Technical Parameterization of Reserves for Open Pit Design and Mine Planning

In this paper, we consider open pit optimization. At present, most methods specify the economic parameters and then find the corresponding optimal pit. But as the economic environment varies (which it does regularly these days), the "optimal" pit changes and quite often changes markedly. The questions are: by how much does it change and which parameters are most influential? The functional approach of Technical Parameterization of Reserves, devised by Matheron in 1975, gives the set of all the different optimal pits, under any economic condition. It separates technical design and economic assumptions and thus permits the use of several optimality criteria when choosing the final pit, and not just the maximization of an additive profit formula. Very efficient specific algorithms are presented to obtain all the potentially optimal pits. Fluctuations in the parameters induce changes in the optimum design. Inclusion relations that exist generate very tight bounds and hence very quickly detect optima, even when using a classical adaptation of maximization techniques (graph theory, moving cone, dynamic programming ...). The advantage of Technical Parameterization of Reserves over other methods is that it provides a nested sequence of optimal pits which can then be used for mine scheduling. Many possible mining schedules can be obtained by using the family of technically optimal projects to split up the orebody. The "optimal" schedule, which is in fact a compromise between the different requirements of the economists, the mine planner and the metallurgist, can be chosen from within the wide scope of possibilities. A practical example of mine scheduling for a chromite mine is presented in detail.