Three-dimensional block models are the most frequently used tool for estimating mineral resources and reserves within a mineral deposit. In open pit mining, the basis of mine design and the long term mining schedule is calculation of the ultimate pit limit. The ultimate pit limit is the pit with the highest profit value. Over the years, different algorithms have been developed that enable us to calculate the final pit: floating or mobile cone, floating cone II and its corrected forms, floating cone III, the Korobov algorithm and its corrected form, the Lerchs–Grossmann 2D algorithm (dynamic programming), and the Lerchs–Grossmann 3D algorithm (graph theory). All these algorithms have advantages and disadvantages. The floating cone method stands out for its simplicity, speed, and easy implementation, even for calculating a pit with a variable slope angle. The main drawback of this method is that it is unable to examine all possible combinations. For this reason, the algorithm does not consistently give optimal results, which is why it has required improvements over time. However, the improved methods still have some problems. To overcome these problems, a new algorithm called the floating cone IV method will be demonstrated in this paper.

Variogram calculation is a fundamental tool for studying ore grade data in mineral deposits. It allows the discovery of hidden structures within the data and preferential directions of mineralization where the geological continuity is longer. The variogram allows us to classify samples and to define both the search radii for interpolation and the use of kriging as an interpolation and resource classification method. It is not difficult to use it in one dimension; complexity increases in two dimensions as the necessity to search for possible grade anisotropies in all directions arises. Three-dimensionally it is even more difficult to try to define the parameters of lag, bandwidth, and tolerances that define the data of the variogram calculation algorithm. There are rules of thumb to help in the development, but a trial-and-error approach is used in order to find enough sample pairs to allow the generation of variograms truly representative of the data. In this paper, two strategies are shown to help in variogram construction, the use of variogram maps and the graphical representation of the pair search areas (cones or pencils). The freeware tool RecMin Variograms has been developed and is freely available for download at its website; it is easy to learn and use. R code based on RGeostats libraries is used to check the operation and results of RecMin Variograms. Applying geostatistics to mineral deposits is essential to know the areas with the highest grades, thus allowing exact planning of future mining exploitation and minimizing mine footprint and environmental impact.