# MineLib: a library of open pit mining problems

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## Abstract

Similar to the mixed-integer programming library (MIPLIB), we present a library of publicly available test problem instances for three classical types of open pit mining problems: the ultimate pit limit problem and two variants of open pit production scheduling problems. The ultimate pit limit problem determines a set of notional three-dimensional blocks containing ore and/or waste material to extract to maximize value subject to geospatial precedence constraints. Open pit production scheduling problems seek to determine when, if ever, a block is extracted from an open pit mine. A typical objective is to maximize the net present value of the extracted ore; constraints include precedence and upper bounds on operational resource usage. Extensions of this problem can include (*i*) lower bounds on operational resource usage, (*ii*) the determination of whether a block is sent to a waste dump, i.e., discarded, or to a processing plant, i.e., to a facility that derives salable mineral from the block, (*iii*) average grade constraints at the processing plant, and (*iv*) inventories of extracted but unprocessed material. Although open pit mining problems have appeared in academic literature dating back to the 1960s, no standard representations exist, and there are no commonly available corresponding data sets. We describe some representative open pit mining problems, briefly mention related literature, and provide a library consisting of mathematical models and sets of instances, available on the Internet. We conclude with directions for use of this newly established mining library. The library serves not only as a suggestion of standard expressions of and available data for open pit mining problems, but also as encouragement for the development of increasingly sophisticated algorithms.

### Keywords

Mine scheduling Mine planning Open pit production scheduling Surface mine production scheduling Problem libraries Open pit mining library## Notes

### Acknowledgements

Eduardo Moreno and Marcos Goycoolea thank CONICYT grants ACT-88 and Basal Center CMM, Universidad de Chile. Daniel Espinoza and Marcos Goycoolea acknowledge FONDECYT grant #1110674. Daniel Espinoza is grateful for ICM Grant #P05-004F. The authors all acknowledge the donors of several anonymous data sets, and the comments of two anonymous referees on previous versions of this paper.

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