Determination of optimal cut-off grade policy to optimize NPV using a new approach with optimization factor

One of the most difficult problems in mining operation is how to determine optimum cut-off grades of ores at different periods over the lifespan of the mine that will maximize the net present value (NPV) of the mine. Maximizing the NPV of a mining operation, subject to different constraints is a nonlinear programming problem. Cut-off grade optimization is used to arrive at an operating strategy that maximizes the value of a mine. Cut-off optimization as a concept has been known for many years, particularly since Lane’s latest revolution, but it is still not widely practised. Cut-off grade optimization maximizes the NPV of a project subject to capacity constraints in the mine, mill and the market. These are usually expressed as annual limits to the tonnage mined, tonnage milled and product sold. At any point in time at least one limit, and possibly two or all three, will be constraining the system. For cut-off optimization to work correctly, capacity constraints must be independent of the cut-off grade. The cut-off grade is used to distinguish ore from waste materials. If the cut-off grade is too high, much of the mined material will go to the waste dump area. If the cut-off is too low, then the input capacity of the entire mining and mineral processing operations will be fully stretched, while revenues do not necessarily increase. The optimal strategy is one that strikes the correct balance between these two limits. This paper describes the determination of a cut-off grade strategy based on Lane’s (Lane, 1964), algorithm adding an optimization factor based on the generalized reduced gradient (GRG) algorithm to maximize the project’s NPV. In this study, a computer program using Excel and Visual Basic has been developed to implement the algorithm. An interactive userfriendly cut-off grade program was coded using Visual Basic in a Wwindows based spreadsheet application (Excel), a well-known application commonly used by mining professionals. The cut-off grade program developed is used to incorporate the optimization factor (σ) which is included in the ultimate cut-off grade equation, which considers the mining (m) cost,