A heuristic algorithm to determine ultimate outline of open pit mines with net present value maximization

SummaryThe aim of this paper is to present a new algorithm to determine ultimate pit outline and mining sequence simultaneously based on the maximization of the net present value (NPV). For this purpose, a nonlinear binary mathematical model was established and then a heuristic algorithm was developed to solve this NP-Hard problem. IntroductionThe ultimate pit limit is an important problem which is determined by maximization of undiscounted profit or NPV. The floating cone algorithm and its modified versions, Korobov algorithm, Lerchs-Grossman method and maximal flow algorithm were developed to generate ultimate pit limit based on the maximization of the undiscounted profit. Nevertheless, it is better to determine the pit outline based on the maximization of NPV. To achieve this goal some algorithms like Wang-Sevim, Latorre-Golosinski and Roman were established.Methodology and ApproachesThe binary and nonlinear mathematical model to determine the ultimate pit limit on the basis of maximizing NPV and a few suggestions for its linearization were presented. Afterwards, by defining the concepts of downward cone, positional weight and nearest ore index, a heuristic algorithm was developed to determine the ultimate pit limit and mining sequence all together.Results and ConclusionsThe algorithm was applied for 2D and 3D block models and the results showed that it is able to produce optimum outcome. Complexity of the algorithm is low and easy to use and as well as for education purpose. It is also able to consider variable slopes and grade-based constraints for production planning in the algorithm.