In mine planning problems, cutoff grade optimization defines a threshold at every time period such that material above this value is processed, and the rest is considered waste. In orebodies with multiple minerals, which occur in practice, the natural extension is to consider a cutoff surface. We show that in two dimensions the optimal solution is a line, and in three dimensions it is a hyperplane.
Department of Economics, Faculty of Economics and Business, University of Chile, Diagonal Paraguay 257 of. 1305 C. Santiago, Chile. SKEMA Business School, Université Côte d’Azur, Lille, France Wm Michael Barnes '64 Department of Industrial \& Systems Engineering Texas A\&M University ETB 4029, College Station, TX 77843-3131, United States.
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