Open Pit Mine Planning: A Practical Optimization and Evaluation Approach Under Uncertain Markets
Sabry A. Sabour
Metal price is among the key variables in the open pit optimization and the economic evaluation process. The common approach to handle metal prices in open pit mine planning is to optimize the ultimate pit and the mining schedules using a fixed, flat metal price. In this respect, metal price is assumed to be known with certainty throughout the entire mine life, which in some cases can reach 80 years. Given the volatile nature of metal markets and the metal price cycles, the conventional pit optimization approach may generate sub-optimized mining plans, which results in either extra costs to mining projects or lost revenues, or both. Long-term operational decisions such as future pit expansions, beyond the currently optimized limits, cannot be handled using the pit optimization approach based on flat metal prices. There is a growing interest in the mining industry to model and manage such market uncertainty in the pit optimization as well as the project evaluations in order to maximize the value of mining operations. In this paper, the author will outline a practical approach to optimize the ultimate pit taking into account the volatility and variability of metal markets. The proposed approach uses a combination of the pit optimizer of the commercial MineSight package and a simulation-based economic modeling real options valuation approach employing the least-squares Monte Carlo algorithm. MineSight pit optimizer employs both the floating cone for initial optimization exercise and the standard Lerchs-Grossmann algorithm. In this paper, Lerchs-Grossmann option will be used to generate the pit shells. Real options valuation approach used in this study is based on generating multiple metal price scenarios. Metal price uncertainty is modeled using stochastic metal price models such as the geometric Brownian motion and the mean-reverting process. The mining operational scenarios corresponding to the simulated metal prices are then optimized using the least-square Monte Carlo approach. The objective is to maximize the discounted cash flow value of the project while incorporating the operating flexibility to revise the operating status of the open pit with time as new information becomes available. The focus of this work is on the practicality of the proposed uncertainty-based pit optimization approach and the difference it can make to the technical operational mining decisions. A case study of a hypothetical open pit poly-metallic mine is provided. The deposit contains copper, gold and silver grades. The run of mine ore is sent to the process plant that produces copper concentrate with copper as the main metal and gold and silver as the by-products. Four uncertain variables are considered here include copper, gold, silver prices and foreign exchange rate. Both copper price and exchange rate are modeled using the mean-reverting process while gold and silver prices are modeled using the geometric Brownian motion. The case study is performed using both the conventional flat price pit optimization approach and the proposed uncertainty-based one to compare results.
open pit mine planning, optimization, evaluation