A non-monetary valuation system for open-pit mine design

Document Type : Research Paper


1 Department of Mining Eng, Geophysics and Petroleum, Shahrood University of Technology

2 shahrood

3 third author


In open-pit mining, different designs are created, such as optimal ultimate pit limit and production planning. In order to determine the ultimate pit limit, two approaches are generally used based on geological and economic block models. In this paper, according to the long-term trend of metals price and mining costs, some suggestions were made to design the ultimate pit limit using the geological block model. In addition, a grade-based objective function was presented for determining the ultimate pit limit. Then, in order to solve the problem, a heuristic algorithm was developed to simultaneously determine the ultimate pit limit and the sequence of block mining. For a 2D geological block model, the final pit was generated using the proposed algorithm. Furthermore, to validate the generated pit limit, the results of a 3D geological block model were compared with those of the Lerchs-Grossman algorithm. The comparison showed that the two pits corresponded to each other with an accuracy value of 97.7 percent.


[1] Pana, M. T. (1965, March). The simulation approach to openpit design. In APCOM SYMPOSIUM (Vol. 5, pp. 127-138).
[2] Wright, A. (1999). MOVING CONE II-A simple algorithm for optimum pit limits design. Proceedings of the 28th APCOM, 367-374.
[3] David, M., Dowd, P. A., & Korobov, S. (1974, April). Forecasting departure from planning in open-pit design and grade control. In 12th Symposium on the application of computers and operations research in the mineral industries (APCOM) (Vol. 2, pp. F131-F142).
[4] Roman, R. J. (1974). The role of time value of money in determining an open-pit mining sequence and pit limits. In Proc. 12th Symp. Application Computers and Operation Research in the Mineral Industry.
[5] Lerchs, H., & Grossman, I. F. (1965). Optimum design of openpit mines. CIM bulletin, 58(633), 47-54.
[6] Yegulalp, T. M., & Arias, J. A. (1992, April). A fast algorithm to solve the ultimate pit limit problem. In 23rd International Symposium on the Application of Computers and Operations Research in The Mineral Industries (pp. 391-398). Littleton, Co: AIME.
[7] Johnson, T. B., & Barnes R. J. (1988). Application of the Maximal Flow algorithm to ultimate pit design. Engineering design: better results through operations research methods, 518-531.
[8] François-Bongarçon, D., & Guibal, D. (1982, April). Algorithms for parameterizing reserves under different geometrical constraints. In Proc. 17th symposium on the application of computers and operations research in the mineral industries (APCOM: AIME) (pp. 297-309).
[9] Wang, Q., & Sevim, H. (1992). Enhanced production planning in open-pit mining through intelligent dynamic search. Institute of Mining Metallurgy (ed), 23, 461-471.
[10] Wang, Q., & Sevim H. (1993). Open-pit production planning through pit-generation and pit-sequencing. Transactions of the American Society for Mining, Metallurgy and Exploration, 294(7), 1968-1972.
[11] Wang, Q., & Sevim H. (1995). Alternative to parameterization in finding a series of maximum-metal pits for production planning. Mining engineering, 178-182.
[12] Gershon, M. (1987). Heuristic approaches for mine planning and production scheduling. International Journal of Mining and Geological Engineering, 5(1), 1-13.
[13] Dimitrakopoulos, R., Farrelly, C. T., & Godoy, M. (2002). Moving forward from traditional optimization: grade uncertainty and risk effects in open-pit design. Mining Technology, 111(1), 82-88.
[14] Dimitrakopoulos, R., & Ramazan, S. (2004). Uncertainty based production scheduling in open-pit mining. SME transactions, 316.
[15] Harrison, S., Leuangthong, O., Crawford, B., & Oshust, P. M. Saleki et al. / Int. J. Min. & Geo-Eng. (IJMGE), 54-2 (2020) 135-145 145 (2009). Uncertainty-based grade modelling of kimberlite: a case study of the Jay kimberlite pipe, EKATI Diamond Mine, Canada. Lithos, 112, 73-82.
[16] Gholamnejad, J., & Moosavi, E. (2012). A new mathematical programming model for long-term production scheduling considering geological uncertainty. Journal of the Southern African Institute of Mining and Metallurgy, 112(2), 77-81.
[17] Moosavi, E., & Gholamnejad, J. (2015). Long-term production scheduling modeling for the open-pit mines considering tonnage uncertainty via indicator kriging. Journal of Mining Science, 51(6), 1226-1234.
[18] Lamghari, A., & Dimitrakopoulos, R. (2016). Network-flow based algorithms for scheduling production in multiprocessor open-pit mines accounting for metal uncertainty. European Journal of Operational Research, 250(1), 273-290.
[19] Gilani, S. O., & Sattarvand, J. (2016). Integrating geological uncertainty in long-term open-pit mine production planning by ant colony optimization. Computers & Geosciences, 87, 31-40.
[20] Baek, J., Choi, Y., & Park, H. S. (2016). Uncertainty representation method for open-pit optimization results due to variation in mineral prices. Minerals, 6(1), 17.
[21] Upadhyay, S. P., & Askari-Nasab, H. (2018). Simulation and optimization approach for uncertainty-based short-term planning in open-pit mines. International Journal of Mining Science and Technology, 28(2), 153-166.
[22] Tahernejad, M. M., Ataei, M., & Khalokakaie, R. (2018). A practical approach to open-pit mine planning under price uncertainty using information gap decision theory. Journal of Mining and Environment, 9(2), 527-537.
[23] Paricheh, M., & Osanloo, M. (2018). A simulation-based risk management approach to locating facilities in open-pit mines under price and grade uncertainties. Simulation Modelling Practice and Theory.
[24] Tahernejad, M. M., Khalo Kakaei, R., & Ataei, M. (2018). Analyzing the effect of ore grade uncertainty in open-pit mine planning; A case study of Rezvan iron mine, Iran. Int. Journal of Mining & Geo-Engineering.
[25] Jamshidi, M., & Osanloo, M. (2018). UPL determination of multi-element deposits with grade uncertainty using a new block economic value calculation approach. Journal of Mining and Environment, 9(1), 61-72.
[26] Dimitrakopoulos, R. G., & Sabour, S. A. A. (2007). Evaluating mine plans under uncertainty: Can the real options make a difference?. Resources Policy, 32(3), 116-125.
[27] Akbari, A. D., Osanloo, M., & Shirazi, M. A. (2009). Reserve estimation of an open-pit mine under price uncertainty by real option approach. Mining Science and Technology (China), 19(6), 709-717.
[28] Haque, M. A., Topal, E., & Lilford, E. (2016). Estimation of mining project values through real option valuation using a combination of hedging strategy and a mean reversion commodity price. Natural Resources Research, 25(4), 459- 471.
[29] Siña, M., & Guzmán, J. I. (2018). Real option valuation of open-pit mines with two processing methods. Journal of Commodity Markets.
[30] Dehghani, H., & Ataee-pour, M. (2012). Determination of the effect of operating cost uncertainty on mining project evaluation. Resources Policy, 37(1), 109-117.
[31] Dehghani, H., Ataee-pour, M., & Esfahanipour, A. (2014). Evaluation of the mining projects under economic uncertainties using multidimensional binomial tree. Resources Policy, 39, 124-133.
[32] Wellmer, F. W., Dalheimer, M., & Wagner, M. (2007). Economic evaluations in exploration. Springer Science & Business Media.