investigating production rate under price and operating cost uncertainty using the real options approach

Selecting the optimal production rate is a strategic decision in mine design that directly impacts key economic indicators. traditional valuation methods, such as discounted cash flow (dcf), often lead to inaccurate project valuation and suboptimal rate selection due to their failure to account for market uncertainties and the value of managerial flexibility. to address this gap, this research proposes an integrated model based on the real options approach and the binomial tree model, which simultaneously incorporates uncertainties in commodity prices and operating costs. the proposed model was applied to a case study of the grasberg copper-gold mine in indonesia for three different production rate scenarios (constant, declining, and increasing). key findings; 1) the project value estimated using the real options approach was approximately 27% higher than that derived from the classical dcf valuation. 2) among the three scenarios, the declining pattern (with an initial rate of 33.3 million tons per year and an annual decrease of 1.15 million tons over 29 years) generated the highest net present value (npv). the constant pattern (29.4 million tons per year, 11-year mine life) and the increasing pattern (low initial rate, 40-year mine life) ranked second and third, respectively. 3) assuming a constant production rate is a primary factor leading to the unrealistic shortening of mine life in traditional optimization models. conclusion in the absence of significant initial capital constraints, initiating extraction at a high rate (the declining pattern) is the optimal strategy, as it maximizes project value while ensuring an economically justifiable mine life. this study confirms the necessity of replacing static traditional models with dynamic real options frameworks for decision-making under market uncertainty conditions.