Adriana Piazza, Optimal cut-off grade: a dynamic programming approach.

In 1964, Kenneth Lane proposed an algorithm to optimize the production schedule of a single-metal, single-processor mine. For this, he proposed a policy based on varying, over time, the so-called “cut-off grade” – or grade threshold used to determine if extracted material should be ore (processed material) or waste (thrown away). Lane’s algorithm had a profound impact on the mining industry. However, though it has been used in multiple commercial software systems and has traditionally been taught in every mining engineering program, it is widely considered a heuristic, and little is known regarding the quality of the solutions it produces. In our work, we formally study Lane’s problem. We show that Lane’s problem can be re-formulated as a dynamic programming problem and retrieve Lane’s optimality conditions by solving a variant of the problem where the future value function is linearly approximated. Furthermore, through a reformulation, we show that Lane’s problem can be solved using convex mixed-integer programming. Computational experiments show that Lane’s algorithm returns an approximately optimal solution in every real-world data set tested, thereby lending solid support for its practical application. In an ongoing work, we extend our results to mines containing two commercial minerals.