Computers & Operations Research 36 (2009) 1064 – 1089 www.elsevier.com/locate/cor LP-based disaggregation approaches to solving the open pit mining production scheduling problem with block processing selectivity Natashia Boland a , Irina Dumitrescu b, ∗ , Gary Froyland b , Ambros M. Gleixner c a Department of Mathematics and Statistics, The University of Melbourne, Parkville, VIC 3010, Australia b School of Mathematics and Statistics, The University of New SouthWales, Sydney, NSW 2052, Australia c Institut für Mathematik, Technische Universität Berlin, D-10623 Berlin, Germany Available online 14 December 2007 Abstract Given a discretisation of an orebody as a block model, the open pit mining production scheduling problem (OPMPSP) consists of finding the sequence in which the blocks should be removed from the pit, over the lifetime of the mine, such that the net present value (NPV) of the operation is maximised. In practice, due to the large number of blocks and precedence constraints linking them, blocks are typically aggregated to form larger scheduling units. We aim to solve the OPMPSP, formulated as a mixed integer programme (MIP), so that aggregates are used to schedule the mining process, while individual blocks are used for processing decisions. We propose an iterative disaggregation method that refines the aggregates (with respect to processing) up to the point where the refined aggregates defined for processing produce the same optimal solution for the linear programming (LP) relaxation of the MIP as the optimal solution of the LP relaxation with individual block processing. We propose several strategies of creating refined aggregates for the MIP processing, using duality results and exploiting the problem structure. These refined aggregates allow the solution of very large problems in reasonable time with very high solution quality in terms of NPV.  2007 Elsevier Ltd. All rights reserved. Keywords: Open pit mining; Constrained scheduling problems; Net present value; Aggregation; Iterative disaggregation; Mixed integer programming 1. Introduction We consider an orebody exploited using open pit mining methods. The orebody is represented as a block model: a discretisation of a volume of earth into blocks. In the presence of mining and processing costs and capacities, as well as precedence constraints with respect to the order in which the blocks can be excavated, the open pit mining production scheduling problem (OPMPSP) consists of finding the sequence in which the blocks should be removed from the pit, over the lifetime of the mine, such that the net present value (NPV) of the operation is maximised. It is intuitively clear that better scheduling decisions can be made when the discretisation of the orebody is very fine, and so current mine planning or modelling tools typically model orebodies using up to millions of blocks. While such block models provide a high resolution description of the orebody, the huge number of blocks makes the OPMPSP very difficult to solve. ∗ Corresponding author. Fax: +61 2 9385 7123. E-mail address: irina.dumitrescu@unsw.edu.au (I. Dumitrescu). 0305-0548/$ - see front matter  2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.cor.2007.12.006