Modelos matemáticos e heurísticas para auxílio ao planejamento de operações de lavra em minas a céu aberto

Abstract

The planning of ore exploitation operations in open pit mines represents an extremely relevant and practical problem due to the fact that production control impacts diverse indicators that are considered critical for the activity. The principal objectives of a ore exploitation plan are meeting production goals, the quality of the ROM (run-of-mine),and stripping ratio. In addition to these objectives, it is also important to minimize costs by using equipment available for transportation, forming optimal pits, maintaining safe conditions, and stabilizing the slopes. From a theoretic point of view, the problem is considered difficult to solve by optimization techniques, and has therefore attracted the interest of many researchers over the last approximately 50 years. During this time,models that are still given extreme importance have been developed and in many cases these models have been incorporated into software used by production administrators, as is the case of the Lerchs-Grossmann algorithm. Many of these models however have a combinatorial nature and a great number of integer variables. Such characteristics can limit or even impede finding the optimal solution in real instances because of the amount of computational time needed to solve the problem. As an alternative, the use of heuristics, dynamic programming, and even control theory have helped to develop more quickly and realistic algorithms. This work presents new models to aid in production planning, especially useful for mid- and long-term forecasting, but that also consider operational factors such as the cost of moving loading equipment. Two on-line models that take advantage of updated location information and some production data are tied to sequential optimization algorithms in order to reduce the number of variables and the quantity of data in the real problem. The tests, which use hypothetical instances, verify the coherence of the proposed methods and they show that high-quality results can be obtained in an amount of time considered acceptable for real-life problems.