تحلیل احتمالاتی ارزش اقتصادی بلوک استخراجی در معادن روباز با در نظر گرفتن تأثیر عدم قطعیت قیمت ماده معدنی و هزینه‌های عملیاتی

نوع مقاله: مقاله پژوهشی

نویسندگان

گروه مهندسی معدن، دانشگاه صنعتی همدان

10.29252/anm.7.13.15

چکیده

داده‌های ورودی در فرآیند بهینه‌سازی محدوده نهایی پیت روباز، مجموعه‌ای از بلوک‌ها است که هر یک از آن‌ها دارای یک ارزش اقتصادی خالص بوده وطراح با انتخاب بلوک‌های مناسب از میان بلوک‌های ذکرشده اقدام به بهینه‌سازی طراحی و بیشینه‌سازی ارزش خالص معدنکاری می‌نماید. ارزش خالص اقتصادی تخصیص داده‌شده به هر بلوک با استفاده از اطلاعاتی چون قیمت ماده معدنی، هزینه‌های عملیاتی، هزینه‌های ذوب وپالایش وهزینه‌های فرآوری و غیره محاسبه می‌گردد. روند تغییرات قیمت فلزات و همچنین هزینه‌های معدنکاری در سال‌های مختلف نشان می‌دهد که قطعی فرض کردن این پارامترها موجب بروز خطا در روند محاسبه ارزش اقتصادی بلوک‌های معدنی می‌شود. در روش‌های معمول برای محاسبه ارزش اقتصادی بلوک، همواره تأکید بر ثابت فرض کردن پارامترهایی چون عیار، هزینه‌های عملیاتی، قیمت ماده معدنی و ... بوده است. این در حالی است که عدم قطعیت پارامترهایی چون قیمت کاملاً بدیهی بوده و ثابت فرض کردن آن‌ها منجر به بروز خطا در فرآیند محاسبه ارزش اقتصادی بلوک می‌شود. در تحقیق حاضر سعی شده است که ابتدا به بررسی نقش عدم قطعیت اقتصادی پرداخته‌شده و سپس با استفاده از روش شبیه‌سازی مونت‌کارلو ارزش اقتصادی بلوک با در نظر گرفتن عدم قطعیت‌های قیمت ماده معدنی و هزینه‌های عملیاتی محاسبه شود. برای نیل به این هدف از داده‌های اقتصادی معدن مس گرسبرگ اندونزی استفاده شده است. نتایج این تحقیق نشان داد که روش شبیه‌سازی مونت‌کارلو توانایی بالایی در تخمین عدم قطعیت‌های اقتصادی پروژه‌های معدنی داشته و ارزش اقتصادی بلوک محاسبه شده از این روش با خطای کمتری نسبت به سایر روش‌ها به مقدار واقعی نزدیک‌تر است. همچنین ملاحظه شد که ارزش فعلی خالص به دست آمده از روش مونت‌کارلو از روش‌های معمول بیشتر بوده و به واقعیت نزدیک‌تر است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

The Probabilistic Analysis of Block Economic Value (BEV) in Open-Pit Mines Considering the Effect of Uncertainties in Metal Price and Operational Costs

نویسندگان [English]

  • Masoud Zare Naghadehi
  • Hesam Dehghani
  • Roya Naderipour
Dept. of Mining, Hamedan University of Technology (HUT), Iran
چکیده [English]

Summary
In this research, the Block Economic Value (BEV) and project NPV in an open-pit mine has been analyzed probabilistically by using the Monte Carlo Simulation (MCS) method to deal with the uncertainties in the nature of the most important economic parameters including metal price and operational costs. The results showed that the outcomes are closer to the reality by this method compared to the results of the classic methods.
 
Introduction
The basic input in the process of open-pit limit optimization is a set of block values representing the net economic worth of each block. Based on the estimated block economic values (BEV’s), the optimizer selects the optimum destination of each block in order to maximize the overall pit value under some given technical constraints. A dollar value is usually assigned to each block by estimating the revenue of recoverable metal at a given fixed metal price and subtracting applicable mining, processing and other costs. The variation trend of metals price and mining costs over the years shows that deterministic assumptions for values of such parameters will result in errors in the process of BEV calculation. The effective parameters such as metal price, operating costs, grade etc. are always assumed deterministic in the conventional methods of BEV calculation. While, these parameters have, obviously, uncertain nature.
 
Methodology and Approaches
In this paper, the BEV and project NPV were initially determined using Whittle’s formula based on deterministic economic parameters. Then the Monte Carlo Simulation (MCS) method was employed and the economic uncertainties such as the metal price and cost uncertainties were taken into account. The economic data of Grassberg Copper Mine were utilized to achieve this goal.
 
Results and Conclusions
The results showed that the Monte Carlo simulation method is highly capable of estimation of economic uncertainties. The estimated block economic values using this method are closer to the actual values compared to other methods and the error percentage is lower. As well, it was observed that the net present values obtained by the Monte Carlo simulation are closer to the reality compared to the other calculations.

کلیدواژه‌ها [English]

  • Economic Uncertainty
  • Block Economic Value
  • Net Present Value
  • Monte Carlo simulation
[1] Whittle, J. (1988). Beyond optimization in open pit design, in Proceedings Canadian Conference on Computer Applications in the Mineral Industries, pp 331-337.

[2] Whittle, J. (1999). A decade of open pit mine planning and optimization: The craft of turning algorithms into packages, In Proceedings of APCOM ’99 Computer Applications in the Minerals Industries 28th International Symposium, pp 15-24.

[3] Ataee-pour, M. (2005). A Linear model for determination of block economic values, the 19th International Mining Congress and Fair of Turkey, pp. 289-294.

[4] Dimitrakopoulos, R., Farrelly, C.T. and Godoy, M. (2002). Moving forward from traditional optimization – Grade uncertainty and risk effects in open pit design, Transactions of the Institutions of Mining and Metallurgy, Mining Technology 111, pp. A82-A88.

[5] Brennan, M.J. and Schwartz, E.S. (1985a). Evaluating natural resource investments, Journal of Business 58(2), pp. 135-157.

[6] Brennan, M.J. and Schwartz, E.S. (1985b). A New approach to evaluating natural resource investments, Midland Corporate Finance Journal 3, pp. 37-47.

[7] Trigeorgis, L. (1993). The nature of option interactions and the valuation of investments with multiple real options, Journal of Financial and Quantitative Analysis 28, pp. 1–20.

[8] Moyen, N., Slade, M. and Uppal, R. (1996). Valuing risk and flexibility a comparison of methods, Resources Policy 22, pp. 63–74.

[9] Kelly, S. (1998). A binomial lattice approach for valuing a mining property IPO, Quarterly Review of Economic Finance 38, pp. 693–709.

[10] Moel, A. and Tufano, P. (2002). When are real options exercised? An empirical study of mine closings, Review of Financial Studies 15, pp. 35–64.

[11] Monkhouse, P.H.L. and Yeates, G. (2005). Beyond naive optimisation. Orebody Model-ling and Strategic Mine Planning 14. In: Dimitrakopoulos, R. (Ed.). The Australasian Institute of Mining and Metallurgy, Melbourne, pp. 3–8.

[12] Abdel Sabour, S.A. and Poulin, R. (2006). Valuing real capital investments using the least-squares Monte Carlo method, The Engineering Economist 51, pp. 141–160.

[13] Camus, J.P. (2002). Management of mineral resources – creatingvalue in the mining business, Society for Mining, Metallurgy and Exploration Inc, Littleton, pp. 107.

[14] Akbari, A., Osanloo, M. and Shirazi, M. (2008). Determination of ultimate pit Limits in Open-pit mines using Real Option approach, IUST International Journal of Engineering Science 19, pp. 23-38.

[15] Akbari, A., Osanloo, M. and Shirazi, M. (2009). Reserve estimation of an open pit mine underprice uncertainty by real option approach, Mining Science and Technology 19, pp. 0709–0717.

[16] Jaszczuk, M. and Kania, J. (2008). Coal production costs components and coal price as crucial factors in the designation of coal output, Archives of Mining Sciences 53, pp. 183-214.

[17] Dimitrakopoulos, R.G. and Sabry, A.S. (2007). Evaluating mine plans under uncertainty: Can the real options make a difference?, Resources Policy 32, pp. 116–125.

[18] Henry, E., Marcotte, D. and Samis, M. (2004). Valuing a mine as a portfolio of European call options - The effect of geological uncertainty and implications for strategic planning, In: Leuangthong, O. and Deutsch, C.V. (eds.), Geostatistics, Banff: Canada, pp. 501-510.

[19] Li, S. and Knights, P. (2009). Integration of real options into short - term mine planning and production scheduling, Mining Science and Technology 9, pp. 674–678.

[20] Movagharnejad, K., Mehdizadeh, B., Banihashemi, M. and Sheikhi Kordkheili, M. (2011). Forecasting the differences between various commercial oil prices in the Persian Gulf region by neural network, Energy 36, pp. 3979-3984.

[21]Evatt, G.W., Soltan, M.O. and Johnson, P.V. (2012). Mineral reserves underprice uncertainty, Resources Policy 37, pp. 340-345.

[22] Erdem, O., Güyagüler, T. and Demirel, N. (2012). Uncertainty assessment for the evaluation of net present value: a mining industry perspective, The Journal of The Southern African Institute of Mining and Metallurgy, pp. 405-412.

[23] Azimi, Y., Osanloo, M. and Esfahanipour, A. (2013). An uncertainty based multi-criteria ranking system for open pit mining cut-off grade strategy selection, Resources Policy 38, pp. 212–223.

[24] Godarzi, A.A., Madadi Amiri, R., Talaei, A. and Jamasb, T. (2014). Predicting oil price movements: A dynamic Artificial Neural Network approach, Energy Policy 68, pp. 371–382.

[25] Curry, J.A., Ismay, M.J.L. and Jameson, G.J. (2014). Mine operating costs and the potential impacts of energy and grinding, Minerals Engineering 56, pp. 70–80.

[26] Dehghani, H., Ataee-pour, M. and Esfahanipour, A. (2014). Evaluation of the mining projects under economic uncertainties using multidimensional binomial tree, Resources Policy 39, pp. 124-133.

[27] Dehghani, H and Shirkavand, R. Evaluation of mining projects under the impact of economic uncertainty by using the time series. The 5th Conference of mining engineering. 22-24 meher. 1393.

[28] Dehghani, H., Joderi shokri, B. and Goodarzi moazzami rad, H. coal price forecast using the method of two-tree and such. The second National Congress of coal, Iran, 5-7 Shahrivar. 1393.

[29] Dehghani, H. and Ataee-pour, M. (2011). Determination of the effect of operating cost uncertainty on mining project evaluation, Resources Policy 37, pp. 109–117.

[30] Palisade Corporation. (2011). @Risk: A hands-on tutorial, Experts Corner

[31] Raii, R and Saidi, A. (1389). The basics of financial engineering and risk management. Publications of the Ministry of culture and Islamic guidance, pp 372.

[32] Roman, R. (1974). The role of time value of money in determining an open pit mining sequence and pit limits. In: Johnson, T. and Gentry, D. (edS.), 12th APCOM, Colorado School of Mines, Golden, CO, pp. 72–85.