Net present value maximization model for optimum cut-off grade policy of open pit mining operations

Cut-off grade is the criterion that discriminates between ore and waste within a given mineral deposit1,2. If material grade in the mineral deposit is above cut-off grade it is classified as ore, and if material grade is below cut-off grade, it is classified as waste. Ore, being the economically exploitable portion of the mineral deposit, is sent to the processing plant for crushing, grinding, and concentration of the metal content. The product of the processing plant is called concentrate, which is fed to the refinery for production of refined metal. Hence, an ideal open pit mining operation consists of three stages i.e. mine, processing plant, and refinery3,4. Long-range production planing of an open pit mining operation is dependent upon several factors; however, cut-off grade is the most significant aspect, as it provides a basis for the determination of the quantity of ore and waste in a given period5. Eventually, the profit over time may be enhanced only by flow of high grade material to the processing plant. This strategy supports the objective function and, depending upon the grade-tonnage distribution of the deposit, higher NPV may be realized during earlier years to recover the initial investment6,7. However, as the deposit becomes depleted, the NPV as well as the cutoff grade decline; hence, cut-off grade policy and the production plan defined as a result of this policy dictate phenomenal influence on the overall economics of the mining operation8,9. The optimum cut-off grades, which are dynamic due to the declining effect of NPV, not only depend on the metal price and cash costs of mining, processing, and refining stages, but also take into account the limiting capacities of these stages and grade-tonnage distribution of the deposit. Therefore, the technique that determines the optimum cut-off grade policy considers the opportunity cost of not receiving future cash flows earlier during mine life, due to the limiting capacities of any of mining, processing, or refining stages10,11. However, metal price and operating costs of mining, processing, and refining change during mine life, and this happens quite often, due to the longer life of most of the open pit mining operations. Ignoring the effect of these changes in the economic parameters on the optimum cut-off grade policy would lead to unrealistic production plans12,13. Further, the declining effect of NPV allows higher cut-off grades in the early years of mine life and lower cut-off grades in the later years, Net present value maximization model for optimum cut-off grade policy of open pit mining operations