view the results, in tables, if the scenario has already been run, inside the software, facilitating the analysis.

Run button

After everything is checked, just Run the scenario.

Progress bar

With the progress bar you can monitor the execution of the scenario and the estimated time it will take to be completely executed, as shown in Figure 2.

Figure 2. Progress bar

Handling Data

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Formatting the Block Model

Block Model Basic requirements

MiningMath requires the following formatting specifications:

  1. Regularized block model: This means 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.

Good practices

  1. Configure Microsoft Windows number formatting to use dot as the decimal separator.

  2. Use the metric system.

  3. Set multiple fields that will consider different economic values, material types, contaminant limits, and any other variable you wish to analyze or control.

Must check

Understanding 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.

Figure 1: Field types

Mandatory Field Types and their meanings

  1. Coordinates X, Y, and Z refer to your geo-referenced information.

  2. Average refers to any variable that could be controlled by means of minimums and maximums considering its average: grades, haulage distance, and other variables.

  3. Economic Value refers to the columns with the economic value, which represent 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 mentioned on the next page.

Optional Field Types and their meanings

  1. Density refers to the block's density. This field is used to calculate the block's tonnage.

  2. Slope refers to slopes varying block-by-block, which gives the flexibility to define slopes by lithotype and sectors.

  3. Recovery refers to recoveries varying block-by-block.

  4. Sum refers to any variable that could be controlled by means of minimums and maximums considering its sum.

  5. Predefined destinations refers to possible fixed destination values. This can be used for example if you want to define pushbacks or apply lithologic restrictions that prevent certain blocks to be processed. However, by fixing destinations you are impeding MiningMath to reach its full potential. More about this here.

  6. Other refers to information that you with to have in the exported outputs.

  7. Skip refers to any variable that should be ignored. This field type might help improving the runtime since these variables will not be considered and exported along with the optimization outputs.

Field names shortcut

Shortcuts can be used for automatic recognition in the importation process. These are listed in the table below.

Field name Shortcuts
Coordinates
X | Y | Z
Average
@ | grade
Density
% | dens | sg
Economic value
$ | dest | val
Recovery
* | recov
Slope
/ | slope
Sum
+
Skip
!

Mandatory requirements

Considering the specifications mentioned before, the formatted data set should have the following information for each block:

  1. Coordinates.

  2. Grades (at least one element assigned as Average).

  3. Economic values (at least 1 process and 1 waste).

The following video gives an introduction on how to setup your block model.

Video 1: Block Model setup.

Attention to software conversions

The model’s origin must be placed at the bottom portion, starting to count from the minimum coordinates at X, Y, and Z.

Figure 1 highlights a block model origin at the corner of the first block and the coordinates on its centroid.

Each software uses its own conventions for data format, naming and numbering systems, etc. These differences should be observed to prevent conflicts when transiting data from multiple software, each one for one specificity.

What you must know:

  1. MiningMath uses coordinates (X,Y,Z) for which Z, which represents the elevation, starts upwards (Figure 3a).

  2. Other mining software may use indexes with IZ starting downwards (Figure 3b). MineSight is an example that uses this notation.

Figure 2: Blocks Matrix.

There is no right or wrong convention, but there is a correct procedure for each software.

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

Figure 3a: The lowest IZ value is at the bottom of the model.
Figure 3b: The lowest Z value is at the top of the model, which will not fit MiningMath requirements.

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 image below shows an example of your model should be displayed.

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.

Figure 4: Example of how block models should look like with a rectangular base.

More Details on Air Blocks

The following video shows how to do remove air blocks using filters on MS Excel. These tips are also applicable to any mining software of your choice.

Video 1: Removing air blocks using filters on MS Excel.

Importing the Block Model

Block Model File

To import the block model, select the option New Project on the left panel of MiningMath (Figure 1). 

Figure showing where to create a new project to import a new model.
Figure 1: Creating a new project to import a new model.

Afterwards, the file name input field is shown in red, indicating a mandatory field. (Figure 2) Browse for and select the CSV formatted file. Press Next to advance.

Figure 2: Importing a CSV model.

Project Naming

In the next window, shown in Figure 3, the Model Name must be entered.

Optionally, the destination folder (Model Folder) can be changed as well as the Scenario Name, and a Scenario Description can be added.

Figure 3: Defining a name for the model and the first scenario.

Imported Fields & Validation

Upon clicking Next, the following window will provide a statistical summary of information for the block model that will be imported (Figure 4).

Check the parameters carefully.

Figure showing the interface to validate your data.
Figure 4: Validating your data.

Geo-reference system, Origin, Dimension and Rotation

Upon clicking Next, the CSV file will be imported into MiningMath, and show data related to the block model geo-reference system, that can be only coordinates. The next steps are to place the rotation degrees (Azimuth rotation), origin accordingly with your mining package, and the block dimension as illustrated in Figure 5. The number of blocks is automatically calculated after the origin and dimensions are provided.

The origin of this project was x=3,475, y=6,480, and z=285, and the block dimensions were 30 meters in each coordinate.

Figure 4: Coordinates input.

Rotated models

MiningMath supports the use of block models that have been rotated using an Azimuth rotation (Figure 5).

Figure 5: Example of Azimuth rotation in the coordinate system.

The amount of rotation degrees can be passed as depicted in Figure 6.

Figure 6: Azimuth rotation depicted when hovering over the RZ field.

After importing, you can see the rotated model in the Viewer tab (Figure 7). The detailed steps with mathematical formulations for the rotation procedure can be seen here.

Figure 7: Example of rotated model in the viewer tab.

Field Type Assignment

When Next is selected, the following form will appear (Figure 8), showing correlations between the imported CSV file header and the available field types in MiningMath.

You must associate each imported column to one of the options located just above the table, for instance: block coordinates X, Y, and Z to Coord. X, Y, and Z field types. For more details on how you can correlate each column, access this link. You can also keep the original data from your previous Mining Package, by using this approach.

If you do not already have an Economic Value function, when importing your block model, you will be directed to the Scenario tab. Then, click on the Function tab to calculate your Economic Value function in the internal calculator as explained here.

Figure 8: Assigning each column to the proper field type.
Notes

  1. MiningMath has mandatory variables (columns) to be assigned to the proper Field Type:

    1) Coordinates (X, Y, Z).

    2) Average

    3) Economic Values (at least two)

  2. Validating data screen might be overlooked, but it is very important to validate one's data based on minimums and maximums. Read more.

  3. Each column imported should be assigned to the proper field type in order for MiningMath to treat each variable accordingly. Read more.

  4. Typically, MiningMath recognizes some columns automatically when their headers are similar to the Field Type name. Otherwise, the MiningMath will automatically assign them to the Field Type sum.

    To enable the Next button, the user needs to assign each one of the mandatory variables to their respective Field Type. 

Grade, Dimension and Origin

After clicking Next, it will demand grade units. As you can see in Figure 10, 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.

Figure 10: Informing block dimensions, origin, and grade units.

View Your Model and Surfaces

After filling in the required fields, the options View Model and Scenarios will be enabled. Before setting up your first scenario you can view it by clicking in the Viewer and Load scenario. Select all the tooltip options and click in load. This option also allows you to view surfaces created, just place them in the scenario folder before loading and do the first validation.

Evaluate your model

After importing your model, you can view it in the Viewer tab as depicted in Fig. 11-14. This should help you answer questions such as:

  1. Where are the high grades distributed?

  2. Does the process economic values, above zero, match with the regions identified in the last question?

  3. How are waste economic values distributed? Are maximum and minimum values reasonable when you compare them with the process?

Figure 11: Checking your model.
Figure 11: Checking your model.
Figure 12: Checking your model.
Figure 12: Checking your model.
Figure 13: Checking your model.
Figure 13: Checking your model.
Figure 14: Checking your model.
Figure 14: Checking your model.

Economic Values

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.

Destinations required

MiningMath requires two mandatory destinations at least:

Therefore, each block must be associated with:

  • 1 Processing stream and its respective economic value

  • 1 Waste dump and its respective economic value

Notes:

  • 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.

  • 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.

Animation (click to see): Simplified flow-chart of blocks' destinations optimization.

Calculation

Each field related to Economic Value (Process/Waste) must report the value of each block as a function of its destination (Process or Waste in this example), grades, recovery, mining cost, haul costs, treatment costs, blasting costs, selling price, etc. The user is not required to pre-set the destination, as the software will determine the best option during the optimization.

To calculate the Economic Values you can use MiningMaths’s internal calculator, available at the “Function” option inside the “Model” tab. To illustrate the calculation of economic values, an example is shown below. The calculation parameters are listed in Table 1.

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

Table 1: Parameters for calculating the economic values.

Figure 1: Internal Calculator.

Block Tonnes

  • Block Tonnes = BlockVolume * BlockDensity

  • Block Tonnes = 30*30*30*[Density]

Figure 2: Block model calculations.

Tonnes Cu

  • Tonnes Cu = Block Tonnes x (Grade Cu/100)

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

Figure 3: Block model calculations.

Mass Au

  • Mass Au = Block Tonnes x Grade Au

  • Mass Au = [BlockTonnes]*[AU]

Figure 4: Block model calculations.

Economic Value Process

  • 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)]

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

Formula for economic price
Figure 5: Process Economic Value calculation.

Economic Value Waste

  • Economic Value Waste = –Block Tonnes x Mining Cost

  • Economic Value Waste = –[BlockTonnes] * 0.9

Figure 6: Economic Value Waste calculation.

The example block in Figures 4-6 would generate -299,880$ if it is 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 prejudice than when it is processed. MiningMath defines the best destination regarding the set of constraints throughout the time, thus this decision a lot more complex than the example above in most cases.

Data Validation

Running an optimization for complex projects with several constraints may demand hours only to validate if the formatting has been done properly. Therefore, we present here an efficient scenario to quickly validate your data.

This page uses the Marvin Deposit as an example. To see its parameters and constraints please check the page here.

Validate it First

In order to validate your data and cut its runtime, we strongly recommend running MiningMath FULL with the following set up:

  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.

The figure below depicts this set up at MiningMath, with the highlighted fields.

Validation fields in the Overview tab.

Results

Results are depicted below, with blocks in the sequencing, surface, surface with blocks and production tonnage.

Block model view
Sequencing
Surface
Surface
Surface with blocks
Surface with blocks
Production result
Production result
Ultimate pit

The surface returned by this data validation process represents the most economically viable pit shell, also known as the ultimate pit.

Questions

  • Did the scenario run properly?

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

  • Is the mining happening in reasonable areas?

  • Is there a reasonable number of periods of life of mine?

Constraints Validation

Continuing the data validation, start to add the first constraints related to your project so that you can understand its maximum potential. The surface generated in this case could also be used as a restrict mining in the last period to reduce the complexity of your block model and the runtime of MiningMath, since it includes a set of constraints inputted.

Example

  • Set up a scenario with 1,000 Mt in the processing plants, which corresponds to a lot more mass than expected in the whole life of the mine.

  • Add the Minimum Bottom Width (100m). This constraint will allow you to have a suitable work-front for your equipment.

  • Restrict Mining surface, if you have this constraint in your project.

  • Grade constraint until 0.7%.

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

Note: Sum constraints can restrict the total amount of handling material (ore + waste) of the mine. Therefore, do not use them in the validation.

Figure 1: Sequencing
Figure 1: Sequencing
Figure 2: Restrict surface
Figure 2: Restrict surface
Figure 3: Surface
Figure 3: Surface

Let's make everything clear

Now that Constraints Validation step is done, you are able to use this final surface as a guide for future optimizations. This approach reduces the runtime and the complexity of the algorithm because when you take it into account, the blocks below this final optimized surface won’t be considered and the heuristics inside the interface would be facilitated. Notice that we did not make any change in the discount rate, thus, this first NPV does not represent the reality. If you need an accurate result in this step, make sure to adjust it.

It’s important to remember that when we restrict the mining into this surface, the number of periods generated in future runs could be reduced because the average parameters of each one will have to meet the constraints of the overall package. Therefore, to achieve the same parameters in a lower timeframe, some blocks may be discarded due to the mining sequence and the optimization of destinations inside the whole mass.

Having this idea in mind, you should already have enough information to decide and structure the next step of the optimization. Based on the amount mined in the last item and in the processing capacity, define a good timeframe to identify the mining sequence. In this case, we had 231 Mt as the ore total mass to split in almost 23 years, since the processing capacity is 10Mt.

To improve efficiency in the optimization, before working on a yearly basis, we made the decision to consider the first 5 years. It is reasonable to generate a 10-year surface to consider the optimization inside this limit due to observations made before. Remember that each assumption here can be done accordingly with your project’s demands and that MiningMath can work with any timeframe to meet your needs.

Exporting Data

Exporting the Model

Select the button Export Model on MiningMath’s Model tab, as shown below.

Figure 1: Clicking on Export.

Clicking on Export, a new page will appear, allowing you to select the folder where the block model exported would be saved with its name.

Figure 2: Exporting data.

Just click on “Next” for your model to be exported to the folder selected.

Public Datasets

MiningMath allows you to learn, practice, and demonstrate, by showing any scenario previously ran the concepts of Strategy Optimization using the full capabilities of using only Marvin Deposit. This version is freely available to mining professionals, researchers, and students who want to develop their abilities considering this standard block model.

Marvin Deposit

DB Information

Below are listed the default parameters for Marvin according to the adaptions made in our formatted model.

Parameter Value
Block size
23000 m³ (X = 30m, Y=30m, Z=30m)
AU - Selling Price
12 $/g
AU - Selling Cost
0.2 $/g
AU - Recovery
0.60
CU - Selling Price
2000 $/ton
CU - Selling Cost
720 $/ton
CU - Recovery
0.88
Mining Cost
0.9 $/ton
Processing Cost
4.0 $/ton
Discount Rate
10% per year
Default Density
2.75 t/m³
Default Slope Angles
45 degrees

Some common constraints applied to the Marvin deposit are listed below.

Constraint Value
Processing capacity
10 Mt per year
Total movement
40 Mt per year
Sum of processing hours
4,000 per year (detailed estimate of the plant throughput)
Vertical rate of advance:
150m per year
Copper grade
Limited until 0.7%
Minimum Mining Width
50m
Minimum Bottom Width
100m
Restrict Mining Surface

Some surface in .csv format. For example due to a processing plant in the area.

Fixed Mining (Stockpiling)
0.9$/t
Rehandling cost (Stockpiling)
0.2$/t

Economic Values

  • Process Function = BlockSize * Density * [GradeCU/100 * RecoveryCu * (SellingPriceCU – SellingCostCU) + GradeAU * RecoveryCu * (SellingPriceAU – SellingCostAU) - (ProcessingCost + MiningCost)]
  • Waste Function = BlockSize * Density * MiningCost

McLaughlin Deposit

DB Information

Below are listed the default parameters for the McLaughlin deposit according to the adoptions made in our formatted model.

Parameter Value
Block size
X = 7.62m (25ft), Y = 7.62m (25ft), Z = 6.096m (15ft)
AU - Selling Price
900 $/oz
AU - Recovery
0.90
Mining Cost
1.32 $/ton
Processing Cost
19 $/ton
Discount Rate
15% per year
Default Density
3.0 t/m³
Default Slope Angle
45 degrees

Economic Values

  • Process Function = BlockSize * Density * [GradeAU * RecoveryCu * (SellingPriceAU) - (ProcessingCost + MiningCost)]
  • Waste Function = BlockSize * Density * MiningCost

Output files

Execution options

The Execution Options or Run Options allow the user to define:

  • Files to be exported.

  • The visual results to be automatically shown on the viewer after each run.

Figure 1 highlights in (A) where the user can trigger this pop-up window and in (B) the options available, among which the user can:

  • Export/not export to CSV files:

    • The resulting surfaces
    • The resulting model in two ways: all blocks or only mined blocks, with/without coordinates and/or index information.

  • Set which results to be shown on the viewer:

    • Surfaces
    • Model
Figure 1: Execution options.

Outputs from MiningMath

MiningMath automatically produces:

  • Formatted reports (XLSX files).

  • Tables (CSV) whose data feeds the reports.

  • Updated block model (MinedBlocks or AllBlocks).

  • Surfaces as a grid of points (CSV)

How those files are organized?

MiningMath organizes files, as listed below:

SSMOD and SSPRJ are important to report any issues you face.

    • Model Folder
    • MiningMath Model file (.SSMOD).
    • MiningMath Project file (.SSPRJ).
    • Scenario folder
      • Output Block Model
        • MinedBlocks.CSV contains information about the mined blocks.
        • AllBlocks.CSV, when requested, contains information about all blocks.
      • Scenario file (.SSSCN) is a XML file read by the interface. Use it for a quick check on parameters used.
      • Report file (.XLSX) summarizes some quantifiable results, including charts such as productions, average grades, and NPV.
      • MiningMath also generates independent report files (.CSV) present in the report file (XLSX) as a backup:
        • Production Process.
        • Production Dump.
        • Production Total.
        • Grade Process.
        • Grade Dump.
        • Metal Process.
        • NPV.
        • Cumulative NPV.
      • Surface files (Surface-##.CSV) formatted as a grid of points.

  • List Item

SSMOD and SSPRJ are important to report any issues you face.

Block Model Output (MinedBlocks.csv x AllBlocks.csv)

After each optimization, MiningMath exports the block model in one of two formats:

  • MinedBlocks.csv: The file presents only the blocks that have been mined from each scenario. Mined Blocks are exported by default, as it is a lighter file.

  • AllBlocks.csv: The All Blocks file presents all the blocks, whether mined or not, from each scenario, so it is basically the original Block Model along with resultant information from the optimization.

The resultant model includes all columns imported (except the skipped ones) besides the following information:

  • Mined Block shows whether (1) or not (0) a block have been mined.

  • Period Mined shows in which period a block have been mined (-99 for blocks that have not been mined). To learn more about the mining sequence within a period, access here.

  • Period Processed shows in which period a block have been processed (-99 for blocks that have not been processed).

  • Destination informs the destination of each block — according to the order the user has added processing stream(s) and waste dump(s).

How to interchange them?

Figure 2 shows where the user can interchange of these options.

  1. Click on the highlighted Execution button (A) to open the Run Options (B).

  2. Select All blocks in model or Only mined blocks, as you need.

  3. Hit OK, then Run.

By default, MiningMath exports the MinedBlocks file as a block model output

Results

MiningMath will generate a report directly on Microsoft Excel, as shown in the following image, and the optimized pit (blocks and surface) in the viewer in case the user chooses this option (right figure above). The automatic preview shows only the mined blocks, colored according to each mining period defined by the scheduler.

Reports

The results presented in the Excel spreadsheet show, in the Charts tab, the graphs relative to the reported results calculated in the Report tab. The processed mass results, discarded mass, stock development, Au/Cu percentage in the process, Au/Cu percentage in the dump, metal contained in the process, net present value and cumulative net present value are arranged individually in the Production Process 1, Production Dump 1, Stock Process 1, AU/CU – Grade Process 1, AU/CU – Grade Dump 1, AU/CU – Metal Process 1, NPV and Cumulative NPV tabs, respectively.

Figure 2: Results report.

Visual Results

By default, MiningMath exports only the Mined Blocks file showing them by period on the viewer, as in the following illustration. The user can change any exporting options on Run Options menu.

Figure 3: Visual results.

Mined Blocks

If the user chooses to export the model, MiningMath will automatically save the list of the scheduled blocks (MinedBlocks.csv) or all blocks (AllBlocks.csv) in the block model folder, as shown in the figure below, which can be imported into other mining software packages.

The files MinedBlocks.csv and AllBlocks.csv may contain indices and/or block coordinates, and all the imported data/parameters along with the following information:

Figure 4: Mined blocks.

  • Mined Block shows whether (1) or not (0) a block have been mined.

  • Period Mined shows in which period a block have been mined (-99 for blocks that have not been mined).

  • Period Processed shows in which period a block have been processed (-99 for blocks that have not been processed).

  • Destination informs the destination of each block — according to the order the user has added processing stream(s) and waste dump(s).

Video 1: Outputs and files’ hiearchy.

Workflow

Articles

Super Best Case

In the search for the upside potential for the NPV of a given project, this setup explores the whole solution space without any other constraints but processing capacities, in a global multi-period optimization fully focused on maximizing the project’s discounted cashflow.

As MiningMath optimizes all periods simultaneously, without the need for revenue factors, it has the potential to find higher NPVs than traditional procedures based on LG/Pseudoflow nested pits, which do not account for processing capacities (gap problems), cutoff policy optimization and discount rate. Traditionally, these, and many other, real-life aspects are only accounted for later, through a stepwise process, limiting the potentials of the project.

MiningMath’s Super Best Case serves as a reference to challenge the best case obtained by other means, including more recent academic/commercial DBS technologies available. See a detailed comparison of these two approaches below.

In modern/traditional technology, large size differences between consecutive periods may render them impractical, leading to the “gap” problem. Such a gap is caused by a scaling revenue factor that might limit a large area of being mined until some threshold value is tested. MiningMath allows you to control the entire production without oscillations due to our global optimization.

In the modern/traditional methodology the decisions on block destinations can be taken following some techniques such as: fixed predefined values based on grades/lithologies post-processing cutoff optimization based on economics post-processing based on math programming or even multiple rounds combining these techniques. With MiningMath the destination optimization happens within a global optimization in a single step, maximizing NPV and accounting simultaneously for capacities, sinking rates, widths, discounting, blending, and many other required constraints.

Modern technology is restricted to pre-defined, less diverse sequences because it is based on step-wise process built upon revenue factor variation, nested pits, and pushbacks. These steps limit the solution space for the whole process. 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.

Due to tonnage restrictions, modern technology might need to mine partial benches in certain periods. With MiningMath’s technology, there isn’t such a division. MiningMath navigates through the solution space by using surfaces that will never result in split benches, leading to a more precise optimization.

Due to tonnage restrictions, modern technology might need to mine partial benches in certain periods. With MiningMath’s technology, there isn’t such a division. MiningMath navigates through the solution space by using surfaces that will never result in split benches, leading to a more precise optimization.

Modern approaches present a difference between the optimization input parameters for OSA (Overall Slope Angle) and what is measured from output pit shells, due to the use of the “block precedence” methodology. MiningMath works with “surface-constrained production scheduling” instead. It 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 the elevation to be above, below, or matching a block’s centroid, which ensures that MiningMath’s algorithm can control the OSA precisely, with no errors that could have a strong impact on transition zones.

Example

Setting up the Super Best Case is simple. There are only two necessary restrictions:

  1. Processing capacity: 10 Mt per year.

  2. Timeframe: Years (1).

Depending on your block model, additional parameters may need to be specified. For example, if you have multiple destinations these could be added for proper destination optimization. The figure below provides a comprehensive overview, highlighting the essential parameters required for running the Super Best Case scenario using the pre-installed Marvin dataset.

Results

Results can be analysed in the Viewer tab and the exported report file. For the pre-installed Marvin dataset, note how the sequencing has no gap problems, and the production is kept close to the limit without without violating any restrictions.

Super Best Case Sequencing
Sequencing Slice
Super Best Case production tonnages

Export files

The block periods and destinations optimized by MiningMath’s Super Best Case (or any other scenario) can be exported in a CSV format. You could use these results to import back into your preferred mining package, for comparison, pushback design or scheduling purposes. Export options are depicted below.

Adding constraints

A refinement of the super best case could be done by adding more constraints, preferably one at the time to evaluate each impact in “reserves”, potential conflicts between them, and so on. You can try to follow the suggestions below for this improvement:

  • All blending constraints.

  • All restrict mining aspects due to forbidden areas.

  • Extra processing or dump routes for proper cutoff optimization.

  • Sum variables (with caution), just in case some aspect must be controlled for the whole LOM at once.

  • In case more efficiency is needed, the resulting surface obtained in the Constraints Validationstep could be used as restrict mining for the runs here.

Optimized Pushbacks

Pushback Optimization is the process of generating and analyzing optimized pushback scenarios by varying the volumes of ore and waste in each case. This procedure is important to ensure the financial and operational viability of the mining project, as excessively large volumes can render the project unfeasible, while excessively small volumes can result in resource wastage or missed opportunities for ore extraction. By testing different volumes, it is possible to find an optimal point that maximizes the net present value (NPV) of the project.

MiningMath utilizes timeframes to generate pushbacks at different levels of detail. Timeframes are time intervals that divide the mine’s lifespan into smaller periods. Different timeframes allow users to perform a fast evaluation of the impact of production volume on the NPV. If necessary, adjustments can be made to optimize production and reduce costs.

In Pushback Optimization, multiple optimized pushback scenarios are created with varying levels of detail, enabling users to have a comprehensive view of the impact of volume variations on the project’s performance.

Create a Pushback

You can Identify timeframe intervals in your project, so that you can work with group periods before getting into a detailed insight. This strategy allows you to run the scenarios faster without losing flexibility or adding dilution for the optimization, which happens when we reblock.

The idea is to make each optimized period represent biennial, triennial, or decennial plans. MiningMath allows you to do it easily by simply adjusting some constraints to fit with the timeframe selected. Try to run with and without dump/total productions to check potential bottlenecks and impacts on waste profiles, which could be useful for fleet management exercises. Also, test with wider mining widths than required, as this is a complex non-linear constraint and you might find better shapes without losing value. Notice that in this example, the processing was not fully achieved, and this kind of approach helps us to understand which constraints are interfering the most in the results.

Example

Dataset: Preinstalled Marvin deposit. It can also be downloaded here.

Property Value
Timeframe custom factor
5
Processing capacity
50Mt in 5 years
Dump capacty
150Mt in 5 years
Vertical rate of advance

 750 m in 5 years

Minimum Mining Width
100m
Minimum Bottom Width
100m
Restrict Mining Surface
Optional
Grade copper
0.88%
Stockpiling parameters
On
Note: Waste control and vertical rate of advance are not recommended if you are just looking for pushback shapes.

Work Through Different Timeframes

Given the previous initial scenario, you might want to consider different timeframes for your pushback design. In order to perform a Pushback Optimization, the timeframes (in green), process and dump production limits (in green) and the vertical rate (in red) will be adjusted.

Pushback Optimization scenario for the Marvin dataset using trienniums.

By varying the highlighted parameters above, the following decision tree has been constructed for Pushback Optimization.

Decision Tree for Pushback Optimization
Decision Tree for Pushback Optimization

Three different timeframes are explored: 3 years, 5 years, and 10 years. Each timeframe is associated with specific process and dump production limits. Such limits not only scale with their respective timeframes but also allow for variations that provide flexibility for testing different production scenarios. Finally, the vertical rate is also adjusted to align with the defined timeframe of each scenario. For instance, the vertical rate is set to 450m for the 3-year timeframe, 750m for the 5-year timeframe, and 1500m for the 10-year timeframe.

Afterward, specific results were carefully selected for comparison, focusing on key parameters such as Net Present Value (NPV), production process, and production dump.

Cumulative NPV for different Pushback Optimization scenarios
Production process for different Pushback Optimization scenarios
Production dump for different Pushback Optimization scenarios

Note: Waste control and vertical rate of advance are not recommended if you are just looking for pushback shapes.

More details

The 2 constraints inputted at the production tab are related to the maximum material handling allowed: the third one is about the processing equipment capacity, and the vertical rate of advance is related to the depth that could be achieved adjusted to this interval. The minimum mining width was added because we are already generating designed surfaces that could be used later as guidance of detailed schedules, thus, it should respect the parameter due to the equipment sizing. Parameters such as average, minimum bottom and restrict mining surface, don’t suffer any change in the time frames.

It’s important to remember that the packages of time here don’t necessarily have to correspond to identical sets of years. You could propose intervals with different constraints until reaching reasonable/achievable shapes for the design of ramps, for example. If you wish to produce more operational results, easier to design, and closer to real-life operations, try to play with wider mining/bottom widths rates. Those changes will not necessarily reduce the NPV of your project.

Considering this approach the discount rate serves just a rough NPV approximation and it doesn’t affect much the quality of the solution, given that the best materials following the required constraints will be allocated to the first packages anyway.

Remember all the constraints

NPV Upside Potential

NPV Upside Potential is the process of generating and analyzing scenarios to measure the impact of each constraint on the project’s net present value (NPV), from the Super Best Case to a detailed setup. Measuring the impact of each constraint on the NPV is important to assess the financial impact and ensure the project’s viability under different scenarios and conditions. Each constraint can have a significant impact on the project’s NPV, and it is crucial to understand how they affect the project’s financial performance.

By evaluating the impact of each constraint on the project’s NPV, it is possible to identify financial bottlenecks and opportunities for improvement, as well as prioritize problem resolution. This can result in better resource allocation and cost reduction, enhancing the project’s profitability and viability.

In NPV Upside Potential, scenarios are created that sequentially incorporate each constraint of the project, allowing users to have a comprehensive view of the impact of each constraint on the project’s performance. In case more efficiency is needed, the resulting surface obtained on the Constraints Validation or in Best Case refinements could be used as Restrict Mining in the last interval, which might reduce the complexity and the runtime. 

Example

Dataset: Preinstalled Marvin deposit. It can also be downloaded here.

To illustrate this process, let’s consider the base scenario of the Marvin dataset (shown in the figure below). The highlighted green fields represent all the targeted constraints that need to be controlled in this project: process capacity, minimum average grade of CU in process, dump capacity, bottom minimum width, mining minimum width and maximum vertical rate.

Base scenario to built for NPV Upside Potential using the Marvin dataset

The decision tree depicted below has been constructed for a NPV Upside Potential process, based on the above scenario. In this decision tree, the scenarios progressively introduce each constraint into the project.

Decision Tree built for NPV Upside Potential using the Marvin dataset

The target scenario is the last one, with the following restrictions: Process Production=10mt, Dump Production=30mt, Bottom Width=100m, Mining Width=100m, Vertical Rate=150m, and average CU=0.5. However, the constraints are added interactively, starting with the process production, followed by the dump production, widths, and so on.

Note how the cumulative NPV usually decreases (as expected) when more restrictions are added (see note at the end for exceptions). Without this interactive process, there might be a lack of information to understand the NPV of the final, desired scenario.

Best-Worst Range Analysis

Best-Worst Range Analysis is the process of generating and analyzing scenarios to measure the impact of mine width constraints on the project’s net present value (NPV), from no restriction to wide widths. Measuring the impact of mine width constraints is crucial to determine the optimal fleet equipment configuration in mining operations, with the aim of optimizing productivity and maximizing the net present value (NPV) of the project.

By analyzing variations in width constraints, it is possible to identify the effect of space limitations on mining operations and evaluate the influence of different bench widths on fleet performance. Appropriate mining widths can bring a series of benefits: higher amount of material to be simultaneously extracted; higher fleet productivity; more efficient transportation; easier road maintenance and so on. Hence, the search for different widths allows finding the best combination of equipment and mining techniques aimed at maximizing production and profit simultaneously in each scenario.

In a Best-Worst Range Analysis, scenarios are created gradually increasing the mine width up to a feasible maximum, allowing users to have a comprehensive view of the impact of space limitations on the project’s performance.

Considering the nature of global optimization and the non-linearity of the problem, it is expected that there will be variations in performance (NPV, production, amount of mine fronts, etc.) as parameter values are modified. Therefore, it is crucial to generate a large number of scenarios to obtain a comprehensive analysis of the impact of these variations on the project. This way, a more precise understanding of how different parameter values affect the overall performance can be achieved.

Example

Dataset: Preinstalled Marvin deposit. It can also be downloaded here.

Consider the following base scenario and decision tree built for a Best-Worst Range Analysis using the Marvin dataset.

Base scenario for Best-Worst Range Analysis using the Marvin dataset

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 analyzed for identification of possible issues when employing different mining widths.

Production process achieved by different scenarios built for Best-Worst Range Analysis using the Marvin dataset
Production dump achieved by different scenarios built for Best-Worst Range Analysis using the Marvin dataset

Selectivity Analysis

Selectivity Analysis is the process of generating and analyzing scenarios to measure the impact of all geometric constraints on the project’s net present value (NPV), from the most selective to the least selective setup. Analyzing the impact of variations in geometric constraints is important to determine the optimal mine configuration and optimize productivity and profit.

By performing such an analysis, it is possible to identify the effect of geometric limitations on mining operations. Moreover, it is possible to evaluate the influence of each parameter and its variation on mine performance. This allows finding the best combination of parameters and mining techniques aimed at maximizing production and profit for each scenario.

In a Selectivity Analysis, scenarios are created including each geometric constraint sequentially and gradually increasing or decreasing their values from the least selective until the desirable requirement. This allows users to have a comprehensive view of the impact of geometric limitations on the project’s performance.

Considering the nature of global optimization and the non-linearity of the problem, it is expected that there will be variations in performance  (NPV, production, amount of mine fronts, etc.) as parameter values are modified. Therefore, it is crucial to generate a large number of scenarios to perform a comprehensive analysis of the impact of these variations on the project.

Example

Dataset: Preinstalled Marvin deposit. It can also be downloaded here.

Consider the following base scenario and decision tree built for a Selectivity Analysis using the Marvin dataset.

Base scenario for Selectivity Analysis using the Marvin dataset
Decision Tree for Selectivity Analysis using the Marvin dataset

The goal is to understand the impact of different values of geometric constraints (mining width, bottom width, and vertical rate of advance). 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.

Cumulative NPV for Selectivity Analysis using the Marvin dataset

A diverse range of results can be achieved with a Selectivity Analysis. However, there are usually two possibilities when they are compared:

  • Contrasting geometrics parameters with small NPV variations: note that when the bottom width changes from 0m to 80m, and the remaining parameters are fixed, the NPV drops from 454 M$ to 444M$. This indicates that large changes in geometric constraints do not necessarily lead to large changes in the NPV. The same for the scenarios SA_BW000_MW100_VR150 and SA_BW100_MW100_VR250.

  • Similar geometric parameters with larger NPV variations: when comparing scenarios SA_BW080_MW100_VR150 and SA_BW100_MW160_VR150 there is a drop in NPV from 444M$ to 370M$, highlighting that the 20m and 60m change in bottom width and mining width respectively can lead to a larger NPV difference in the project.

In conclusion, it is important to create several scenarios in a Selectivity Analysis. 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.

Production process for Selectivity Analysis using the Marvin dataset
Production dump for Selectivity Analysis using the Marvin dataset

Design Enhancement

Design Enhancement is the process of creating scenarios to conduct extensive searches for solutions with similar NPV values but with fewer violations and improved shapes. This process allows finding more efficient and sustainable solutions that meet specific mine constraints and needs. Hence, seeking these kinds of scenarios is important for optimizing mining operations and for reducing risks and costs. 

In Design Enhancement, scenarios are created with more rigorous geometric constraints without compromising the desirable requirements. The goal is  to reduce violations and find better forms for the project. This is possible due to the global nature of optimization and the non-linearity of the problem, enabling the use of stricter requirements for the geometric constraints that could lead to a better  performance of the project.

Example

Dataset: Preinstalled Marvin deposit. It can also be downloaded here.

Consider the initial scenario and respective decision tree built for a Design Enhancement process. The goal is to evaluate stricter variations in the geometric constraints (in green).

Base scenario for Design Enhancement using the Marvin dataset
Decision Tree for Design Enhancement using the Marvin dataset

Note the variation of results for Cumulative NPV and production. The base scenario has a small violation on dump production for period 1. However, when modifying the minimum width to 120m (scenario DE_BW100_MW120_VR150) this violation is not present anymore. Hence, this is an example of how small variations in geometric constraints could lead to less violations.

Cumulative NPV for Design Enhancement using the Marvin dataset
Production process for Design Enhancement using the Marvin dataset
Production dump for Design Enhancement using the Marvin dataset

NPV Enhancement

NPV Enhancement is the process of creating scenarios to conduct extensive searches for solutions with higher net present value (NPV) values and similar violations, while considering minimum requirements for project constraints. Scenarios are created that gradually modify constraints from desirable requirements to minimum requirements, with the goal of increasing project profitability.

Example

Dataset: Preinstalled Marvin deposit. It can also be downloaded here.

Consider the initial scenario and respective decision tree built for a NPV Enhancement process. The constraints in green (production capacities, geometric constraints, and average CU) are considered for modifications, from desirable requirements to minimum requirements, in order to identify solutions with higher net present value (NPV).

Base scenario for NPV Enhancement using the Marvin dataset
Decision Tree for NPV Enhancement using the Marvin dataset

Results show a high variation in NPV while the production remains in its limits. Hence, it shows that it is possible to achieve higher NPVs when employing minimum requirements defined by the user.

Cumulative NPV for NPV Enhancement using the Marvin dataset
Cumulative NPV period-by-period for NPV Enhancement using the Marvin dataset
Production process for NPV Enhancement using the Marvin dataset
Production dump for NPV Enhancement using the Marvin dataset

Bottleneck Analysis

Bottleneck Analysis involves generating scenarios to conduct extensive searches for solutions with fewer violations while preserving NPV, keeping geometries, optimizing mining operations, and reducing risks. This allows for the discovery of more efficient and sustainable solutions that meet specific constraints and needs of the mine.

In Bottleneck Analysis, after analyzing a desirable scenario it is possible to identify the constraint/s with demanding requirements that directly impact the optimization results and cause significant violation issues. Then, scenarios should be created by relaxing these demanding parameters, enabling users to make decisions to mitigate risks and ensure project viability.

Example

Dataset: Preinstalled Marvin deposit. It can also be downloaded here.

Consider the base scenario overview and the respective report on the dump production. Note how the first period has violated the 30Mt constraint.

A Bottleneck Analysis can help us identifying the constraint/s with demanding requirements that directly impact the optimization results and cause the violation in the dump production. Four different scenarios are built using a decision tree to analyze different values for dump production limits, minimum average of CU and vertical rate of advance.

Note: To decide which parameters need to be changed, you can consider the contraint priority order that MiningMath employs in order to always deliver a solution. However, adjustments usually depend on the unique characteristics of each project and the flexibility available to modify its requirements.

Base scenario for Bottleneck Analysis using the Marvin dataset
Decision Tree for Bottleneck Analysis using the Marvin dataset

The graphs below depict a comparative analysis of the results for the scenarios in the decision tree.

Cumulative NPV for Bottleneck Analysis using the Marvin dataset
Production dump for Bottleneck Analysis using the Marvin dataset
Production process for Bottleneck Analysis using the Marvin dataset

This analysis shows that the minimum average constraint of CU, production dump and vertical rate of advance are all restricting the base scenario. When relaxing these parameters, there is an increase of approximately 5% in the cumulative NPV, while the dump productions are kept within their limits and the process productions are closer to the target for some scenarios.

Multivariate Sensitivity Analysis

Multivariate Sensitivity Analysis is the process of creating and analyzing scenarios based on a range of possible values for selected constraints. Analyzing the impact of constraints variations is important for determining the optimal mine configuration and for optimizing productivity and profitability.

In Multivariate Sensitivity Analysis, scenarios are created gradually increasing or gradually decreasing the values of the constraints within a desired range, covering all combinations of values. This allows users to have a comprehensive view of the impact of combinations of constraint values on the project’s performance.

Considering the nature of global optimization and the nonlinearity of the problem, it is expected that there will be variations in performance as certain parameter values are modified. Therefore, it is crucial to generate a large number of scenarios to obtain a comprehensive analysis of the impact of these variations on the project.

Example

Dataset: Preinstalled Marvin deposit. It can also be downloaded here.

Consider the base scenario overview and the respective decision tree built for a Multivariate Sensitivity Analysis depicted below.

Base scenario for Multivariate Sensitivity Analysis using the Marvin dataset
Decision Tree (part 1) for Multivariate Sensitivity Analysis using the Marvin dataset
Decision Tree (part 2) for Multivariate Sensitivity Analysis using the Marvin dataset

Results are depicted below. Note how a diverse range of cumulative NPVs is reported when compared to the Base scenario. Also not how certain productions are more stable than others, demonstrating the importance of performing a Multivariate Sensitivity Analysis.

Cumulative NPV for Multivariate Sensitivity Analysis using the Marvin dataset
Production process for Multivariate Sensitivity Analysis using the Marvin dataset
Production dump for Multivariate Sensitivity Analysis using the Marvin dataset

Optimized Schedules

In the early years of the project you will find many concerns and the most value in terms of NPV. Knowing that, we decide to consider a 10-year surface to optimize the first 5 years. By a logical assumption, as the surface used corresponds to a decade, it will contain the interval from the 1st to 5th period and represents a lot more mass. However, this simple input can restrict the space where the algorithm has to find a solution, which could reduce the run-time and help it to deliver better results respecting the set of constraints given.

Example:

Figure 1: Sequencing
Figure 1: Sequencing
Figure 2: Surface
Figure 2: Surface
Figure 3: Production result
Figure 3: Production result
Figure 4: Processing hours
Figure 4: Processing hours
    Parameters Value
    Timeframe
    Years (1)
    Processing capacity
    10 Mt per year
    Total movement
    40 Mt per year
    Vertical rate of advance
    150m per year
    Maximum of processing hours
    4,500 processing hours per year
    Minimum Mining
    50m
    Bottom width
    100m
    Restrict Mining Surface
    Surface002 from Exploratory Analysis
    Stockpiling parameters
    On
    Grade copper
    Until 0.7%
    Figure 5: Production constraints
    Figure 5: Production constraints
    Figure 6: Geometric constraints
    Figure 6: Geometric constraints
    Figure 7: Average constraints
    Figure 7: Average constraints
    Figure 8: Sum constraints
    Figure 8: Sum constraints

    Short-term Planning

    MiningMath allows the integration between long and short-term. By running the Best Case, surfaces to guide the optimization were generated and they could be used as a guide based on the NPV upper bound. The Exploratory Analysis provides insights on what could be the challenges of our project and also operational designs that could be used in further steps. At last, we obtained a detailed Schedule by using, or not, a surface, which could be the final pit or any intermediary one, as a guide.

    Considering this workflow, now you may have enough information on a reasonable long-term view to enhance the adherence/reconciliation of your plans. You could choose a surface and use it as force and restrict mining to refine everything inside it. Remember that Force Mining is responsible for making the mining achieve at least the surface inserted, which means that all the material inside its limits should be extracted, respecting the slope angles, while Restrict Mining aims to prohibit the area below the surface inserted to be mined until the period in which it has been applied.

    Thus, MiningMath will reach this exact surface in the time-frame required and enable you to test different geometries, blending constraints, and any other variable that could be required in the short-term planning without interfering in the long-term overview. Additional helpful features in these refinements are the concepts of mining fronts and the design optimization, based on surfaces modification, that could be done respecting all the parameters and generating results accordingly with your needs.

    Figure 1: Results generated using different helpful features.

    Example

    Parameters Value
    Timeframe
    Custom factor (0.5)
    Processing capacity
    5 Mt per semester
    Total movement
    20 Mt per semester
    Vertical rate of advance
    60m per semester
    Minimum Mining
    120m
    Bottom width
    100m
    Force and Restrict Mining Surface
    Surface005 from Schedule Optimization
    Stockpiling parameters
    On
    Play with steeper slope angles in the short term?
    Yes

    Table 1: Set of constraints example (1).

    Figure 2: Production constraints as listed in Table 1.
    Figure 2: Production constraints as listed in Table 1.
    Figure 3: Geometric constraints as listed in Table 1.
    Figure 3: Geometric constraints as listed in Table 1.
    Figure 4: Average constraints as listed in Table 1.
    Figure 4: Average constraints as listed in Table 1.
    Figure 5: Sum constraints as listed in Table 1.
    Figure 5: Sum constraints as listed in Table 1.

    Results examples

    Figure 6: Resulting schedule from example in Table 1.
    Figure 6: Resulting schedule from example in Table 1.
    Figure 7: Resulting production from example in Table 1.
    Figure 7: Resulting production from example in Table 1.
    Figure 8: Resulting stock process tonnage from example in Table 1.
    Figure 8: Resulting stock process tonnage from example in Table 1.

    Further details

    The example above used fewer constraints, geometries were changed and the average grade was let free. It is very helpful to define the early years based on a semester timeframe, which can assist you to manage stocks and any other variables in the firsts 3 years, for instance. Note that the period ranges on MiningMath are based on the timeframe selected, therefore, you should adjust your variables accordingly with this value.

    When we use Force+Restrict, we are telling the optimizer to break this volume into pieces and that it must mine this volume entirely, even if it is waste, so that the long-term view is respected. This way, you keep regarding the whole deposit while deciding what to do in the first periods. The approach here is quite different than a set of Revenue Factors for a series of LG/Pseudoflow runs, followed by adjustments to find pushbacks without math optimization criteria. It is worth mentioning that this kind of suggestion must be only applied at the beginning or at the end of the life of mine, since Force+Restrict Mining surfaces used in intermediate periods could interfere directly with the results.

    Using timeframes

    Another strategy is to optimize the short-term along with the long-term using different timeframes. In this approach, the integration between the short and long term visions is made in the same optimization process, facilitating the analysis and strategic definitions.

    It is possible to consider:

    • shorter time horizons (weeks, months, quarters...) for the initial periods of the operation;

    • annual plans as far as needed, for a precise definition of discounted cash flow;

    • less detail for longer time horizons. They need to be considered in the overall view of the mine, up to exhaustion, but they consume optimization processing time that can be more focused on the early years of operation.

    Thus, there is value maximization at the strategic level, and feasibility at the tactical level simultaneously. In addition, there’s minimizing compliance and reconciliation problems, as well as improving communication between teams, by working in an integrated system.

    On this strategy, each period range will represent the time interval chosen in the timeframe, and discount rate will be adjusted in alignment with the time interval choice. Other constraints such as production and vertical rate of advance (VRA) must be adjusted to match each interval on the period ranges.

    In order to clarify this strategy, Table 2 and Figure 9 present a possible list of constraints for an example using timeframes:

    Table 2: Set of constraints for a timeframe example.

    Constraints chosen in the interface for a timeframe example.

    Multi-mine

    Multi-mine projects often have hidden opportunities to maximize value. Accordingly with the natural level of complexity, it is pretty commom to make a few simplifications that might reduce value, producing sub-optimal solutions from the mathematical perspective, while using the traditional LG/Pseudoflow methodology.

    MiningMath has global optimization algorithm which can overcome such challenges, when working with integrated multi-mine projects to find solutions that regards all the pits been mined or mixed at the same time, instead of an individual pit optimization within a multi-mine project, which provides a totally different overview. To handle with such projects, the block model must contain all the mining regions which should be considered to the simultaneous optimization, thus, if you have the pits mapped in different datasets, it is important to follow the steps suggested below:

    1. Work with a single block model or single pit first, run the initial tests and understand this region before handling the block model modification.

    2. Try to eliminate meaningless blocks, which would not affect the solution and could increase complexity.

    3. Join a second model/pit* and understand the manipulation process to work with multi-mine projects.

      - Play with surfaces, if you wish to refine the results, filter regions to not mine, and any other guide. Since the surface files on MiningMath has always the same order, a good way to work with it could be using an excel file, available here, which is pretty useful to such modifications.

      - Play with Mining Fronts, if you want to control the material which is extracted from each region.

    4. Add the other regions and start use everything that you wish.

    This joint block model file should fulfill the same requirements of a single block, as mentioned at the formating data page, having unified characteristics.

    Figure 1: Multiple pits project

    The current version of MiningMath consider the same Vertical Rate, Bottom Width and Mining Width for the entire block model. However, in a multiple pit overview, each one could have different geometric parameters that influence the levels of selectivity. Regarding these scenarios, the main recommendation is to set the parameter from one pit, fix solutions of this one, since force+restrict mining has the highest level of priority, and start the optimization of the others which would already consider the mass that would be extracted from the first pit fixed.

     
    Figure 2: Surface obtained in the first optimization

    An efficient workflow is to run the first scenario without geometric parameters, which should be the validating or the Best Case, for scheduling optimization. Then set up a scenario with geometric parameters from the most selective mine which means, the smallest widths and biggest vertical rate (VR), which would be the least constrained scenario considering geometric aspects. Therefore, each surface generated by this approach will be used to fix solutions for Mine 1.

    For instance, you could take the surface 1 generated and decrease the elevation in the other areas to regard the mass from the period one of mine 1 and what could be mined in the second pit. By having these results you can refine either surfaces or mining fronts to get the best results and do a sensitivity analysis of geometric parameters for multi-projects still preserving the global optimization.