The Open Pit Mine Production Scheduling Problem (OPMPSP) studied in recent years is usually based on a single geological estimate of material to be excavated and processed over a number of decades. However techniques have now been developed to generate multiple stochastic geological estimates that more accurately describe the uncertain geology. While some attempts have been made to use such multiple estimates in mine production scheduling, none of these allow mining and processing decisions to flexibly adapt over time, in response to observation of the geological properties of the material mined. In this paper, we use multiple geological estimates in a mixed integer multistage stochastic programming approach, in which decisions made in later time periods can depend on observations of the geological properties of the material mined in earlier periods. Since the material mined in earlier periods is determined by our decisions, the information received about uncertain properties, and when that information is available, is decision-dependent. Thus we tackle the difficult case of stochastic programming with endogeneous uncertainty. We extend a successful mixed integer programming formulation of the OPMPSP to this stochastic case, and show that non-anticipativity can be modelled with linear constraints involving variables already present in the model. We extend this observation to the general class of endogenous stochastic programs, and exploit the special structure of our model to show that in some cases we can omit a significant proportion of these constraints. Using data supplied by our industry partner, (a multinational mining company), we show that this approach is reasonably tractable, and demonstrate the improvements that can be made to mine schedules through the explicit use of multiple geological estimates.
Submitted to Operations Research.