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

One of the main concerns of the mining industry is to determine ultimate pit limits. Final pit is acollection of blocks, which can be removed with maximum profit while following restrictions on theslope of the mine’s walls. The size, location and final shape of an open-pit are very important indesigning the location of waste dumps, stockpiles, processing plants, access roads and other surfacefacilities as well as in developing a production program. There are numerous methods for designingultimate pit limits. Some of these methods, such as floating cone algorithm, are heuristic and do notguarantee to generate optimum pit limits. Other methods, like Lerchs–Grossmann algorithm, arerigorous and always generate the true optimum pit limits. In this paper, a new rigorous algorithm isintroduced. The main logic in this method is that only positive blocks, which can pay costs of theiroverlying non-positive blocks, are able to appear in the final pit. Those costs may be paid either bypositive block itself or jointly with other positive blocks, which have the same overlying negativeblocks. This logic is formulated using a network model as a Linear Programming (LP) problem. Thisalgorithm can be applied to two- and three-dimension block models. Since there are many commercialprograms available for solving LP problems, pit limits in large block models can be determined easilyby using this method.

Keywords:

Linear Programming (LP) , Network Optimization , Open pit mining , ultimate pit limits