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.
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.
Rahmanpour, M., Osanloo, M., & Mirabedi, S. M. M. (2022). Estimation of mining time-span to improve the solution time in long-term production planning. International Journal of Mining and Geo-Engineering, 56(2), 159-165. doi: 10.22059/ijmge.2021.313699.594876
MLA
Mehdi Rahmanpour; Morteza Osanloo; S. M. Mahdi Mirabedi. "Estimation of mining time-span to improve the solution time in long-term production planning", International Journal of Mining and Geo-Engineering, 56, 2, 2022, 159-165. doi: 10.22059/ijmge.2021.313699.594876
HARVARD
Rahmanpour, M., Osanloo, M., Mirabedi, S. M. M. (2022). 'Estimation of mining time-span to improve the solution time in long-term production planning', International Journal of Mining and Geo-Engineering, 56(2), pp. 159-165. doi: 10.22059/ijmge.2021.313699.594876
VANCOUVER
Rahmanpour, M., Osanloo, M., Mirabedi, S. M. M. Estimation of mining time-span to improve the solution time in long-term production planning. International Journal of Mining and Geo-Engineering, 2022; 56(2): 159-165. doi: 10.22059/ijmge.2021.313699.594876