Using MILP to Optimize Period Fix Costs in Complex Mine Sequencing and Scheduling Problems

For mine production problems in mines with varying qualities, both open pit and underground, the linear programming method (LP) has been used successfully. By this method it is possible to keep the total production blend for each period within a required range of qualities while optimizing objectives like production costs, net return, ore grades, other qualities, or a combination of these. Technical restrictions like constrained capacities can be added to the model. This makes LP a flexible and powerful tool for mine production planning. Practical experiences have shown the major influence fix costs have on the actual economic result of a planning decision. It can be proven that fix costs cannot be included in LP models. We describe a way to address this fix cost problem by using mixed integer linear programming (MILP) as an extension to LP in the optimization of a mine planning problem. This raises the issue of complexity. We discuss the computational complexity of the resulting models and the enhancement of model flexibility for the user of a planning system. We demonstrate the method embedded in a practicable everyday planning system for a complex underground coal mine. By computational examples we show how the method improves the economical results of the planning.