519
Views
21
CrossRef citations to date
0
Altmetric
Original Articles

Production scheduling under uncertainty of an open-pit mine using Lagrangian relaxation and branch-and-cut algorithm

ORCID Icon & ORCID Icon
Pages 343-361 | Received 06 Jun 2018, Accepted 10 Jun 2019, Published online: 01 Jul 2019

References

  • K. Dagdelen and T.B. Johnson, Optimum open pit mine production scheduling by Lagrangian parameterization, in Proceedings of 19th International APCOM Symposium, R. V. Ramani, ed., Littleton, CO, 1986, pp. 127–142.
  • W.A. Hustrulid, M. Kuchta, and R.K. Martin, Open Pit Mine Planning and Design, 3rd ed., CRC Press, Boca Raton, FL, 2013.
  • A. Kumar and S. Chatterjee, Open-pit coal mine production sequencing incorporating grade blending and stockpiling options: An application from an Indian mine, Eng. Optimiz. 49 (2017). doi:10.1080/0305215X.2016.1210312
  • S. Ramazan and R. Dimitrakopoulos, Traditional and new MIP models for production scheduling with in-situ grade variability, Int. J. Surface Min. Reclam. Environ. 18 (2004), pp. 85–98. doi:10.1080/13895260412331295367.
  • S. Chatterjee, M. Sethi, and M.W.A. Asad, Production phase and ultimate pit limit design under commodity price uncertainty, Eur. J. Oper. Res. 248 (2016), pp. 658–667. doi:10.1016/j.ejor.2015.07.012.
  • T.B. Johnson, Optimum production scheduling, in Proceedings of the 8th International Symposium on Computers and Operations Research in the Minerals Industry, Society of Mining Engineers of AIME, Salt Lake City, 1969, pp. 539–562.
  • M.E. Gershon, Mine scheduling optimization with mixed integer programming, Min. Eng. 35 (1983), pp. 314–329.
  • L. Caccetta and S.P. Hill, An application of branch and cut to open pit mine scheduling, J. Glob. Optimiz. 27 (2003), pp. 349–365. doi:10.1023/A:1024835022186.
  • S. Ramazan, The new fundamental tree algorithm for production scheduling of open pit mines, Eur. J. Oper. Res. 177 (2007), pp. 1153–1161. doi:10.1016/j.ejor.2005.12.035.
  • A. Bley, N. Boland, C. Fricke, and G. Froyland, A strengthened formulation and cutting planes for the open pit mine production scheduling problem, Comput. Oper. Res. 37 (2010), pp. 1641–1647. doi:10.1016/j.cor.2009.12.008.
  • D. Bienstock and M. Zuckerberg, Solving LP relaxations of large-scale precedence constrained problems, in Integer Programming and Combinatorial Optimization. IPCO 2010. Lecture Notes in Computer Science, F. Eisenbrand, F. B. Shepherd, eds., Vol. 6080, Springer, Berlin, Heidelberg, 2010, pp. 1–14.
  • E. Topal and S. Ramazan, Strategic mine planning model using network flow model and real case application, Int. J. Min. Reclam. Environ. 26 (2012), pp. 29–37. doi:10.1080/17480930.2011.600827.
  • R. Chicoisne, D. Espinoza, M. Goycoolea, E. Moreno, and E. Rubio, A new algorithm for the open-pit mine production scheduling problem, Oper. Res. 60 (2012), pp. 517–528. doi:10.1287/opre.1120.1050.
  • C. Cullenbine, R.K. Wood, and A. Newman, A sliding time window heuristic for open pit mine block sequencing, Optimiz. Lett. 5 (2011), pp. 365–377. doi:10.1007/s11590-011-0306-2.
  • R. Dimitrakopoulos and S. Ramazan, Stochastic integer programming for optimising long-term production schedules of open pit mines: Methods, application and value of stochastic solutions, Min. Technol. 117 (2008), pp. 155–160. doi:10.1179/174328609X417279.
  • W.B. Lambert and A. Newman, Tailored Lagrangian Relaxation for the open pit block sequencing problem, Ann. Oper. Res 222 (2014), pp. 419–438. doi:10.1007/s10479-012-1287-y.
  • A. Lamghari and R. Dimitrakopoulos, A diversified Tabu search approach for the open-pit mine production scheduling problem with metal uncertainty, Eur. J. Oper. Res. 222 (2012), pp. 642–652. doi:10.1016/j.ejor.2012.05.029.
  • Y. Li, E. Topal, and D. Williams, Waste rock dumping optimisation using mixed integer programming (MIP), Int. J. Min. Reclam. Environ. 27 (2013), pp. 425–436. doi:10.1080/17480930.2013.794513.
  • P.A. Dowd, Risk assessment in reserve estimation and open-pit planning, Trans. Inst. Min. Metall. 103 (1994), pp. A148–A154.
  • B. Tachefine and F. Soumis, Maximal closure on a graph with resource constraints, Comput. Oper. Res. 24 (1997), pp. 981–990. doi:10.1016/S0305-0548(97)00008-7.
  • P.J. Ravenscroft, Risk analysis for mine scheduling by conditional simulation, Trans. Inst. Min. Metall. Sec. A Min. Ind. 101 (1992), pp. A104–A108.
  • J. Whittle, Beyond optimization in open pit design, Proceedings of the Canadian Conference on Computer Applications in the Mineral Industries, Rotterdam, the Netherlands, 1988, pp. 331–337.
  • J. Whittle, A decade of open pit mine planning and optimisation - the craft of turning algorithms into packages, Proceedings of the 28th International Symposium on Application of Computers and Operations Research in the Mineral Industry (APCOM) (1999), Golden, CO, pp. 15–24.
  • R. Dimitrakopoulos, C.T. Farrelly, and M. Godoy, Moving forward from traditional optimization: Grade uncertainty and risk effects in open pit design, Trans. Inst. Min. Metall. Min. Technol. 111 (2002), pp. A82–A88.
  • M. Godoy and R. Dimitrakopoulos, Managing risk and waste mining in long-term production scheduling, Trans. Soc. Min. Eng. AIME 316 (2004), pp. 43–50.
  • R. Goodfellow and R. Dimitrakopoulos, Algorithmic integration of geological uncertainty in pushback designs for complex multi-process open pit mines, Min. Technol. 122 (2013), pp. 67–77. doi:10.1179/147490013X13639459465736.
  • R. Goodfellow and R. Dimitrakopoulos, Simultaneous stochastic optimization of mining complexes and mineral value chains, Math. Geosci. 49 (2017), pp. 341–360. doi:10.1007/s11004-017-9680-3.
  • A. Boucher and R. Dimitrakopoulos, Block simulation of multiple correlated variables, Math. Geosci. 41 (2008), pp. 215–237. doi:10.1007/s11004-008-9178-0.
  • P. Goovaert, Geostatistics for Natural Resources Evaluation (Applied Geostatistics Series), Oxford University Press, Oxford, 1997.
  • H. Mustapha and R. Dimitrakopoulos, High-order stochastic simulation of complex spatially distributed natural phenomena, Math. Geosci. 42 (2010), pp. 457–485. doi:10.1007/s11004-010-9291-8.
  • I. Minniakhmetov, R. Dimitrakopoulos, and M. Godoy, High-order spatial simulation using Legendre-like orthogonal splines, Math. Geosci. 50 (2018), pp. 753–780. doi:10.1007/s11004-018-9741-2
  • S. Ramazan and R. Dimitrakopoulos, Stochastic optimization of long term production scheduling for open pit mines with a new integer programming formulation, in Orebody Modelling and Strategic Mine Planning, the AusIMM, Spectrum Series, R. Dimitrakopoulos, ed., Vol. 14, 2005, pp. 353–360.
  • N. Boland, I. Dumitrescu, and G. Froyland, A multistage stochastic programming approach to open pit mine production scheduling with uncertain geology, Optimization (2008), 1–33. Available at http://www.optimization-online.org/DB_FILE/2008/10/2123.pdf
  • A. Leite and R. Dimitrakopoulos, A stochastic optimization model for open pit mine planning: Application and risk analysis at a copper deposit, Min. Technol. 116 (2007), pp. 109–118. doi:10.1179/174328607X228848.
  • F.C. Albor and R. Dimitrakopoulos, Stochastic mine design optimization based on simulated annealing: Pit limits, production schedules, multiple orebody scenarios and sensitivity analysis, Min. Technol. 118 (2009), pp. 79–90. doi:10.1179/037178409X12541250836860.
  • H. Lerchs and I.F. Grossmann, Optimum design of open pit mines, Trans. CIM 58 (1965), pp. 17–24.
  • S. Ramazan and R. Dimitrakopoulos, Production scheduling with uncertain supply: A new solution to the open pit mining problem, Optimiz. Eng. 14 (2013), pp. 361–380. doi:10.1007/s11081-012-9186-2.
  • L. Montiel and R. Dimitrakopoulos, Optimizing mining complexes with multiple processing and transportation alternatives: An uncertainty-based approach, Eur. J. Oper. Res. 247 (2015), pp. 166–178. doi:10.1016/j.ejor.2015.05.002.
  • A. Rimélé, R. Dimitrakopoulos, and M. Gamache, A stochastic optimization method with in-pit waste and tailings disposal for open pit life-of-mine production planning, Resou. Policy (2018). doi:10.1016/J.RESOURPOL.2018.02.006.
  • J.C. Picard, Maximal closure of a graph and applications to combinatorial problems, Manage. Sci. 22 (1976), pp. 1268–1272. doi:10.1287/mnsc.22.11.1268.
  • C. Meagher, S.A. Abdel Sabour, and R. Dimitrakopoulos, Pushback design of open pit mines under geological and market uncertainties, Adv. Orebody Model. Strategic Mine Plann. AusIMM Spectr. Ser. 17 (2010), pp. 291–299.
  • M.W.A. Asad and R. Dimitrakopoulos, Implementing a parametric maximum flow algorithm for optimal open pit mine design under uncertain supply and demand, J. Oper. Res. Soc. 64 (2013), pp. 185–197. doi:10.1057/jors.2012.26.
  • H. Kellerer, U. Pferschy, and D. Pisinger, Knapsack Problems, Springer, Berlin, 2004.
  • A. Goldberg, A new Max-Flow algorithm, Technical report MIT/LCS/TM-291, Laboratory of Computer Science, MIT, USA (1985)
  • I.B.M. ILOG, CPLEX User’s Manual, Version 12 Release 6, International Business Machines Corporation, 2014. Available at https://www.ibm.com/support/knowledgecenter/SSSA5P_12.6.2/ilog.odms.studio.help/pdf/usrcplex.pdf
  • M. Godoy, The effective management of geological risk, Ph.D thesis, University of Queensland, Australia (2003).
  • A. Boucher and R. Dimitrakopoulos, Multivariate block-support simulation of the Yandi iron ore deposit, Western Australia, Math. Geosci. 44 (2012), pp. 449–468. doi:10.1007/s11004-012-9402-9.
  • M.N. Vallejo Garcia and R. Dimitrakopoulos, Stochastic orebody modelling and stochastic long-term production scheduling at the KéMag iron ore deposit, Quebec, Int. J. Min. Reclam. Environ. (2018). doi:10.1080/17480930.2018.1435969.
  • L. Montiel and R. Dimitrakopoulos, A heuristic approach for the stochastic optimization of mine production schedules, J. Heuristics 23 (2017), pp. 397–415. doi:10.1007/s10732-017-9349-6.
  • A.V. Goldberg and R.E. Tarjan, A new approach to the maximum flow problem, J. Assoc. Comput. Mach. 35 (1988), pp. 921–940. doi:10.1145/48014.61051.
  • R. Dimitrakopoulos, L. Martinez, and S. Ramazan, A maximum upside/minimum downside approach to the traditional optimization of open pit mine design, J. Min. Sci. 43 (2007), pp. 73–82. doi:10.1007/s10913-007-0009-3.
  • J. Benndorf and R. Dimitrakopoulos, Stochastic long-term production scheduling of iron ore deposits: Integrating joint multi-element geological uncertainty, J. Min. Sci. 49 (2013), pp. 68–81. doi:10.1134/S1062739149010097.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.