# Cut-off grades

The concept of cut-off grade has been conceived to delineate what is ore and waste, considering the life of mine. Usually, **manual assumptions** are made **to pre-define what must be considered ore or not**, while using the LG or Pseudoflow methodologies. These approaches **do not consider the value of the money through time** in the **decision-making process**, which could generate a whole different mining sequence due to the choices of **what and when it should be mined**. Another challenge, that is faced when planning projects which involve multiple destinations, blending constraints, restrict mining areas, and all the complexities present in a real global optimization. MiningMath allows for such Global Optimization and you can still combine it with your current strategies!

MiningMath has **no pre-defined assumptions **in order to identify the **cut-off limit,** which is **based on a math optimization **considering a discounted cash flow **while respecting ****production capacity, blending constraints, vertical advances, widths, and any other assumption**. Another key aspect in this regard is that **MiningMath is not constrained by fixed pits, pushbacks, or phases**. Instead, the **mining sequence** is an optimized output, which **is a consequence of each set of parameters used,** allowing more flexibility to find completely new solutions. The **advantages** of these differences are even more evident for **more complex cases **with multiple destinations, or complex constraints that could be neglected, hiding opportunities.

As the algorithm here has **no manual ****destinations**** appointments**, it always sends the **less valuable blocks to the dump,** considering the set of constraints imposed, what means that MiningMath **tries to comply with all the constraints inserted,** by respecting this priority order, **to define an optimized cut-off that can meet all of the requirements and increase the NPV as a consequence **of a global optimization. Meanwhile, **blocks that have positive values **when processed **can also be discarded** to increase NPV based on the **minimum economic value** (economic value cut-off)** going to the plant at that a specific period**. Scenarios without stockpiling policy could have even higher positive values going to the waste since they do not have any other destination. Considering these examples, MiningMath **can deliver quite different results **from what you were expecting from your previous assumptions. However, you can also** get closer, **as much as you wish, **to any solution** by using the approaches suggested below.

Forcing a cut-off grade on MiningMath will likely make you **lose part of the advantages** it can offer. However, for many reasons, mining professionals might still be willing to use either to compare different approaches, to understand the practical effects of using it, or not, etc.** **The approaches mentioned could also be** used to forbid any material type** on the plant, and the** use of the item 2.1. could** even **reduce the complexity** of the algorithm, since it could use fewer constraints to deal with it.

You can create multiple columns of economic values, each one for a cut-off you want to test. Then, **force** MiningMath to use **this limit** by defining **very negative values **for the destination you want to avoid, as it is shown in *Figure 1, *for a cut-off of 0.5. The math is:

**Economic Value Process = ***If [Ore_Grade] > [0.5], then [f(Economic Value)], else [-999,999,999.00]*

Figure 1: Block model setup to incorporate cut-off grades when defining economic values.

Grades in MiningMath are controlled as a **minimum and/or maximum average calculation,*** which means that* * these limits do not represent cut-off values* since the algorithm can use lower values to blend higher ones. Thus, to use this approach, just set a

**very negative value on the grades below the cut-off**so that these blocks

**would reduce substantially the average**when processed. It can also work to constraint

**a contaminant maximum limit by adding a high grade on it**, as it can be viewed in

*Figure 2*

**.**Once again, the math is:

**Ore_Grade1 = ***If [Ore_Grade] < [0.5], then [-999,999,999.00], else [Ore_Grade]*

Figure 2: Block model setup to incorporate cut-off grades using average.

Another option is by using the sum tab to **control material types**. Therefore, it would be required to create a field to **calculate only waste blocks mass** and set the **constraint of the maximum limit of it in the plant as zero**, as it is seen in *Figure 3*. It is worth mentioning that this approach could increase the complexity of the optimization due to the priority order within the algorithm.

**Tonnage_Waste = ***If [Ore_Grade] < [0.5], then [Volume*density], else [0]*

Figure 3: Block model setup to incorporate cut-off grades using sum.

The **mined blocks file**, as seen in *Figure 4,* is the main output **to trace the blocks** from each destination, to understand the results, and to find the best way to **enhance your reporting** based on any detail that you wish to disclose. There are many useful tips to** identify, and understand the results generated**, some of them, are listed below:

**Filter results**where the period mined is equal to the period processed.**Check process economic values**of those blocks, which were processed,**identify the lower one**(which means the cut-off value at the plant), and**compare it with higher**processing economic**value**of those**who went to the dump**.**Calculate the average grade**of any material in period mined equal to the period processed filter.**Check if the blocks, which are going to dump**, would have**exceeded any limit**in the plant, if so,**even having good economic values**, they would not comprise the constraints in place.

To sum up, there are **a lot of validations that can be done** to understand why the algorithm is taking such decisions. It is also worth** mentioning that any constraint can influence the results**, even geometric ones, which could change the sequence and change the destination of the block at any period.

Figure 4: Mined blocks output file.