Journal of Central South University

, Volume 25, Issue 6, pp 1475–1488 | Cite as

Optimized algorithm in mine production planning, mined material destination, and ultimate pit limit

  • Rahimi EsmaeilEmail author
  • Moosavi Ehsan
  • Shirinabadi Reza
  • Gholinejad Mehran


An integral connection exists among the mine production planning, the mined material destination, and the ultimate pit limit (UPL) in the mining engineering economy. This relation is reinforced by real information and the benefits it engenders in the mining economy. Hence, it is important to create optimizing algorithms to reduce the errors of economic calculations. In this work, a logical mathematical algorithm that considers the important designing parameters and the mining economy is proposed. This algorithm creates an optimizing repetitive process among different designing constituents and directs them into the maximum amount of the mine economical parameters. This process will produce the highest amount of ores and the highest degree of safety. The modeling produces a new relation between the concept of the cutoff grade, mine designing, and mine planning, and it provides the maximum benefit by calculating the destination of the ores. The proposed algorithm is evaluated in a real case study. The results show that the net present value of the mine production is increased by 3% compared to previous methods of production design and UPL.

Key words

mined material destination ultimate pit limit net present value production planning 



在采矿工程经济中,矿山生产计划、开采材料目的地和最终开采极限(UPL)之间存在着整体 的联系,而实际信息及其在采矿经济中产生的效应会加强这种联系,因此,建立优化算法来减少经济 计算的误差是非常重要的。本文提出一种考虑重要设计参数和经济性的逻辑数学算法,该算法在不同 的设计成分之间建立了一个优化的重复过程,并使其将矿山经济参数最大化,产生最大的矿石量和最 高的安全度。该模型在截止品位、矿井设计和矿山规划之间建立了新的关系,并通过计算目标提供了 最大的效益。结果表明:与以往的生产设计和生产方法相比,矿山生产的净现值提高了3%。


开采材料目的地 最终坑限 净现值 生产计划 


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The authors are grateful to Golgohar Company for providing related information. We are also grateful to Mrs. Azarme for her assistance in editing this paper.


  1. [1]
    LANE K F. Choosing the optimum cut-off grade [J]. Quarterly of the Colorado School of Mines, 1964, 59: 811–829.Google Scholar
  2. [2]
    LANE K F. Cut-off grades for two minerals [C]//Proceedings of the 18th International Symposium on the Application of Computers and Operations Research in the Minerals Industries (APCOM1984). London, 1984: 485–492.Google Scholar
  3. [3]
    LANE K F. The economic definition of ore: Cut-off grades in theory and practice [M]//Mining Journal Books (ISBN: 0 900117 45 1). London, UK, 1988.Google Scholar
  4. [4]
    SHINKUMA T, NISHIYAMA T. The grade selection rule of the metal mines: An empirical study on copper mines [J]. Resources Policy, 2000, 26: 31–38.CrossRefGoogle Scholar
  5. [5]
    CAIRNS R D, SHINKUMA T. The choice of cutoff grade in mining [J]. Resource Policy, 2003, 29: 75–81.CrossRefGoogle Scholar
  6. [6]
    ATAEI M, OSANLOO M. Determination of optimum cut-off grades of multiple metal deposits by using the golden section search method [J]. Journal of the Southern African Institute of Mining and Metallurgy, 2003, 103(8): 493–499.Google Scholar
  7. [7]
    ATAEI M, OSANLOO M. Methods for calculation of optimal cut-off grades in complex ore deposits [J]. Journal of Mining Science, 2003, 39(5): 499–507.CrossRefGoogle Scholar
  8. [8]
    ATAEI M, OSANLOO M. Using a combination of genetic algorithm and the grid search method to determine optimum cut-off grades of multiple metal deposits [J]. International Journal of Surface Mining, Reclamation and Environment, 2004, 18(1): 60–78.CrossRefGoogle Scholar
  9. [9]
    RASHIDINEJAD F, OSANLOO M, REZAI B. Cut off grades optimization with environmental management: A case study: Sungun copper project, IUST [J]. Int J Eng Sci, 2008, 19: 1–13.Google Scholar
  10. [10]
    RASHIDINEJAD F, OSANLOO M, REZAI B. An environmental oriented model for optimum cut-off grades in open pit mining projects to minimize acid mine drainage [J]. Int J Environ Sci Tech, 2008, 5(2): 183–194.CrossRefGoogle Scholar
  11. [11]
    RENDU J M. An introduction to cutoff grade estimation [M]. Littleton: The Society for Mining, Metallurgy and Exploration Inc, 2008.Google Scholar
  12. [12]
    RENDU J M. Cut-off grade estimation–old principles revisited–Application to optimisation of net present value and internal rate of return, orebody modelling and strategic mine planning [M]. Perth, 2009: 165–169.Google Scholar
  13. [13]
    GHOLAMNEJAD J. Determination of the optimum cut-off grade considering environmental cost [J]. Journal of International Environmental Application and Science, 2008, 3(3): 186–194.Google Scholar
  14. [14]
    GHOLAMNEJAD J. Incorporation of rehabilitation cost into the optimum cut-off grade determination [J]. Journal of the Southern African Institute of Mining and Metallurgy, 2009, 108(2): 89–94.Google Scholar
  15. [15]
    NEWMAN A, RUBIO N, CARO R, WEINTRAUB A, EUREK K. A review of operation research in mine planning [J]. Interface, 2010, 40(3): 222–245.CrossRefGoogle Scholar
  16. [16]
    GANGULI R, DAGDELEN K, GRYGIEL E. Mine scheduling and cut-off grade optimization using mixed integer linear programming. Chapter 9.10: Systems Engineering [M]//SME Mining Engineering Handbook (ISBN: 978–0-87335-264-2). 3rd Edition. 2011: 850–852.Google Scholar
  17. [17]
    ABDEL S S A, DIMITRAKOPOULOS R. Incorporating geological and market uncertainties and operational flexibility into open pit mine design [J]. J Min Sci, 2011, 47(2): 191–201. DOI: 10.1134/S1062739147020067.CrossRefGoogle Scholar
  18. [18]
    DIMITRAKOPOULOS R. Stochastic optimization for strategic mine planning: A decade of developments [J]. Journal of Mining Science, 2011, 47(2): 138–150.CrossRefGoogle Scholar
  19. [19]
    JOHNSON P V, EVATT G W, DUCK P W, HOWELL S D. The determination of a dynamic cut-off grade for the mining industry [C]//Electrical Engineering and Applied Computing, Lecture Notes in Electrical Engineering 90, Chapter 32, 2011: 391–403.Google Scholar
  20. [20]
    AZIMI Y, OSANLOO M. Determination of open pit mining cut-off grade strategy using combination of nonlinear programming and genetic algorithm [J]. Archives of Mining Sciences, 2011, 56(2): 189–212.Google Scholar
  21. [21]
    AZIMI Y, OSANLOO M, ESFAHANIPOUR A. Selection of the open pit mining cut-off grade strategy under price uncertainty using a risk based multi-criteria ranking system [J]. Archives of Mining Sciences, 2012, 57(3): 741–768.CrossRefGoogle Scholar
  22. [22]
    ABDOLLAHISHARIF J, BAKHTAVAR E, ANEMANGELY M. Optimal cut-off grade determination based on variable capacities in open-pit mining [J]. Journal of the Southern African Institute of Mining and Metallurgy, 2012, 112(12): 1065–1069.Google Scholar
  23. [23]
    ASAD M W A, DIMITRAKOPOULOS R. A heuristic approach to stochastic cut-off grade optimization for open pit mining complexes with multiple processing streams [J]. Resources Policy, 2013, 38: 591–597.CrossRefGoogle Scholar
  24. [24]
    AZIMI Y, OSANLOO M, ESFAHANIPOUR A. An uncertainty based multi-criteria ranking system for open pit mining cut-off grade strategy selection [J]. Resources Policy, 2013, 38: 212–223.CrossRefGoogle Scholar
  25. [25]
    NIETO A, ZHANG K Y. Cut-off grade economic strategy for by-product mineral commodity operation: Rare earth case study [J]. Transactions of the Institution of Mining and Metallurgy: Mining Technology, 2013, 122(3): 166–171.Google Scholar
  26. [26]
    THOMPSON M, BARR D. Cut-off grade: A real options analysis [J]. Resources Policy, 2014, 42: 83–92.CrossRefGoogle Scholar
  27. [27]
    YASREBI A B, WETHERELT A, FOSTER P. Determination of optimized cut-off grade utilizing non-linear programming Arab J Geosci, 2015, 8(10): 8963–8967. DOI: 10.1007/s12517-014-1756-5.Google Scholar
  28. [28]
    RAHIMI E, ORAEE K, SHAFAHI T.Z, GHASEMZADEH H. Considering environmental costs of copper production in cut-off grades optimization [J]. Arab J Geosci, 2014, 8(9): 1–15. DOI: 10.1007/s12517-014-1646-x.Google Scholar
  29. [29]
    RAHIMI E, ORAEE K, SHAFAHI Z, GHASEMZADEH H. Determining the optimum cut-off grades in sulphide copper deposits [J]. Archives of Mining Sciences, 2015, 60(1): 313–328. DOI: 10.1515/amsc-2015-0021.CrossRefGoogle Scholar
  30. [30]
    RAHIMI E, AKBARI A. Application of KKT in determining the final destination of mined material in multi-processing mines [J]. Resources Policy, 2016, 50: 10–18. DOI: org/10.1016/j.resourpol.2016.08.003.CrossRefGoogle Scholar
  31. [31]
    AKBARI A, RAHIMI E. The effect of copper slag recovery on hydrometallurgical cut-off grades considering environmental aspects [J]. Journal of Central SouthUniversity, 2016, 23(4): 798–807. DOI: 10.1007/s11771-016-3126-9.CrossRefGoogle Scholar
  32. [32]
    GOODFELLOW R, DIMITRAKOPOULOS R. Global optimization of open pit mining complexes with uncertainty [J]. Applied Soft Computing, 2016, 40: 292–304.CrossRefGoogle Scholar
  33. [33]
    JOHNSON T B. Optimum open pit mine production scheduling [D]. Berkeley: Operations Research Department, University of California, 1968; 539–562.CrossRefGoogle Scholar
  34. [34]
    JOHNSON T B. Optimum production scheduling [C]//Processing of the 8th International Symposium on Computers and Operations Research. 1969: 539–562.Google Scholar
  35. [35]
    DAGDELEN K. Optimum multi-period open pit mine production scheduling [D]. Colorado: Colorado School of Mines, Golden, 1985.Google Scholar
  36. [36]
    DAGDELEN K, JOHNSON T B. Optimum open pit mine production scheduling by Lagrangian parameterization [C]//19th International Symposium on the Application of Computers and Operations Research in the Mineral Industry (APCOM) Ch, 1986, 13: 127–142.Google Scholar
  37. [37]
    KAWAHATA K. A new algorithm to solve large scale mine production scheduling problems by using the Lagrangian relaxation method [D]. Colorado School of Mines, 2007.Google Scholar
  38. [38]
    BOLAND N, DUMITRESCU I, FROYLAND G, GLEIXNER A M. LP-based disaggregation approaches to solving the open pit mining production scheduling problem with block processing selectivity [J]. Computer Operation Research, 2009, 36(4): 1064–1089.CrossRefzbMATHGoogle Scholar
  39. [39]
    MOOSAVI E, GHOLAMNEJAD J, ATAEE-POUR M, KHORRAM E. Optimal extraction sequence modelling for open pit operation considering dynamic cut-off grade [J]. Mineral Resources Management, 2014, 30(2): 173–186.Google Scholar
  40. [40]
    MOOSAVI E, GHOLAMNEJAD J. Long-term production scheduling modeling for the open pit mines considering tonnage uncertainty via indicator kriging [J]. Journal of Mining Science, 2015, 51(6): 1226–1234.CrossRefGoogle Scholar
  41. [41]
    AKAIKE A, DAGDELEN K. A strategic production scheduling method for an open pit mine [C]//Proceedings of the 28th Application of Computers and Operation Research in the Mineral Industry. 1999: 729–738.Google Scholar
  42. [42]
    MOGI G, ADACHI T, AKAIKE A, YAMATOMI J. Optimum production scale and scheduling of open pit mines using revised 4D network relaxation method [C]//Proceedings of the 17th International Symposium on Mine Planning and Equipment Selection. 2001: 337–344.Google Scholar
  43. [43]
    KUMRAL M, DOWD P A. Short-term mine production scheduling for industrial minerals using multi-objective simulated annealing [C]//2002-International Symposium on the Application of Computers and Operations Research in the Minerals Industry. Littleton, Colorado, 2002: 731–741.Google Scholar
  44. [44]
    KUMRAL M, DOWD P A. Simulated annealing approach to mine production scheduling [J]. Journal of the Operational Research Society, 2005, 56: 922–930.CrossRefzbMATHGoogle Scholar
  45. [45]
    GODOY M C, DIMITRAKOPOULOS R. Managing risk and waste mining in long-term production scheduling [J]. Trans of SME, 2004, 316: 43–50.Google Scholar
  46. [46]
    CONSUEGRA F R A, DIMITRAKOPOULOS R. Stochastic mine design optimization based on simulated annealing: Pit limits, production schedules, multiple orebody scenarios and sensitivity analysis [J]. Transactions of the Institution of Mining and Metallurgy, Section A: Mining Technology, 2009, 118(2): 79–90.Google Scholar
  47. [47]
    SHISHVAN M S, SATTARVAND J. Long term production planning of open pit mines by ant colony optimization [J]. European Journal of Operational Research, 2015, 24(3): 825–836.CrossRefzbMATHGoogle Scholar
  48. [48]
    KHAN A, NIEMANN-DELIUS C. Production scheduling of open pit mines using particle swarm optimization algorithm [J]. Advances in Operations Research, 2014, Article ID 208502. DOI: Google Scholar
  49. [49]
    LAMGHARI A, DIMITRAKOPOULOS R. A diversified Tabu search approach for the open-pit mine production scheduling problem with metal uncertainty [J]. European Journal of Operational Research, 2012, 222(3): 642–652.CrossRefzbMATHGoogle Scholar
  50. [50]
    RAHIMI E, GHASEMZADEH H. A new algorithm to determine optimum cut-off grades considering technical, economical, environmental and social aspects [J]. Resources Policy, 2015, 46: 51–63.CrossRefGoogle Scholar
  51. [51]
    RAMAZAN S. The new fundamental tree algorithm for production scheduling of open pit mines [J]. European Journal of Operational Research, 2007, 177(2): 1153–1166.CrossRefzbMATHGoogle Scholar
  52. [52]
    WANG Q, GU X, CHU D. A dynamic optimization method for determining cutoff grades in underground mines [J]. Mineral Resources Management, 2008, 3(2): 133–142.Google Scholar
  53. [53]
    LERCH S, GROSSMANN L. Optimum design of open-pit mines [J]. CIM Bulletin, 1965, 58: 47–54.Google Scholar
  54. [54]
    LERCH S, GROSSMANN L. Optimum design of open pit mines [J]. CIM Transaction, 1965, 68: 17–24.Google Scholar
  55. [55]
    ZHAO Y, KIM Y C. A new ultimate pit limit design algorithm [C]//23rd APCOM. 1992: 423–434.Google Scholar
  56. [56]
    YAMATOMI J, MOGI G, AKAIKE A, YAMAGUCHI U. Selective extraction dynamic cone algorithm for three dimensional open pit designs [C]//25th APCOM. 1995: 267–274.Google Scholar
  57. [57]
    GERSHON M E. A linear programming approach to mine scheduling optimization [C]//17th APCOM. 1982: 483–493.Google Scholar
  58. [58]
    HUTTAGOSOL P, CAMERON R E. A computer design of ultimate pit limit by using transportation algorithm [C]//23rd APCOM. 1992: 443–460.Google Scholar
  59. [59]
    TOLWINSKI B, UNDERWOOD R. An algorithm to estimate the optimal evolution of an open pit mine [C]//23rd APCOM. 1992: 399–409.Google Scholar
  60. [60]
    WANG Q, SEVIM H. Enhance production planning in open pit mining through intelligent dynamic search [C]//23rd APCOM. 1992: 461–471.Google Scholar

Copyright information

© Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mining Engineering, Islamic Azad UniversitySouth Tehran BranchTehranIran

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