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

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.