A dynamic stochastic programming approach for open-pit mine planning with geological and commodity price uncertainty

Over the last decade, geological uncertainty and its effects on long-term or strategic mine planning and methods for related risk management have been studied. However, the combined effect of geological and commodity price uncertainty has received relatively less attention in the technical literature. A research experiment that addresses both these sources of uncertainty is presented herein and accounts for their differences. In particular, while the current commodity price is known at the beginning of every new mining period, the geology, including the mineral grades, metal content, material types and so on, remain uncertain, even when additional information becomes available. The proposed method first uses a two-stage model to manage the geological uncertainty that leads to a scenario-independent extraction sequence. Based on different metal production targets, a pool of subsets of mining blocks is also precomputed for every period. Then, a stochastic dynamic programming algorithm is developed and employed to define the best policy in terms of metal production targets to follow, depending on the evolution of the related commodity price. This policy follows the scenario tree of the commodity price, as it is scenario-dependent (price only) with non-anticipativity constraints, which is similar to an operator that adapts to a fluctuating market. This new approach is tested through a case study that reveals the counter-intuitive combined effects of both sources of uncertainty. For instance, based on the previous evolution of the commodity price, the obtained policy suggests adaptations of the metal production target that go against common practices of mining operators.