Stochastic Optimisation of Long-Term Production Scheduling for Open Pit Mines with a New Integer Programming Formulation S. Ramazan and R. Dimitrakopoulos Abstract Conventional approaches to optimising open pit mine design and pro- duction scheduling are based on a single estimated orebody model, which does not account for geological variability. Conditional simulation can be employed to quantitatively address the resulting grade uncertainty. Multiple simulated orebody models provide a suitable input for stochastic integer programming (SIP), a type of mathematical programming that generates the optimal result for a defined set of objectives under uncertainty. In the case of production scheduling, the objectives are to maximise the total net present value (NPV) and to minimise unsatisfied demand for processed ore. Using a set of multiple simulated orebody models as input into an SIP model allows for the integration of in situ deposit variability and uncertainty directly into the production scheduling optimisation process. Introduction Stochastic integer programming (SIP) is a type of mathematical programming and modelling that considers multiple equally probable scenarios and generates the optimal result for a set of defined objectives within the feasible solution space bounded by a set of constraints. SIP is defined as an extension of mixed integer programming (MIP) with uncertainty in one or more of the related coefficients (Escudero 1993). This tends to increase problem size and complexity when com- pared with scheduling formulations based on MIP (Ramazan 2001). Different approaches in SIP formulations are discussed in (Birge and Louveaux 1997); S. Ramazan (&) MAusIMM, Rio Tinto, GPO Box A42, Perth, WA 6000, Australia e-mail: salih.ramazan@riotinto.com R. Dimitrakopoulos MAusIMM COSMO Laboratory, Department of Mining Metals and Materials Engineering, McGill University, Frank Dawson Adams Building Room 107, 3450 University Street, Montreal, QC H3A 2A7, Canada e-mail: roussos.dimitrakopoulos@mcgill.ca © The Australasian Institute of Mining and Metallurgy 2018 R. Dimitrakopoulos (ed.), Advances in Applied Strategic Mine Planning, https://doi.org/10.1007/978-3-319-69320-0_11 139