Strategic planning of an underground mine with variable cut-off grades

We present a mixed-integer programming model for solving the long-term planning problem of an underground mine. This model, which establishes the sequence of mining for a horizon of 20 years, determines which lens of the geological model will be mined and in what order, while respecting the operational constraints. For each lens to be mined, a specific cut-off grade has to be selected to maximize the net present value. The choice of a cut-off grade affects the volume and the average grade of each lens, which increases the size of problems to be solved. To reduce the computation time, different acceleration strategies and a Fix-and-Optimize heuristic are proposed. Computational experiments on instances of different sizes are performed to (1) assess the quality of the solution found by each method and (2) present the impact of the variable cut-off grade.