Optimizing underground mine design with method-dependent precedences

This article addresses an underground mine design and scheduling problem, in which ore extraction methods are determined and resulting mining activities are scheduled. The mining method influences necessary infrastructure, the activities selected, and their timing. We divide the ore body into partitions (i.e., panels), each of which is extracted using a specific method, if at all. We consider two extraction methods, namely open-stope mining and bottom-up stoping with backfill, as well as an option of doing nothing. The myriad decisions present a challenging integer-programming problem for which we propose an optimization-based heuristic to generate an initial feasible solution. We further expedite solutions to the monolith by (i) eliminating unnecessary variables and (ii) strengthening the formulation.Our empirical study, conducted using 36 instances – four of which are directly obtained from our industry partner, demonstrate that the proposed model and corresponding solution methodology provide good-quality solutions with gaps averaging less than 8% and superior to those obtained via several general-purpose-solver heuristics; CPU times of two hours or fewer are considered to be reasonable for long-term planning purposes. Our results also show that instances with irregular disposition and lower development rates are more tractable. We provide managerial insights gained from our solutions which reveal that the mining method selected depends heavily on the extraction rate. Finally, we note that solving an industry-partner-provided instance results in a design with 44% additional value compared to that obtained via industry practice.