LP-based disaggregation approaches to solving the open pit mining production scheduling problem with block processing selectivity

Authors:
Natashia Boland;Irina Dumitrescu;Gary Froyland;Ambros M. Gleixner
Affiliations:
Department of Mathematics and Statistics, The University of Melbourne, Parkville, VIC 3010, Australia;School of Mathematics and Statistics, The University of New South Wales, Sydney, NSW 2052, Australia;School of Mathematics and Statistics, The University of New South Wales, Sydney, NSW 2052, Australia;Institut für Mathematik, Technische Universität Berlin, D-10623 Berlin, Germany
Venue:
Computers and Operations Research
Year:
2009

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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.