Determination of optimum cut-off grade of an open-pit metalliferous deposit under various limiting conditions using a linearly advancing algorithm derived from dynamic programming

Abstract

In the process of planning an open-pit, the determination of optimum cut-off grade plays a vital role. The classical approach of Lane's algorithm yields infinitely many solutions when the metal price is very high and mining, milling and refining costs are low. This problem has been addressed through a new algorithm. This study deals with the optimization of cut-off grade of a real-life case study of an open-pit copper mine in India considering fixed annual production of mine, mill and refinery facilities. However, the optimization ignores uncertainty in input parameters. The optimization has been carried out with the objective of maximizing the discounted total profit in terms of Net Present Value (NPV). As the process of determination of optimum cut-off grade of the deposit is dependent on many parameters which can suitably be addressed using a linearly advancing algorithm derived from dynamic programming approach. Considering a precision of 0.01% in the grade interval, the optimum cut-off grades, the amount of metal produced per ton and the NPV have been evaluated. Accordingly, the optimum cut-off grade of the Malanjkhand copper deposit has been found to be 0.32% amounting to a maximum NPV of ₹ 12123 million. The calculation reveals that the life of mine is 37.5 years and the average mill head grade optimises to 1.12%. The results also reveal that the present value of net cash-flow increases in the initial years, reaches a maximum value at a certain mid-life time and then declines with the depletion of the reserve. The NPV finally reaches a zero value at the end of mine life corroborating the general trend as seen in other mining organisations.