A Chance Constrained Integer Programming Model for Open Pit Long-Term Production Planning

Abstract

The mine production planning defines a sequence of block extraction to obtain the highest NPV under a number of constraints. Mathematical programming has become a widespread approach to optimize production planning, for open pit mines since the 1960s. However, the previous and existing models are found to be limited in their ability to explicitly incorporate the ore grade uncertainty into the planning process. To overcome this shortcoming, this paper presents an Integer Programming (IP) model, for long-term planning of open pit mines. This model is set up to account for grade uncertainty. The grade distribution function, in each block is used as a stochastic input, to optimize the model. The deterministic equivalent of this model is then achieved by using stochastic programming, which is a form of nonlinear in binary variables. Because of the difficulties in solving large scale nonlinear models, the model is then approximated by a linear one.This formulation will yield schedules with high chance of achieving planned production targets, while maximizes the expectation of net present value, it simultaneously minimizes the variance in function.