Inside out

  1. Undestarding differences

1.2. Traditional technology

The traditional mining planning models have developed shortcuts and approximations to try to deliver acceptable results that consider all the complexities and constraints of the project. To handle it, they require powerful machines that can find a solution to simultaneously determine the optimum pit limit and mining sequence that deliver the maximum project value.

As Figure 1 shows, Lerchs-Grossmann (LG) or Pseudoflow algorithm, aims to initially find the final pit limit that maximizes the undiscounted cash flow and then to focus on block sequence within this final pit envelope. By constraining the problem and predefining inputs, these shortcuts (approximations) help to save time and computer resources so that they are able to consider complexities such as ore blending requirements, different processing routes, stockpiling policy, and truck fleet considerations, etc.

To define the mining sequences LG approach gradually reduces the Ore Price or Revenue Factor to produce a set of nested pits, and the final pit is then selected by considering the incremental value of each pit shell. This heuristic methodology generates a set of pits that begin with the higher-value/lower-cost blocks, followed by lower-value/lower-cost ones until reaching the final pit limit.

These methods can guide us towards determining the optimal mining sequence and a reasonable Net Present Value (NPV) of the whole ore extraction. However, since LG neither considers the value of money over time nor capacity constraints, it is unable to consider the dynamic and inter-temporal aspects of the mining sequence.

Figure 1: Lerchs-Grossmann (LG) or Pseudoflow algorithm process.

Accepting these limitations, LG and Pseudoflow can generate multiple scenarios, although they are still guided and constrained by the first boundaries obtained, which could easily lead to non-optimal results. At this point, calculations start to take into account the discounted cash flow, capacity constraints, and all assumptions disregarded to define the pit limit previously. Thus, all the variables (mine capacity, mining sequence, stockpiling, etc.) within the traditional methods are treated as input parameters at the pre-defined boundaries.

1.2. Direct Block Scheduling (DBS)

The Direct Block Scheduling (DBS), algorithm used by MiningMath, allows you to enhance your decision-making process and reduces the time to analyze your results in a global view since it can consider a wide range of additional constraints during the optimization process (Figure 2). The software allows you to build decision trees that enable a broader view of your project and an understanding of what are the impacts of each variable. This is all possible because MiningMath has a global optimization that regards all the variables simultaneously to generate the results instead of the stepwise process.

Figure 2: MiningMath optimization process.

With standard optimization approaches, thousands of potential schedules can be generated, but they are all based on the same set of nested pits and other fixed input parameters such as geotechnics, metallurgical performance, blending constraints, etc. Therefore, the results frequently present similar behaviors and restrict the full exploration of the solution space.


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