Open-pit mine production scheduling under grade uncertainty

Abstract

Common challenges associated with grade uncertainty involve failing to meet decisive operational targets, which include (among others) the following: ore tonnage sent to the mill, total metal processed at the mill, blending requirements on ore feed, total waste tonnage mined, maximum allowable proportion of potentially deleterious materials (e.g., toxic elements such as arsenic). These challenges reflect, to an important extent, the uncertainty involved in defining precisely the mineral grades in an ore deposit. This has motivated a vast body of research directed at improving understanding stochastic mine planning techniques, with an aim of incorporating its tools to mine production scheduling. One popular paradigm for stochastic mine planning consists of formulating fully stochastic linear programming (SLP) models which adopt sets of realizations of the orebody to represent uncertainty regarding grades (Dimitrakopoulos et al., 2014). Since constraints must be met with total certainty, solutions from these formulations provide a decision maker with an absolute aversion to risk, i.e., one who (invariably) favors the most certain of two possible outcomes, regardless of their corresponding payoffs. Such production schedules may be too conservative in satisfying the production targets, while simultaneously producing sub-optimal results in those circumstances in which some flexibility in meeting targets exists. In a second paradigm, mine planners overcome the shortcomings of traditional production scheduling by incorporating geologic and grade uncertainty through geostatistical conditional simulations. However, this means that it is conceivable that one could also potentially benefit from any favorable development regarding previously “uncertain” domains of the ore deposit. The work undertaken in this dissertation focuses on generating production schedules that take into account grade uncertainty, as described by geostatistically simulated realizations of the ore deposit, and provide optimized production schedules that also consider the desired degree of risk in meeting the production planning outcomes. To do this, the production scheduling problem is formulated as a large-scale linear program (LP) that considers grade uncertainty as characterized by a resource block model. The large-scale LP problem is solved using an iterative decomposition algorithm whose subproblems are multi-time-period sequencing problems. At each iteration, one solves a master problem that generates a series of Lagrange multipliers (dual variables) that modify the objective function of the subproblems. In turn, the subproblem solutions modify the feasible region in the master problem and the approach is proven to converge to the optimal solution (Bienstock & Zuckerberg, 2009). The resulting LP solution is a multi-time-period mine production schedule that meets mining company’s required level of risk tolerance in mine production plans. The production scheduling formulation based on new risk-quantified linear programming models (LP) and their subsequent solutions do not only provide the risk profile of a given mine production schedule, but also allow the decision maker to define the level of acceptable risk in the mine plans generated and adopted