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17 USC 105 interim-entered record; under review. The article of record as published may be found at http://dx.doi.org/10.1016/j.ejor.2021.01.011 Underground mine schedules seek to determine start dates for activities related to the extraction of ore, often with an objective of maximizing net present value; constraints enforce geotechnical precedence between activities, and restrict resource consumption on a per-time-period basis, e.g., development footage and extracted tons. Strategic schedules address these start dates at a coarse level, whereas tactical schedules must account for the day-to-day variability of underground mine operations, such as unanticipated equipment breakdowns and ground conditions, both of which might slow production. At the time of this writing, the underground mine scheduling literature is dominated by a deterministic treatment of the problem, usually modeled as a Resource Constrained Project Scheduling Problem (RCPSP), which precludes mine operators from reacting to unforeseen circumstances. Therefore, we propose a stochastic integer programming framework that: (i) characterizes uncertainty in duration and economic value for each underground mining activity; (ii) formulates a new stochastic variant of the RCPSP; (iii) suggests an optimization-based heuristic; and, (iv) produces implementable, tactical schedules in a practical amount of time and provides corresponding managerial insights. National Institute of Occupational Safety and Health National Agency for Research and Development (ANID)

The open pit mine production scheduling (OPMPS) problem seeks to determine when, if ever, to extract each notional, three-dimensional block of ore and/or waste in a deposit and what to do with each, e.g., send it to a particular processing plant or to the waste dump. This scheduling model maximizes net present value subject to spatial precedence constraints, and resource capacities. Certain mines use stockpiles for blending different grades of extracted material, storing excess until processing capacity is available, or keeping low-grade ore for possible future processing. Common models assume that material in these stockpiles, or “buckets,” is theoretically immediately mixed and becomes homogeneous. We consider stockpiles as part of our open pit mine scheduling strategy, propose multiple models to solve the OPMPS problem, and compare the solution quality and tractability of these linear-integer and nonlinear-integer models. Numerical experiments show that our proposed models are tractable, and correspond to instances which can be solved in a few seconds up to a few minutes in contrast to previous nonlinear models that fail to solve.

A large number of metal deposits are initially extracted via surface methods, but then transition underground without necessarily ceasing to operate above ground. Currently, most mine operators schedule the open pit and underground operations independently and then merge the two, creating a myopic solution. We present a methodology to maximize the NPV for an entire metal deposit by determining the spatial expanse and production quantities of both the open pit and underground mines while adhering to operational production and processing constraints. By taking advantage of a new linear programming solution algorithm and using an ad-hoc branch-and-bound scheme, we solve real-world scenarios of our transition model to near optimality in a few hours, where such scenarios were otherwise completely intractable. The decision of where and when to transition changes the net present value of the mine by hundreds of millions of dollars.

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 and (ii) precedence constraints. 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 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.

We present a mixed-integer program to schedule long- and short-term production at LKAB’s Kiruna mine, an underground sublevel caving mine located in northern Sweden. The model minimizes deviations from monthly preplanned production quantities while adhering to operational constraints. Because of the mathematical structure of the model and its moderately large size, instances spanning a time horizon of more than a year or two tend to be intractable. We develop an optimization-based decomposition heuristic that, on average, obtains better solutions faster than solving the model directly. We show that for realistic data sets, we can generate solutions with deviations that comprise about 3–6% of total demand in about a third of an hour.

Motivated by an underground mining operation at Kiruna, Sweden, we formulate a mixed integer program to schedule iron ore production over multiple time periods. Our optimization model determines an operationally feasible ore extraction sequence that minimizes deviations from planned production quantities. The number of binary decision variables in our model is large enough that directly solving the full, detailed problem for a three year time horizon requires hours, or even days. We therefore design a heuristic based on solving a smaller, more tractable, model in which we aggregate time periods, and then solving the original model using information gained from the aggregated model. We compute a bound on the worst case performance of this heuristic and demonstrate empirically that this procedure produces good quality solutions while substantially reducing computation time for problem instances from the Kiruna mine.