Underground long-term mine production scheduling with integrated geological risk management S. Carpentier* 1,2 , M. Gamache 1,3 and R. Dimitrakopoulos 2,3 A stochastic integer programming (SIP) model is presented to optimise long-term scheduling of underground mine operations while considering geological uncertainty. To integrate this uncertainty, a set of stochastic simulations is generated, corresponding to representations of the deposit, and is used as primary inputs to optimisation. The two-stage SIP model developed considers a variable cut-off grade and accounts for maximum development, material handling flow conservation, mill and mine capacity, and activity precedencies for an underground nickel mine. The results show that the schedule generated has a higher expected value when considering and managing grade risk. They also demonstrate the benefits of risk control, which this approach allows. Keywords: Underground mine, Stochastic optimisation, Production scheduling, Long-term-planning, Geological uncertainty Introduction Over the last decades, stochastic optimisation methods have been developed to deal with geological uncertainty in open pit mine design and life-of-mine production scheduling (e.g. Menabde, Froyland, Stone and Yeates 2005; Boland, Dumitrescu and Froyland 2008; Dimitrakopoulos 2011; Goodfellow and Dimitrakopoulos 2013; others). These efforts stem from earlier documentations of the adverse effects of geo- logical uncertainty of mining projects and production performance (e.g. Dowd 1994, 1997; Morley, Snowdon and Day 1999; Vallee 2000; Dimitrakopoulos, Farrelly and Godoy 2002) and aim to provide effective geological risk management, leading to more robust mine pro- duction forecasts and improved net present value (NPV) assessments. Similar efforts in underground mine plan- ning and production scheduling are very limited, as the required optimisation developments are dependent, unlike in open pit mines, on the mining method employed, which makes generalisations of solutions challenging. Optimisation methods in underground mining were introduced in the 1980s (Lizotte and Elbrond 1985; Chatterjee and Sridhar 1986) and to date remain largely conventional. Mixed integer linear programming (MILP) approaches were further developed in the 1990s to consider mine production scheduling, including haulage capacity and backfill (Trout 1997; Topal 1998), optimisation of stope geometry (Ovanic 1998), large- scale production scheduling in sublevel caving iron mines (Topal 2003) and block caving mining (Rahal et al. 2003), but were, in general, unable to solve realistic industrial mining scenarios. Additional information can be found in a review by Alford, Brazil and Lee (2007). More recently, Nehring, Topal and Little (2010) present a new MIP model for underground mine planning aiming to accelerate the computational time needed for practical applications. Accordingly, while binary vari- ables are defined to represent all four typical production phases (development, drilling, extraction and backfill), the authors simplify the model by assigning a single variable for the entire production, thereby significantly reducing the model complexity and computational time. Little, Knights and Topal (2013) consider the impact of the interaction between underground stope design and long-term scheduling, and O’Sullivan and Newman (2014) propose a model for underground mine schedul- ing, which aims to maximise metal production and respect resource constraints, while considering sequen- cing of backfill and rock extraction operations. A heuristic is used to provide a solution to the formu- lation. Notable is the approach in Roberts and Bloss (2014), who show an adaptation of BHP Billiton’s BLASOR (e.g. Stone et al. 2005), an open pit planning optimiser and life-of-mine production scheduling software based on MILP, to the optimisation of underground strategic mine planning. Other determi- nistic optimisation applications in underground mining include decline optimisation (Brazil et al. 2003), cost optimisation of mining networks (Brazil et al. 2005), and joint optimisation of designing access and scheduling (Sirinanda et al. 2014). Geological risk is not considered in any of the past work, with initial efforts limited to quantifying risk in stope designs (Myers, Standing, 1 Department of Mathematics and Industrial Engineering, E ´ cole Polytechnique, Montreal, QC, Canada 2 COSMO – Stochastic Mine Planning Laboratory, Department of Mining and Materials Engineering, McGill University, Montreal, QC, Canada 3 Research Group in Decision Analysis (GERAD), Montreal, QC, Canada *Corresponding author, email sabrina.carpentier@polymtl.ca Ñ 2016 Institute of Materials, Minerals and Mining and The AusIMM Received 21 April 2015; accepted 22 July 2015 DOI 10.1179/1743286315Y.0000000026 Published by on behalf of the Institute and The AusIMM Taylor & Francis Mining Technology 2016 VOL. 125 NO. 2 93 Downloaded by [McGill University Library] at 08:53 09 June 2016