Stope boundary optimization: A mathematical model and efficient heuristics

Solving the stope boundary optimization problem is the primary step that should be taken after selecting an underground mining method. Obviously, this solution should be optimal because suboptimal boundaries may lead to wasting both mining capital and mineral resources. Four decades have passed since the first algorithm was developed to solve this problem, and no comprehensive method has yet been reported. The current study presents an integer programming (IP) model to solve the stope boundary optimization (SBO) problem. The application domain of this model is limited to non-complex problems, and thus, to cover all the stope boundary optimization problems, a greedy algorithm is also developed. The greedy algorithm was implemented on three real cases and its optimality gap on these cases is 1.85%, 0.47%, and 1.42%, respectively. However, to obtain better results and decrease the optimality gap, this paper introduces a new iterative enumeration algorithm. The proposed algorithm uses two inner algorithms: the Improved Greedy and Approximate Dynamic Programming algorithms. The optimality gap of the Iterative Enumeration algorithm in all the mentioned cases was less than 0.6%.