Risk Averse Approaches in Open-pit Production Planning under Ore Grade Uncertainty: a Ultimate Pit Study

During early phases of open-pit mining production planning many parameters are uncertain, and since the mining operation is performed only once, any evaluations based only on on average outcomes neglects the very real chance of obtaining an outcome that is below average. Taking into account also that operation costs are considerable and the mining horizon usually extends over several decades it is clear that open-pit production planning is a risky endeavor. In this work we take a risk-averse approach on tackling uncertainty in the ore-grades. We consider an extended Ultimate-Pit problem, where extraction and processing decisions have to be taken. We apply and compare the risk-hedging performance of two approaches from optimization under uncertainty: minimize Conditional Value-at-Risk (CVaR) and minimization of a combination of expected value and CVaR. Additionally, we compare two decision schemes: a static variant, where all decisions have to be taken ―now‖, and a two-stage or recourse variant, where we take extraction decisions now, then we see the real ore-grade, and just then processing decision is taken. Our working assumption is that we have available a large number of oregrade scenarios. Computational results on one small size vein-type mine illustrate how minimizing average loss provides good on-average results at the cost of having high probability of obtaining undesired outcomes; and on the other hand our proposed approaches control the risk by providing solutions with a controllable probability of obtaining undesired outcomes. Results also show the great risk-hedging potential of using multi-stage decision schemes.