A MATHEMATICAL MODEL FOR SIMULTANEOUS OPTIMIZATION OF THE ULTIMATE PIT LIMIT AND BLOCK SEQUENCING IN OPEN PIT MINING

Determination of the ultimate pit limit is one of the most important design in open pit mining. In the present methods, the final pit is determined based on the maximization of undiscounted profit. For this purpose, various mathematical, heuristic and meta- heuristic algorithms have been developed. Among these methods the most used one is the Lerchs-Grossman (LG) algorithm. It has been mentioned that it is better to design the ultimate pit based on the maximization of the net present value. In other words, the optimal arrangement of blocks and the final pit outline must be determined simultaneously. For that reason, in this paper the binary and nonlinear mathematical model of this problem and some suggestions for its linearization have been presented. In addition, in order to reduce the number of decision variables the concepts of the earliest and the latest possible time for extracting a block have been defined. In the following, with the use of downward cone and positional weight and the earliest extraction time of ore blocks, two heuristic algorithms have been developed for simultaneous determination of the final pit and blocks extraction sequence. At the end the results of these algorithms have been compared with the LG algorithm. The results show that these algorithms are capable to produce good result.