Four-Dimensional Network Relaxation Method for Long-Term Open Pit Mine Scheduling

The four-dimensional (4D) network relaxation method, originally developed by Akaike in 1999, uses Lagrange relaxation and is known for its ability to include the price change and possible better outputs, but the computation time is huge. However, the continuous advancement in computer technologies allows the use of higher-speed computers with more memory capacity. Therefore, in this paper the authors have tried to implement the method with adjustments and improvements in its algorithm to suit the current computing system. As a result, the computation time has been drastically reduced and more constraints can be included, which makes the scheduling a more realistic one. The case study of an open pit gold mine with 129 500 blocks can be solved considering the capacity constraints in 71 seconds. In previous case studies, the mined ore had to be processed or disposed of immediately. Now, stockpiling can be included as another option. Since the details of the algorithm are still being improved, the computation time is a little longer than the previous cases without the stockpiling option. However, it is found that scheduling with the stockpiling option is possible in a reasonable time. In conclusion, the 4D network relaxation method has become more useful with advances in computer technologies and provides better results.