Methods for Improving the Tractability of the Block Sequencing Problem for Open Pit Mining

Abstract : A surface mine optimizes its profits by maximizing the net present value (NPV) of minerals extracted from the orebody. This is accomplished by creating a production schedule that defines when each section, or block, of ore is removed. Doing so efficiently requires adherence to geospatial and operational constraints. A common exact method for determining this block extraction sequence is formulating the problem as a mixed integer program where each block is a time-indexed binary variable representing when (and if) a given block is removed from the orebody. We describe the complexities involved in such a formulation and suggest methodologies to expedite the solution times for instances of this block sequencing problem. We adopt three approaches to make the model more tractable: (1) we apply deterministic variable reduction techniques to eliminate blocks from consideration in the model; (2) we produce cuts that strengthen the model's formulation; and (3) we employ Lagrangian relaxation techniques. These three techniques allow us to determine an optimal (or near-optimal) solution more quickly than solving the monolith (original problem). Applying our techniques to data sets ranging from 100 to 10,000 blocks reduces solution times by over 90%, on average.

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