An ad hoc solution to the transition mine problem

A current challenge faced by the mining industry is solving the integrated transition mine problem (TMP) that maximizes the net present value (NPV). This study aims to develop an optimization framework capable of solving the TMP. The problem is NP-hard and therefore computationally intractable. Three ad hoc approaches – Exact solution, Benders’ decomposition, and Benders’ decomposition with Bienstock-Zuckerberg (BZ) algorithm – are compared for different scheduling periods. The TMP is formulated as a mixed integer linear programming model, implemented in Python, and solved with the Gurobi optimizer. The results showed that Bender's decomposition with the BZ algorithm outperforms the other approaches in execution time, computational cost, and feasibility to address large problems in exchange for a marginal cost in the quality of the NPV obtained. In addition, the probability of finding the optimal point of transition is higher regardless of the number of feasible crown pillar locations evaluated. This is achieved through the optimality cuts proposed in the algorithm.