Estimation of mining time-span to improve the solution time in long-term production planning

Document Type : Research Paper

Authors

1 School of Mining Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran

2 Department of Mining Engineering, Amirkabir University of Technology, Tehran, Iran

Abstract

Long-term production planning in open-pit mines is a precedence-constraint knapsack problem. A spatial representation of the mining region (called the block-model) is the primary input of mine planning models. One should note that as the number of blocks and periods to be planned increases, the number of decision variables increases. This paper presents a fast yet straightforward algorithm to reduce binary variables in open-pit mine production planning models. The algorithm considers mining capacity, processing capacity, and pit deepening rate to estimate the time span within which a block is mineable. This paper applies the algorithm in 12 different cases. The number of blocks varies from 1000 to 240000, and the mining periods range from 6 to 30 years. According to the results, this algorithm is helpful for problem size reduction.

Keywords


  • Goodwin, G. C., Seron, M. M., and Mayne, D. Q., (2008), Optimization opportunities in mining, metal and mineral processing, Annual Reviews in Control, 32, 17-32, doi:10.1016/j.arcontrol.2008.02.002
  • Osanloo, M., Gholamnejad, J., and 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, doi:10.1080/17480930601118947
  • Newman, A. M., Rubio, E., Caro, R., Weintraub, A., and Eurek, K., (2010), A review of operations research in mine planning, Interfaces, 40(3), 222-245, doi:10.1287/inte.1090.0492
  • Dagdelen, K., (2007), Open pit optimization — strategies for improving economics of mining projects through mine planning, in Dimitrakopoulos, R., (Ed.), Orebody modelling and stochastic mine planning, 2nd Ed., Spectrum Series No 14, AusIMM, 145-148
  • Rahmanpour, M., Osanloo, M., (2016), Determination of value at risk for long-term production planning in open pit mines in the presence of price uncertainty, Journal of the Southern African Institute of Mining and Metallurgy, 116(03), 229-236
  • Caccetta, L., Hill, S. P., (2003), An application of branch and cut to open pit mine scheduling, J. Global Optimization, 27, 349–365, doi:10.1023/A:1024835022186
  • Albach, H., (1976), Long range planning in open pit mining, Management science, 13(10), B549-B568
  • Gangwar, A., (1982), Using geostatistical ore block variance in production planning by integer programming, 17th APCOM, New York: SME, 443-460
  • Tolwinski, B., and Underwood, R., (1996), A scheduling algorithm for open pit mines, Journal of Mathematics Applied in Business & Industry, 247-270, doi:10.1093/imaman/7.3.247
  • Kumral, M., (2003), Application of chance-constrained programming based on multi-objective simulated annealing to solve a mineral blending problem, Engineering Optimization, 35(6), 661-673, doi:10.1080/03052150310001614837
  • Gholamnejad, J., Osanloo, M., and Karimi, B., (2006), A chance-constrained programming approach for open pit long-term production scheduling in stochastic environments, The Journal of The Southern African Institute of Mining and Metallurgy, Vol. 106 (Feb. issue), 105-114, ISSN 0038–223X/3.00 +0.00.
  • Boland, N., Dumitrescu, I., and Froyland, G., (2008), A multistage stochastic programming approach to open pit mine production scheduling with uncertain geology, Optimization, online, 33 pages, available at: http://www.optimization-online.org/DB_FILE/2008/10/ 2123.pdf
  • Dimitrakopoulos, R., and Ramazan, S., (2008), Stochastic integer programming for optimizing long term production schedules of open pit mines, methods, application and value of stochastic solutions, Mining Technology, 117(4), 155-160, doi:http://dx.doi.org/10.1179/174328609X417279
  • Bley, A., Boland, N., Fricke, C., and Froyland, G., (2010), A strengthened formulation and cutting planes for the open pit mine production scheduling problem, Computers and Operation Research, 37(9), 1641-1647, doi:http://dx.doi.org/10.1016/j.cor.2009.12.008
  • Kumral, M., (2010), Robust stochastic mine production scheduling, Engineering Optimization, 42(6), 567-579, doi:10.1080/03052150903353336
  • Liu SQ, Kozan E (2016), New graph-based algorithms to efficiently solve large scale open pit mining optimisation problems. Expert Systems Appl. 43(1):59–65
  • Muñoz G,  Espinoza  D,  Goycoolea  M,  Moreno  E,  Queyranne  M, Rivera O (2018), A study of the Bienstock-Zuckerberg algorithm, Applications  in  mining  and  resource  constrained  project scheduling. Comput. Optim. Appl. 69(2):501–534
  • Vossen TWM, Wood KRK, Newman AM (2016), Hierarchical benders decomposition for open-pit mine block sequencing. Oper. Res. 64(4):771–793
  • Journel, A., and Kyriakidis, P.C., (2004), Evaluation of mineral reserves: a simulation approach, Oxford University Press, 215 pages
  • Rojas, C.R., Goodwin, G.C., Seron, M.M., and Zhang, M., (2007), Open-cut mine planning via closed-loop receding-horizon optimal control, in Ricardo S., and Joseba, Q., (eds.), Identification and Control, Springer, 43- 60, doi:10.1007/978-1-84628-899-9_2
  • Noble, A. C., (2011), Mineral Resource Estimation, in Darling, P. (Editor), SME mining engineering handbook, 3rd edition, CHAPTER 4.5, 203-217, Society for Mining, Metallurgy, and Exploration Inc. (SME)
  • Caccetta, L., and Giannini, L. M., (1985), On bounding techniques for the optimum pit limit problem, The AusIMM Bulletin, 290(4): 87-89
  • Picard, J. C., Smith, B. T., (2004), Parametric maximum flows and the calculation of optimal intermediate contours in open pit mine design, INFOR, 42(2), 143-153, ISSN 0315-5986
  • Askari-nasab, H., Awuah-Offei, K., (2009), Open pit optimization using discounted economic block values, Mining Technology, 118 (1), 1-12, http://dx.doi.org/10.1179/037178409X12450752943243
  • Osanloo, M., Rahmanpour, M., Sadri, A., (2010), Ultimate pit limit of iron ore mines using maximum, proceeding of MPES 2010, Fremantle, AusIMM, pp. 81-87
  • Ramazan, S., Dagdelen, K., Johnson, T. B., (2005), Fundamental tree algorithm in optimizing production scheduling for open pit mine design, Mining Technology, 114(March), pp. 45-54, http://dx.doi.org/10.1179/037178405X44511
  • Boland, N., Dumitrescu, I., Froyland, G., Gleixner, A. M., (2009), LP-based disaggregation approaches to solving the open pit mining production scheduling problem with block processing selectivity, Computers & Operations Research, 36, pp. 1064 - 1089, doi:10.1016/j.cor.2007.12.006
  • Askari-nasab, H., Tabesh, M., Badiozamani, M. M., Eivazy, H., (2010), Hierarchical clustering algorithm for block aggregation in open pit mines, MPES, pp. 469-479
  • Jelvez, E., Morales, N., Nancel-Penard, P., Peypouquetd, J., Reyes, P., (2016), Aggregation heuristic for the open-pit block scheduling problem, European Journal of Operational Research, 249, 1169–1177
  • Elkington, T., Durham, R., (2011), Integrated open pit pushback selection and production capacity optimization, Journal of Mining Science, 47(2), pp. 177-190, doi:1134/S1062739147020055
  • Whittle, J., (2011), Long-Term Scheduling, In E. Y. Baafi, R. J. Kininmonth, I. Porter (Eds.), 35th APCOM, Wollongong: AusIMM, 75-80
  • Letelier, O.R., Espinoza, D., Goycoolea, M., Moreno, E., Muñoz, G., (2020), Production scheduling for strategic open pit mine planning: a mixed-integer programming approach, Operations Research, INFORMS, DOI: 10.1287/opre.2019.1965
  • Lotfian, R., Gholamnejad, J., and Mirzaeian, Y.L., (2020), Effective solution of the long-term open pit production planning problem using block clustering, Engineering Optimization, DOI: 10.1080/0305215X.2020.1771703
  • Goodwin, G.C., Seron, M.M., Middleton, R.H., Mayne, D.Q., (2006), Receding horizon control applied to optimal mine planning, Automatica, vol. 42, pp. 1337 – 1342, doi:10.1016/j.automatica.2006.01.016
  • Topal, E., (2008), Early start and late start algorithms to improve the solution time for long-term underground mine production scheduling, The Journal of the Southern African Institute of Mining and Metallurgy, 108(February), 99-107
  • Gaupp, M P., (2008), Methods for improving the tractability of the block sequencing problem for open pit mining, Ph.D. thesis, Colorado School of Mines, Golden, CO, 159 pages
  • Chicoisne, R., Espinoza, D., Goycoolea, M., Moreno, E., and Rubio, E., (2012), A new algorithm for the open-pit mine scheduling problem, Operations Research, 60(3), 517–528, doi: http://dx.doi.org/10.1287/opre.1120.1050
  • Caccetta, L., and Giannini, L. M., (1988), The generation of minimum search pattern in the optimum design of open pit mines, The AusIMM Bulletin, 293(5):57-61
  • Espinoza, D., Goycoolea, M., Moreno, E., Newman, A., (2012), MinLib: a library of open pit mining problems, Ann Oper Res, 22 pages, doi: 10.1007/s10479-012-1258-3.