#Cut-off #Grade #Optimization - What is the Catch, if any?

Cut-off grade is one of the most important parameters in strategic mine planning. Choosing the best cut-off grades that maximize net present value (NPV) has been a major research topic ever since the 1960’s. Lane’s work has been considered as the landmark in cut-off grade optimization. His model aims to maximize NPV, subject to the capacity constraints of mining, concentrating and refining stages, as well as the capacity balancing of the three stages (Lane 1965).

Optimum Cut-off grade is dynamic in nature. It changes with time (mining periods) and space (mining zones). Lane’s work accounts for the dynamic nature of cut-off grade over time, resulting in different cut-off grades in different mining periods, but as it uses the grade distribution of the entire mining reserve, it fails to address the dynamic nature of cut-off grade with respect to space or locations in which mining takes places. This is a serious limitation, because in all but trivial deposits, different mining zones have different ore grade distributions and ignoring such variation will result in unrealistic cut-off grade policies. For example, it is well known that in the Lane’s method, the resulting cutoff grade decreases over time. In an open-pit deposit where the ore grade is low in the upper portion of the deposit and high in the lower portion, using higher cut-off grades in the early stage would not be appropriate and may not even be practical due to the absence of high grade ore in the upper portion!

Many commercial cut-off grade optimizers that are based on the Lane’s method suffer from this limitation and the cut-off grade policies generated by such optimizers should only be considered as a theoretical guide, i.e., they are of little practical significance.

How can we address the dynamic nature of cut-off grade with respect to space? The answer is actually quite simple (although the implementation is far from it): instead of a single grade distribution, we must consider multiple grade distributions, one per mining zone. For open-pits, each phase pit can be treated as one mining zone with its own grade distribution and for underground mines, each stope or a group of stopes can be treated as one mining zone, again with its own grade distribution. Furthermore, geometric and precedence constraints, e.g., push-back or stoping sequences between mining zones, must also be obeyed.

Over the past few years, ThreeDify has devoted a large portion of its R&D resources to incorporating the above modifications into its then experimental cut-off grade optimizer, OptimCut, which is based on a Constrained Dynamic Programming algorithm. The result is a cut-off grade optimizer and strategic scheduler that is capable of generating cut-off grade and production rate policies that are not only optimal over mining periods, but also practical for respective mining zones.

Finally, a picture is worth a thousand words - here is an introductory video for GeoMine OptimCut.