Combined optimisation of an open-pit mine outline and the transition depth to underground mining

Miners harvest minerals from ore-bodies in the ground by a variety of specialised mining methods, with most falling into the categories of open-pit and underground. Some ore-bodies are harvested by a combination of open-pit and underground methods. In these cases there is often material that could be mined by either method, and an economic choice has to be made. This is referred to as the transition problem and it has received some attention in the mining literature since the 1980s and more recently has had attention in the mathematics literature. The transition problem is complicated by the need in many cases to leave a crown pillar (un-mined rock above the underground mine) and for this crown pillar to have a prescribed shape. We have developed a method to optimise the design of an open-pit mine, while solving the transition problem and taking into account the need for a crown pillar with a prescribed shape. We base it on an existing method to optimise the design of an open-pit mine, framed as a maximum graph closure problem. Our method introduces non-trivial strongly connected sub-graphs (NSCSs) of the graph, a complication that previous authors on maximum graph closure problems do not appear to have covered. To obviate the need to check every method for compatibility with NSCSs, we reduce the problem to an equivalent problem without them. This has the added advantage of reducing overall processing time in cases where the number of NSCSs is large. (C) 2018 Elsevier B.V. All rights reserved.