A new mathematical programming model for production schedule optimisation in underground mining operations

Abstract

Mixed integer programming (MIP) has been used for optimizing production schedules of mines since the 1960s and is recognized as having significant potential for optimizing production scheduling problems for both surface and underground mining. The major problem in long-term production scheduling for underground ore bodies generally relate to the large number of variables needed to formulate a MIP model, which makes it too complex to solve. As the number of variables in the model increase, solution times are known to increase at an exponential rate. In many instances the more extensive use of MIP models has been limited due to excessive solution times. This paper reviews production schedule optimization studies for underground mining operations. It also presents a classical MIP model for optimized production scheduling of a sublevel stoping operation and proposes a new model formulation to significantly reduce solution times without altering results while maintaining all constraints.A case study is summarized investigating solution times as five stopes are added incrementally to an initial ten stope operation, working up to a fifty stope operation. It shows substantial improvement in the solution time required when using the new formulation technique. This increased efficiency in the solution time of the MIP model allows it to solve much larger underground mine scheduling problems within a reasonable timeframe with the potential to substantially increase the net present value (NPV) of these projects. Finally, results from the two models are also compared to that of a manually generated schedule which show, the clear advantages of mathematical programming in obtaining optimal solutions.