Optimization of mine production rate using conditional NPV maximization

Production rate is one of the most effective variables in design and economic evaluation of mining projects. Several factors such as ore deposit characteristics، market economy as well as technical aspects of the project affect the production rate. Generally، there are two types of methods for selection of mine production rate: empirical and optimized based methods. Empirical rules are mainly related to the physical characteristics of ore (depth & tonnage) or economic characteristics of the project (cash flow، project life، market، etc.). These rules could present an appropriate production rate option suitable for pre-feasibility study levels. In the second method، a production rate which maximized a certain economic indicator is defined as optimum production rate. One of the well-known economic indicators is the Net Present Value (NPV). However، the NPV maximum value may lead to an excessively high production rate (a very short mine life). The higher rates of production are practically unachievable or undesirable، i. e. it imposes a great risk of failure، with less time in hand to recover from a bad start. Moreover، shorter lives also have maximum environmental disturbances and minimum local social advantages. So، an optimized production rate could be acceptable once in one hand it safeguards a project’s minimum life and on the other hand، has the NPV maximum. Similarly، for the practical concerns of the optimum production rate، it must consider: the maximum capacity of mining (ore and waste)، maximum financial facilities، and safeguarding number of working days in a year. This study tries to present a new model to determine the optimum mine production rate employing conditional NPV maximization approach considering all mentioned constrains. The selection of an optimum production rate is performed through an iterative process. At first، reserve tonnage and average grade are determined considering a preliminary cut off grade. Then، noticing this reserve، an initial production rate is considered، and then revenue، capital and operating costs are estimated for the whole project. A new cut-off grade is obtained based on these costs and revenues and a corresponding reserve tonnage is estimated. Considering the NPV value، this iterative process must be repeated until the most suitable production rate is achieved. Applying this iterative process، a set of the possible production rates is computed. For each production rate، the related NPV is computed and consequently، the production rate corresponding to the NPV maximum value is determined. As mentioned before، this production rate is practically unachievable. Using the proposed approach the optimized production rate can be selected conditionally whilst considering all the constraints. The proposed model has been tested applying a hypothetical porphyry copper mine، and its optimum production rate has been computed.