Using chance constrained binary integer programming in optimising long term production scheduling for open pit mine design

Abstract

The present paper attempts to model long term production scheduling problems by chance constrained binary integer programming in a stochastic environment. This stochastic model is set up to account for ore block grade uncertainty. The probability distribution function of grade in each block is used as a stochastic input to the optimisation model. This distribution function in each block should be determined using geostatistical simulation approach. The deterministic equivalent of proposed chance constrained model is then achieved which is the form of non-linear quadratic in binary variables. A confidence level at which it is desire that the uncertain constraints holds, is specified in each scheduling period. Rather than previous risk based model, this formulation will yield schedules with high chance of achieving planned production targets while maximises the expectation of net present value and minimises the variance function simultaneously. Using this method the grade uncertainty is integrated explicitly into the optimisation process.