A new approach to constrained open pit pushback design using dynamic cut-off grades

An integral part of open pit optimization is deciding which section of the ultimate pit to mine during a specific period. For a given period there are often operational and marketing constraints that restrict what can be removed or processed. The operational constraints arise from a number of different limitations such as safe slope of internal mining walls, mill and mining capacity. Traditional methods for pushback (phase) design that incorporate these constraints are ad-hoc and can lead to suboptimal solutions. Another important optimization decision that must be made is the cut-off grade to be used for a specific period. In this paper, a new method is presented that generates near maximal expected profit and dynamically defines the optimal cut-off grade for each mining period or pushback over the life-of-mine, thus deciding whether a block is ore or waste during the optimization process. More specifically, a method for converting a fractional linear program solution into an integral solution known as pipage rounding is applied to an integer program formulation of a pushback design optimization problem. The proposed method aims to produce a set of pushbacks in a way that the total discounted profit to be generated through production scheduling is maximized. Two case studies demonstrate the applied aspects of the proposed method.