MiningMath

MiningMath

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Math Optimization models that integrate multiple business’ areas

Vertical Rate

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Introduction

The vertical rate of advance (VR) or sinking rate is also considered within the objective function on MiningMath. This parameter is defined as the vertical distance mined on each period. The total vertical distance mined across all periods should be consistent with the pit depth and equipment available. In cases of unfeasibility it will respect the constraints hierarchy in which it is placed at a lower priority.

Bottom width, mining width and vertical rate of advance.

Complexity and recommendations

It is important to understand that this is also a 3-dimensional non-linear model, which means that it is a complex parameter within the optimization. The VR works as an upper bound to avoid operationally unfeasible solutions. Therefore, testing different values is a great strategy to identify opportunities that could bring the best mining sequence and NPV.

The Mining Width (MW) is not mandatory when using VR, but it plays an important role when defining its value. The MW and VR, together, define volumes of material for each mining period. A reduced MW might create additional challenges for the algorithm to comply with the VR. Therefore, it is important to play with different values, especially when VR is not being fully respected. 

Vertical Rate: Definition, Hierarchy of Constraints & Complexity

The vertical rate of advance is one of the first constraints to be relaxed within MiningMath’s Hierarchy of Constraints (read more). To ensure VR is at least closer to what you need, relax low-priority constraints manually. This way you will lead the algorithm to a more flexible scenario and a broader solution space, which may help it to find a feasible solution for the new set of constraints.

Besides, if the user aims to force a maximum vertical rate for a given period, it can be created a flat surface constraint regarding the achievable depth and input it as a Restrict Mining. Beyond that is important to notice that even the goal of achieving “process full” could result in a non-feasible solution while the VR is still respected, therefore, this feature is very sensitive to any other parameter.

Vertical rates controlled by surface constraints

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