Recursive formulae for the floating cone algorithm

ABSTRACT To the author's knowledge, the algorithm for establishing the sequential logic that defines the final limit of an open pit of maximum benefit remains to be developed. In a retrospective analysis on economic models and on optimization techniques applied to pit design, Kim (1979) recognizes the widely acceptance of the tri-dimensional block model and, in connection with it, of the heuristic method known as the floating cone. A recursive algorithm for building up floating cones of distinct shapes linked to the notion of norm (or distance) in a vectorial space is presented. Likewise, corresponding expressions for expanded floating cones are developed but, in contrast with the two-dimensional case, where all possible combinations of single floating cones can be generated, in the three-dimensional block model only unidirectional and isotropic expansions are considered. An hypothetical example illustrates results among three final pit designs generated on the same block model under different norm defini...