Selection of ore from multiple pits

Abstract

When ore is being selected from a regularised block model, a common procedure is to accept as ore any block whose iron content exceeds a cut-off value, and whose content in each contaminant analyte is below an appropriate cut-off value. This method defines a quadrant within the multidimensional analyte space, such that any block lying within the quadrant is accepted as ore and any block lying outside the quadrant is rejected as waste. The cut-off levels can be adjusted to maximise ore tonnage at a target grade (or analyte vector). When the method is applied to a project comprising multiple pits with systematically differing grades, it is found that ore tonnage at target grade is maximised if different cut-off quadrants are used for the different pits. This is apparently illogical, because it implies that an ore block from one pit may be accepted as ore, but an identical block from another pit rejected as waste, even when ore from both pits is to be blended into the same product and there are no production cost differences between the pits. The paradox is an example of the Theory of the Second Best: if there are multiple conditions for optimality and one condition is broken, then obeying the other conditions may not be the best policy. The problem lies with the quadrant cut-off method, which is shown to be inconsistent even for selecting ore from a single pit. A criterion that is inconsistent cannot be optimal. It is shown that a linear composite cut-off function provides maximum ore tonnage, and that a single composite cut-off criterion is consistent and optimal over multiple pits. Further, it is shown that a composite cut-off function not only maximises ore tonnage at a specified composition, but also can be used to select ore so as to maximise project value, if marginal costs and values are available.