Hybrid model of evaluation of underground lead—zinc mine capacity expansion project using Monte Carlo simulation and fuzzy numbers

Abstract

Large capital intensive projects, such as those in the mineral resource industry, are often associated with diverse sources of both endogenous and exogenous risks and uncertainties. These risks can greatly influence the project profitability. Having the ability to plan for these uncertainties is increasingly recognized as critical to long-term mining project success. In the mining industry in particular, the relationships between input variables that are controllable, and those that are not, and the physical and economic outcomes are complex and often nonlinear. The value of managerial flexibility is assessed using data on prices, costs, discount rates, grades, ore extraction, and metal output. Monte Carlo simulation of the mean reversion process is used to forecast revenue data based on an initial metal price, by using annualized volatility. Monte Carlo simulation of the Geometric Brownian Motion is used to forecast operating costs. To quantify the uncertainty in the parameters within a project such as capital investment, ore grade, and mill recovery, we used triangular, uniform, and normal statistical distribution, respectively. To decrease uncertainty related to selection of the appropriate discount rate, we have applied the concept of fuzzy sets theory. The result is a Net Present Value (NPV) based on the cash flows generated by the simulation over the timeframe of the project. When using fuzzy numbers, the fuzzy NPV itself is the payoff distribution from the project. The model explains investment behavior satisfactorily, both from a statistical and from an economic point of view.

Long‐Term Room and Pillar Mine Production Planning Based on Fuzzy 0‐1 Linear Programing and Multicriteria Clustering Algorithm with Uncertainty

“…Operating costs are incurred directly in the production process. These costs include the ore and waste development of individual stopes, the actual stopping activities, the mine services that provides logistical support to the miners, and the milling and processing of the ore at the plant [43]. Some components of operating cost such as fuel, electricity, lubricants, tyres, replacement parts, and inputs that is used for mineral processing, etc.…”

Selection of the open pit mining cut-off grade strategy under price uncertainty using a risk based multi-criteria ranking system / Wybór strategii określania warunku opłacalności wydobycia w kopalniach odkrywkowych w warunkach niepewności cen w oparciu o wielokryterialny system rankingowy z uwzględnieniem czynników ryzyka

“…Cortazaret et al (2008), have also extended the approach to cover the three-factor risk models more suitable for long-term commodity real options. Gligoric et al (2011), proposed a hybrid model of the evaluation based on Monte Carlo simulation and fuzzy numbers. Totally, the extended LSM method is mainly based on simulating multiple realizations of the uncertain variables and making the optimal decision at each period using value expectations.…”

“…Brennan and Schwartz (1985), were the first to apply the RO analysis in the mineral industry. Since then, RO analysis has been extended by valuing various types of managerial flexibilities inherent in the mineral industry using different valuation methods, (Mardones, 1993, Abdel Sabour & Poulin, 2006, Samis et al, 2006, Dimitrakopoulos & Abdel Sabour, 2007Topal, 2008, Cortazar et al, 2008Akbari et al, 2009, Gligoric et al, 2011.…”

Underground Lead-Zinc Mine Production Planning Using Fuzzy Stochastic Inventory Policy / Planowanie Wydobycia Cynku I Ołowiu W Kopalniach Podziemnych Z Wykorzystaniem Podejścia Stochastycznego Z Elementami Logiki Rozmytej Do Określania Niezbędnego Poziomu Zapasów

“…Azimi et al (2012) applied multi-criteria ranking to select the optimal open pit mining cut-off grade strategy under metal price uncertainty. Gligoric et al (2011) developed a hybrid model of evaluation of mine capacity expansion project in an underground lead-zinc mine using simulation and fuzzy numbers.…”