| Underground mine production scheduling possesses mathematical structure similar to and yields many of the same challenges as general scheduling problems. That is, binary variables represent the time at which various activities are scheduled. Typical objectives seek to minimize costs or some measure of production time, or to maximize net present value; two principal types of constraints exist: (i) resource constraints, which limit the number of activities committed to a time period based on the availability of a given supply and on the amount of that supply required to perform the activity, and (ii) precedence constraints, which dictate the order in which activities must be completed. In our setting, we maximize "discounted metal production" for the remaining life of an underground lead and zinc mine that uses three different underground methods to extract the ore. Resource constraints limit the grade, tonnage, and backfill paste (used for structural stability) in each time period, while precedence constraints enforce the sequence in which extraction (and backfill) is performed in accordance with the underground mining methods used. We tailor existing exact and heuristic approaches to reduce model size, and develop an optimization-based decomposition heuristic; both of these methods transform a computationally intractable problem to one for which we obtain solutions in seconds, or, at most, hours for problem instances based on data sets from the Lisheen mine near Thurles, Ireland. Our solution adds value to the Lisheen mining operation by: (i) shifting metal production forward in the schedule; (ii) reducing waste mining and backfilling delays; (iii) avoiding expensive mill-halting drops in ore production; and (iv) enabling smoother workforce management. Our modeling approach could be applied to other mines, especially to operations with flat lying deposits that practice retreat, i.e., room-and-pillar, mining, such as coal mines, and to mines that are approaching the end of their operational life. |
