grossmann algorithm

Open pit mining is one of the most important methods of surface mining in which extraction of mineral deposit is carried out in benches. Ultimate limits of an open pit which define its size and shape at the end of the mine’s life must be designed before to start the operation. Manual and computer methods can be used to determine optimum ultimate pit limits. Manual methods of designing pit limits are based on stripping ratios and involve determining break even pit limits. The objective of computer methods is to determine the optimum ultimate pit outline for which the net profit is maximized. A number of algorithms such as floating or moving cone method, the Korobov algorithm and the corrected form of this method and the Lerchs and Grossmann algorithm based on graph theory have been developed to find out the optimum final pit limits. Each of these methods has special advantages and disadvantages. The designers of the corrected form of Korobov algorithm claim that this method is able to yield the true optimum pit in all the cases. The aim of this paper is to examine this method for being as a true optimum pit algorithm. This method is compared with the Lerchs-Grossmann algorithm which is the only method that can be proved, rigorously, always to yield the true optimum pit. The results show that the corrected form of Korobov algorithm is not always able to find out a true optimum pit outline.

The Lerchs and Grossmann algorithm is a rigorous technique Based on Dynamic Programming, developed for optimization of open pit limits. This algorithm guarantees the true optimum solutions in 2D sections, but is may be used only for pit slope constraints of 1:1, 2:1 or more. In circumstances, where the geomechanical conditions impose less slopes such as 1:2, an adjustment of the block sizes and reconstruction of the block model is needed. A new algorithm is introduced in this paper to overcome this shortcoming. The conventional block model is transformed into an intermediate and a final block model to reflect the pit slope constraints. Then the modified Lerchs and Grossmann algorithm consisting of a recursive formula with two criteria is implemented on the final model. Using this algorithm, there is no need for reconstruction of the block model.