Optimising the ramp design in an open pit mine APCOM 2021

In open pit mining, ore and waste are hauled outside of the excavation area by trucks that move along a system of ramps. The design of these ramps must be carefully addressed because they have to comply with geomechanical constraints to ensure the stability of the pit walls, provide access to the different levels and phases, but also maximise the value of the extracted ore and reduce the extraction of waste. Because an optimisation approach able to deal with the design of the full ramp system seems to be out of reach at the moment, this paper addresses the problem of designing one ramp providing access to a single pushback, which has been determined beforehand. The optimisation objective is therefore to find a ramp that gives access to one given potential volume, while minimising its impact on the economic value of the volume. Two versions of the problem are formalised. One version allows the extraction of ore and waste only if this extraction is necessary for the ramp system. This version somehow minimises the intrinsic value of the ramp system. In the second version, it is possible to extract more than is needed by the ramp system. For instance, this takes into account the possibility of attaining ore on the wall opposite to the ramp as soon as the ramp reaches its level. In the setting mentioned above, the contribution of this work is three-fold. First, the computational complexity of the two different versions of the problem is presented and discussed; in particular, they are shown to be NP-hard. Second, compact integer programs modelling these two versions are proposed. Third, an efficient GRASP algorithm able to cope with the large instances of the problem is proposed. To assess the proposed approaches, the models and algorithms are applied to real instances with an off-the-shelf solver, illustrating and discussing their potential and relevance for the two versions of the problem. They are also compared with other approaches from the literature in terms of value and resulting designs.