# MineLib: a library of open pit mining problems

- 1.2k Downloads
- 29 Citations

## 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.

## References

- Ahuja, R. K., Magnanti, T. L., & Orlin, J. B. (1993).
*Network flows: theory, algorithms, and applications*. Englewood Cliffs: Prentice Hall. Google Scholar - Akaike, A., & Dagdelen, K. (1999). A strategic production scheduling method for an open pit mine. In C. Dardano, M. Francisco, & J. Proud (Eds.),
*Proceedings of the 28th applications of computers and operations research in the mineral industries conference (APCOM)*, Golden, CO (pp. 729–738). Google Scholar - Amaya, J., Espinoza, D., Goycoolea, M., Moreno, E., Prevost, T., & Rubio, E. (2009). A scalable approach to optimal block scheduling. In
*35th APCOM*, Vancouver, Canada. Google Scholar - Askari-Nasab, H., Awuah-Offei, K., & Eivazy, H. (2010). Large-scale open pit production scheduling using mixed integer linear programming.
*International Journal of Mining and Mineral Engineering*,*2*, 185–214. CrossRefGoogle Scholar - Askari-Nasab, H., Pourrahimian, Y., Ben-Awuah, E., & Kalantari, S. (2011). Mixed integer linear programming formulations for open pit production scheduling.
*Journal of Mining Science*,*47*, 338–359. URL:http://dx.doi.org/10.1134/S1062739147030117. CrossRefGoogle Scholar - Beasley, J. (1990). OR-library: distributing test problems by electronic mail.
*Journal of the Operational Research Society*,*41*(11), 1069–1072. Google Scholar - Bienstock, D., & Zuckerberg, D. (2009). A new LP algorithm for precedence constrained production scheduling.
*Optimization Online*. URL:http://www.optimization-online.org/DB_HTML/2009/08/2380.html. Unpublished. Columbia University, BHP Billiton, August. - Bienstock, D., & Zuckerberg, D. (2010). Solving LP relaxations of large-scale precedence constrained problems. In:
*Lecture notes in computer science*(Vol. 6080, pp. 1–14). Google Scholar - Bixby, R. E., Boyd, E. A., & Indovina, R. R. (1992). MIPLIB: a test set of mixed integer programming problems.
*SIAM News*,*25*, 16. Google Scholar - Boland, N., Dumitrescu, I., Froyland, G., & Gleixner, A. (2009). LP-based disaggregation approaches to solving the open pit mining production scheduling problem with block processing selectivity.
*Computers & Operations Research*,*36*(4), 1064–1089. CrossRefGoogle Scholar - Brickey, A. (2012). Personal communication. Google Scholar
- Busnach, E., Mehrez, A., & Sinuany-Stern, Z. (1985). A production problem in phosphate mining.
*Journal of the Operational Research Society*,*36*(4), 285–288. Google Scholar - Caccetta, L., & Hill, S. (2003). An application of branch and cut to open pit mine scheduling.
*Journal of Global Optimization*,*27*(2–3), 349–365. CrossRefGoogle Scholar - Carlyle, W. M., Royset, J., & Wood, R. K. (2008). Lagrangian relaxation and enumeration for solving constrained shortest-path problems.
*Networks*,*52*, 256–270. CrossRefGoogle Scholar - Chandran, B., & Hochbaum, D. (2009). A computational study of the pseudoflow and push-relabel algorithms for the maximum flow problem.
*Operations Research*,*57*(2), 358–376. CrossRefGoogle Scholar - Chicoisne, R., Espinoza, D., Goycoolea, M., Moreno, E., & Rubio, E. (2012). A new algorithm for the open-pit mine scheduling problem.
*Operations Research*,*60*(3), 517–528. doi: 10.1287/opre.1120.1050. CrossRefGoogle Scholar - Cullenbine, C., Wood, R., & Newman, A. (2011). A sliding time window heuristic for open pit mine block sequencing.
*Optimization Letters*,*88*(3), 365–377. CrossRefGoogle Scholar - Dagdelen, K., & Johnson, T. (1986). Optimum open pit mine production scheduling by Lagrangian parameterization. In
*19th APCOM*, University Park, PA (pp. 127–141). Google Scholar - Denby, B., & Schofield, D. (1994). Open-pit design and scheduling by use of genetic algorithms.
*Transactions of the Institution of Mining and Metallurgy, Section A: Mining Industry*,*103*, A21–A26. Google Scholar - Deutsch, C. (2004). The place of geostatistical simulation in resource/reserve estimation. In
*Intern. conf. mining innovation (MININ)*, Santiago, Chile. Google Scholar - Fytas, K., Pelley, C., & Calder, P. (1987). Optimization of open pit short- and long-range production scheduling.
*CIM Bulletin*,*80*(904), 55–61. Google Scholar - Fytas, K., Hadjigeorgiou, J., & Collins, J. (1993). Production scheduling optimization in open pit mines.
*International Journal of Surface Mining*,*7*(1), 1–9. Google Scholar - Gay, D. M. (1985). Electronic mail distribution of linear programming test problems.
*Mathematical Programming Society COAL Bulletin*,*13*, 10–12. Data available at http://www.netlib.org/netlib/lp. Google Scholar - Gershon, M., & Murphy, F. (1989). Optimizing single hole mine cuts by dynamic programming.
*European Journal of Operational Research*,*38*(1), 56–62. CrossRefGoogle Scholar - Gleixner, A. (2008).
*Solving large-scale open pit mining production scheduling problems by integer programming*. Master’s thesis, Technische Universität Berlin. Google Scholar - Hochbaum, D. (2001). A new-old algorithm for minimum cut in closure graphs.
*Networks*,*37*(4), 171–193. CrossRefGoogle Scholar - Hochbaum, D., & Chen, A. (2000). Performance analysis and best implementations of old and new algorithms for the open-pit mining problem.
*Operations Research*,*48*(6), 894–914. CrossRefGoogle Scholar - Johnson, T. (1969). Optimum open pit mine production scheduling. In A. Weiss (Ed.),
*A decade of digital computing in the mining industry*. New York: American Institute of Mining Engineers. Chap 4. Google Scholar - Johnson, D., & Niemi, K. (1983). On knapsacks, partitions, and a new dynamic programming technique for trees.
*Mathematics of Operations Research*,*8*(1), 1–14. CrossRefGoogle Scholar - Kawahata, K. (2006).
*A new algorithm to solve large scale mine production scheduling problems by using the Lagrangian relaxation method*. PhD thesis, Colorado School of Mines. Google Scholar - Kim, Y., & Zhao, Y. (1994). Optimum open pit production sequencing—the current state of the art. In
*Preprint—soc. mining, metallurgy and exploration annual meeting proc.*, Littleton, CO: SME of the AIME. Google Scholar - Klingman, D., & Phillips, N. (1988). Integer programming for optimal phosphate-mining strategies.
*Journal of the Operational Research Society*,*39*(9), 805–810. Google Scholar - Krige, D. (1951). A statistical approach to some basic mine valuation problems on the Witwatersrand.
*Journal of the Chemical, Metallurgical and Mining Society of South Africa*,*52*(6), 119–139. Google Scholar - Lambert, W., Brickey, A., Eurek, K., & Newman, A. (2012).
*Open pit block sequencing formulations: a tutorial*(Working Paper). Google Scholar - Lane, K. (1988).
*The economic definition of ore: cutoff grade in theory and practice*. London: Mining J. Books Limited. Google Scholar - Lee, T. (1984). Planning and mine feasibility study—an owners perspective. In G. McKelvey (Ed.),
*Proceedings of the 1984 NWMA short course ‘Mine feasibility—concept to completion’*, Spokane, WA. Google Scholar - Lerchs, H., & Grossmann, I. (1965). Optimum design of open-pit mines.
*CIM Bulletin*,*LXVIII*, 17–24. Google Scholar - Munoz, G. (2012).
*Modelos de optimizacion lineal entera y aplicaciones a la mineria*. Master’s thesis, Dpto. Math. Engineering, Universidad de Chile, Santiago, Chile. Google Scholar - Newman, A., Rubio, E., Caro, R., Weintraub, A., & Eurek, K. (2010). A review of operations research in mine planning.
*Interfaces*,*40*(3), 222–245. CrossRefGoogle Scholar - Osanloo, M., Gholamnejad, J., & Karimi, B. (2008). Long-term open pit mine production planning: a review of models and algorithms.
*International Journal of Mining, Reclamation and Environment*,*22*(1), 3–35. CrossRefGoogle Scholar - O’Sullivan, D., & Newman, A. (2012).
*Long-term extraction and backfill scheduling in a complex underground mine*(Working Paper). Google Scholar - Ramazan, S. (2007). The new fundamental tree algorithm for production scheduling of open pit mines.
*European Journal of Operational Research*,*177*(2), 1153–1166. CrossRefGoogle Scholar - Reinelt, G. (1991). TSPLIB—a traveling salesman library.
*ORSA Journal on Computing*,*3*, 376–384. CrossRefGoogle Scholar - Sevim, H., & Lei, D. (1998). The problem of production planning in open pit mines.
*INFOR. Information Systems and Operational Research*,*36*(1–2), 1–12. Google Scholar - Somrit, C. (2011).
*Development of a new open pit mine phase design and production scheduling algorithm using mixed integer linear programming*. Dissertation, Colorado School of Mines, Golden, CO. Google Scholar - Sundar, D., & Acharya, D. (1995). Blast schedule planning and shiftwise production scheduling of an opencast iron ore mine.
*Computers & Industrial Engineering*,*28*(4), 927–935. CrossRefGoogle Scholar - Tabesh, M., & Askari-Nasab, H. (2011). Two-stage clustering algorithm for block aggregation in open pit mines.
*Mining Technology*,*120*, 158–169. CrossRefGoogle Scholar - Tan, S., & Ramani, R. (1992). Optimization models for scheduling ore and waste production in open pit mines. In
*23rd APCOM*(pp. 781–791). Tucson: SME of the AIME. Google Scholar - Underwood, R., & Tolwinski, B. (1998). A mathematical programming viewpoint for solving the ultimate pit problem.
*European Journal of Operational Research*,*107*(1), 96–107. CrossRefGoogle Scholar - Whittle (2009).
*Whittle consulting global optimization software*. Melbourne, Australia. Google Scholar - Zhang, M. (2006). Combining genetic algorithms and topological sort to optimize open-pit mine plans. In M. Cardu, R. Ciccu, E. Lovera, & E. Michelotti (Eds.),
*15th mine planning and equipment selection*(pp. 1234–1239). Torino: FIORDO S.r.l. Google Scholar - Zuckerberg, M. (2011). Personal communication. Google Scholar