Using equivalent grade factors to find the optimum cut-off grades of multiple metal deposits

One of the most important aspects of mine design is to determine the optimum cut-off grades. Material grading above and below the cut-off is directed to different destinations. Optimization of cut-off grade is now an accepted principle for open pit planning studies. The most commonly criteria used in cut-off grade optimization is to maximize net present value. Lane formulated the concept of cut-off grade optimization for single metal deposit but this method cannot be use in multiple metal deposits. Because in single metal deposits six points are possible candidates for the optimum cut-off grade, in multiple metal deposits an infinite number of points are possible candidates for the optimum cut-off grades. The objective function evaluation of these infinite points is impossible. In this paper, the equivalent grade factor is used to find optimum cut-off grade of multiple metal deposits. First, the objective function is defined for multiple metal deposits and then objective function is converted to one variable function by using equivalent factors. The optimum equivalent cut-off grade of main metal can be found by the optimization techniques such as the Lane algorithm or elimination methods. At final step, the optimum cut-off grades will be determined by interpolation of grade-tonnage distribution of deposit.