A New Algorithm for Determining Ultimate Pit Limits Based on Network Optimization

Document Type : Research Paper


School of Mining Engineering, College of engineering, University of Tehran, Tehran, Iran


One of the main concerns of the mining industry is to determine ultimate pit limits. Final pit is a collection of blocks, which can be removed with maximum profit while following restrictions on the slope of the mine’s walls. The size, location and final shape of an open-pit are very important in designing the location of waste dumps, stockpiles, processing plants, access roads and other surface facilities as well as in developing a production program. There are numerous methods for designing ultimate pit limits. Some of these methods, such as floating cone algorithm, are heuristic and do not guarantee to generate optimum pit limits. Other methods, like Lerchs–Grossmann algorithm, are rigorous and always generate the true optimum pit limits. In this paper, a new rigorous algorithm is introduced. The main logic in this method is that only positive blocks, which can pay costs of their overlying non-positive blocks, are able to appear in the final pit. Those costs may be paid either by positive block itself or jointly with other positive blocks, which have the same overlying negative blocks. This logic is formulated using a network model as a Linear Programming (LP) problem. This algorithm can be applied to two- and three-dimension block models. Since there are many commercial programs available for solving LP problems, pit limits in large block models can be determined easily by using this method.