Mine Planning Above and Below Ground: Generating a Set of Pareto-Optimal Schedules Considering Risk and Return

Recent years have seen increasing efforts to incorporate risk and uncertainty into optimal and heuristic methods for mine planning and scheduling. The recent volatility in the prices of metals and minerals has provided further impetus for developing new methods that facilitate integrated optimization and risk analysis in mining. We consider a long-term problem of determining a plan for above- and underground mining, allowing for different ways in which the material can be extracted, such as choice of cutoff grade and mining speed. We develop a methodology based on a longest-path network framework that allows us to identify the mining plans that produce the k highest values of expected profit, where k can be chosen by the decision-maker. We couple this with a methodology for evaluating each of these plans with respect to various measures of risk, such as variance, probability of achieving a profit target, or conditional value-at-risk. The framework is easily extendible to other risk measures. The methodology provides a means to construct a set of Pareto-optimal solutions with expected profit and the selected risk measure as the two performance metrics. We illustrate our approach using a simple example in which the risk measure is value-at-risk (VaR).