A new algorithm for the open-pit mine scheduling problem

For the purpose of production scheduling, open pit mines are discretized into threedimensional arrays known as block models. Production scheduling consists in deciding which blocks should be extracted, when they should be extracted and how each extracted block should be processed. Blocks which are on top should be extracted first, and capacity constraints limit the production each time period. Since the 1960s it has been known that this problem can be modeled with integer programming. However, the large size of real instances (3-10 million blocks, 15-20 time periods) has made these models impractical for use in real planning applications, thus leading to the use of numerous heuristic methods. We propose a new decomposition method for the precedenceconstrained knapsack problem, and show how we can use this to solve the LP relaxation of large production-scheduling formulations. Our computations show that we can solve, in minutes, the LP relaxation of real-sized mine-planning applications with up to 5 million blocks and 20 time periods. Combining this with a quick rounding algorithm based on topological sorting, we obtain solutions within less than 6% of optimality in seconds. A second heuristic step, based on local search, allow us to find solutions within 3% in one hour on all instances considered. For most instances we obtain solutions within 1-2% of optimality if we let this heuristic run longer. Previous methods have only been able to tackle instances with up to 150,000 blocks and 15 time periods.