A stochastic optimization formulation for the transition from open pit to underground mining

As open pit mining of a mineral deposit deepens, the cost of extraction may increase up to a threshold where transitioning to mining through underground methods is more profitable. This paper provides an approach to determine an optimal depth at which a mine should transition from open pit to underground mining, based on managing technical risk. The value of a set of candidate transition depths is calculated by optimizing the production schedules for each depth's unique open pit and underground operations which provide yearly discounted cash flow projections. By considering the sum of the open pit and underground mining portion's value, the most profitable candidate transition depth is identified. The optimization model presented is based on a stochastic integer program that integrates geological uncertainty and manages technical risk. The proposed approach is tested on a gold deposit. Results show the benefits of managing geological uncertainty in long-term strategic decision-making frameworks. Additionally, the stochastic result produces a 9% net present value increase over a similar deterministic formulation. The risk-managing stochastic framework also produces operational schedules that reduce a mining project`s susceptibility to geological risk. This work aims to approve on previous attempts to solve this problem by jointly considering geological uncertainty and describing the optimal transition depth effectively in 3-dimensions.