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

摘要

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 orebodies 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 limes 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 sloping operation and proposes a new model formulation to significantly reduce solution limes without altering results while maintaining all constraints. A case study is summarized investigating solution times as five slopes are added incrementally to an initial ten stope operation, working up to a fifty slope operation. It shows substantial improvement in the solution lime required when using the new formulation technique. This increased efficiency in the solution lime of the MIP model allows it to solve much larger underground mine scheduling problems within a reasonable lime frame with (he 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.