Effect of Different Mining, Processing, and Marketing Capacities on the Relationship between Price and Optimum Cut-off Grade in Open Pit Mining Operations

Maximizing Net Present Value (NPV) is the most common goal in cut-off grade optimization of open-pit mining operations. In the case, price of product has a critical effect on the optimum value of cut- off grade. In this paper, the relationship between optimum cut-off grade and price was investigated in different mining, processing and marketing capacities. In order to visualize this relationship, an illustrative mine was employed. For determining the optimum value of cut-off grade in different cases, a nonlinear programming model was formulated, and then all models were solved with Solver in Excel. The main decision variables of the model are g (cut-off grade), and T (mine life-time). the objective function of the model is maximizing NPV of mining operation, and the constraints are related to the capacity of mining, processing, and market activities, as well as the relationships between tonnage and grade in the pit. The  outcomes of this paper can be summarized as follows: 1- When objective of cut-off grade optimization is maximizing the present value, increasing of price may cause increasing or decreasing of the cut-off grade, or even it may have no effect on it. This is due to the fact that when objective of optimization is maximizing the present value, the cut-off grade will be subject to two opposite forces. Increasing of price increases the value of less valuable material and so decreased the cut-off grade .on the other hand, it increases the value of the material remained in the pit, so the opportunity cost grows, tending to upper cut-off grades. When the price increases, the result of these two opposite forces determines direction of optimum cut-off grade variation. When capacities of activities (mining, processing and market) change, sometimes the force resulted from the opportunity cost overcomes other force, so optimum cut-off grade increases when the price arises, and sometimes vice versa .So optimum cut-off grade decreases when the price arises. In addition, sometimes the two forces are equal, and so increasing of the price has no effect on optimum cut-off grade. 2- Variation of maximum present value versus price in all capacities is absolutely ascending.