Linear programming approximations for modeling instant-mixing stockpiles

Stockpiles are a crucial part of mine planning. However, they are often ignored in longterm planning due to the difficulty of correctly evaluating their impact in mine scheduling. This difficulty arises mainly because materials of different grades are mixed in a stockpile, and the final grade of the material leaving the stockpile is a complex non-linear function of the material inside the stockpile. In practice, computational software uses different (usually linear) approximations for estimating this grade, but it is not clear how good these approximations are. In this paper, we discuss different optimization models to approximate the real impact of a stockpile on long-term mine planning. We discuss the properties of these models and compare the quality of the approximations computationally. We show that it is possible to obtain good upper and lower bounds on the resulting grade of the stockpile, and realistic and accurate estimations of the behavior of the stockpile. We also discuss how to extend these models to address different minerals and their corresponding grades.