Math Optimization models that integrate multiple business’ areas

Decision Trees

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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.

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.

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 strategiesThe 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.

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