# Theory Validation

MiningMath’s results are only possible due to its proprietary Math Programming Solver ©. It consists of a Mixed Integer Linear Programming (MILP) formulation and linearization methods that tackle the challenging non-linear aspects of the mining optimization. In addition, it has its own Branch & Cut algorithm, which provides more efficiency than standard MILP optimizers since it’s fine tuned to this specific optimization problem.

Another major advantage of MiningMath comes from the mathematical formulations based on surfaces (Goodwin et al., 2006; Marinho, 2013), instead of usual block precedences. Block precedence methods might lead to higher errors (Beretta and Marinho, 2014), providing slopes steeper (i.e. riskier, more optimistic) than requested. The use of surfaces eliminates these geotechnical errors and allows for block-by-block geotechnical zones, if needed.

These surface-based formulations allow MiningMath to include geometric constraints, and, consequently, find solutions that are closer to real mining operations. The user can guide geometries by including mining and bottom widths, mining lengths, maximum vertical advance rates, and forcing/restricting mining areas. You can better understand how each constraint interacts with all others here. Such constraints give freedom to the user to work, or not, with predefined cut-offs and pushbacks which might limit the space of potential solutions. An in-depth view of MiningMath’s formulations and algorithm can also be seen here.

This approach (Figure 1) has been applied for years by clients, such as Vale, Rio Tinto, Codelco, Kinross, AMSA and MMG, with a growing number of licenses sold, press releases and academic research also proving the consistency of the implementation. With constant developments since 2013, MiningMath has reached a mature and robust state. It is the first and only singlestep mining optimization engine available in the market.

*Figure 1: MiningMath’s approach. From block model to schedule in a single step solved by its proprietary Math Programming Solver ©. *