A Binary Integer Linear Programming Model for Optimizing Underground Stope Layout

Abstract Underground mine planning engineers face significant challenges when determining what design and layout provides the most profitable and safe stope for extraction. While researchers have developed several techniques and optimization algorithms in recent years to solve this problem, most fail to find optimal solutions because they are heuristic or LP-based without efficient shape constraints. This work proposes a two-dimensional binary integer linear programming (BILP) model for determining the optimal combination of blocks in a stope that maximizes the economic value of the layout of stopes while respecting all constraints. The work draws on Queyranne and Wolsey’s (2017 & 2018) formulations of tight constraints for bounded up/down times in production planning problems to formulate novel and efficient geometric constraints along with geotechnical and grade constraints for the stope layout optimization problem. Results of the case study indicate that it is possible to formulate efficient shape constraints in LP-based stope optimization models. The block model used for the numerical example contained 144 valuable blocks out of 774 blocks. The BILP model selected 60 valuable blocks and 13 waste blocks that met all constraints translating into a maximum economic value of $34.4 M in 1.83 h with a gap tolerance of 0.00%. A series of experiments show that the model is sensitive to cutoff grade, stope frame size, pillar size, number of stopes, and problem size as these key parameters affect the objective function value, solution time, and final layout of stopes. The main limitation of the proposed model is that pillar constraints are implemented in the Z–X or Z–Y directions but not implemented diagonally.