A New Approach to Flexible Open Pit Optimisation and Scheduling

摘要

Traditionally pit optimisation and scheduling is carried out assuming that the resources, the commodity prices and production costs are all known. Once the pit contour and the mining schedule have been determined, geostatistical simulations can be used to assess the impact of the uncertainty in the resources on the pit design and the schedule, and likewise stochastic simulations can be used to test its robustness to fl uctuations in costs and prices. But it would be more interesting to have a dynamic procedure for optimising the pit as the resources become better known and as economic factors such as commodity prices and costs evolve over time. This paper presents a novel approach for doing this. Rather than working with millions of small selective mining units, it was decided to work with large blocks, called macro-blocks. Mining sequences are defi ned as the quantities to be extracted from each macro-block in each time period. Feasible mining sequences are mining sequences that respect the accessibility constraints, and also the geometric constraints on the amounts that can be extracted from any one block over time, or from all the active blocks at a given time. Having defi ned feasible mining sequences, their mathematical properties were studied. It was found that natural breakpoints occur in the sequences when one set of blocks have been completely mined out, thereby opening up access to others. It was discovered that families of sequences exist, and that they are convex and closed under certain types of row permutation operations. Convexity is an advantage when optimising. The closure property opens up the possibility of mixing and matching subsequences of rows in the sequences. Another interesting property is that the sequences form branching families, rather like the binomial and trinomial trees used to model prices in fi nance and in real options. It is easy to generate large numbers of feasible mining sequences randomly. A two-step procedure is used to fi nd the best one (or the best few) using three economic criteria: 1. expected NPV, 2. the probability of a negative NPV, and 3. the percentage of years when the cash fl ow is negative. The procedure was tested on a synthetic gold mine based on the characteristics of the Essakane mine in Burkina Faso. The results were encouraging.