Inside Out

  1. Understanding differences

1.1. Traditional technology

The traditional mining planning models have developed shortcuts and approximations to try to deliver acceptable results that consider all the project's complexities and constraints. To handle it, powerful machines are required to 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 to then 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, enabling that such software to consider complexities such as ore blending requirements, different processing routes, stockpiling policy, 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 disregarded assumptions 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. MiningMath's Global Optimization

MiningMath's algorithm built upon Direct Block Scheduling (DBS) is the only one able to simultaneously consider all periods and constraints. This allows you to improve your decision-making process and reduce time to analyze results, since it considers a wide range of additional constraints during the optimization process (Figure 2).

Our software allows you to build Decision Trees, which enable a broader view of your project and a deeper understanding of the impacts of each variable. This is all possible because MiningMath works with a global optimization which simultaneously regards all variables, instead of using a step-wise approach.

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.

2. Bonus: Learn More!

This case study shows in theory and practice how a global optimization takes into account the inter-temporal factors underlying the definition of an optimal mining sequence, and the gains this approach can provide.

MiningMath's technology is recognized by the industry, being awarded in a Mining Technical Challenges and Solutions Competition, and academically, with several publications and research being published.

A license to operate is the risk for mining, according to EY. Meanwhile, a Life Cycle Sustainability Assessment is an unprecedented approach, only possible with Global Optimization, to help mine managers to quantify and evaluate socio-environmental aspects .

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