Abstarct: Optimization of the final pit limit is one of the most important aspects of the design of open pit mining. In the last decades, there have been two major approaches to determining the final pit limit. The first approach is undiscounted profit maximization and the other is maximizing the NPV of the ultimate pit limit. For each approach, some methods and algorithms are presented. In the first approach, initially, the final pit outline with the aim of maximizing undiscounted profit is determined. Then achievement of the highest net present value (NPV) is planned for the pit production scheduling. Ideally, it is better to optimize the final pit by maximizing NPV rather than profit. The aim of the second method is to maximize NPV so that the optimal long-term production planning of ore blocks is determined immediately. The pit with the highest cumulative NPV will be accepted as the final pit. In the common methodology of open pit design, after ultimate pit determination short/mid/long-term production planning should be determined. In this dissertation, at first the mathematical modelling of optimum ultimate pit determination with NPV maximization was developed. The developed models are nonlinear and some techniques were applied for their linearization. Subsequently, to solve the models three heuristic algorithms were developed. In these algorithms the concepts of economic value, positional weight, nearest ore index and earliest mining time were used to find the extraction sequence of blocks and ultimate pit limit that has the maximum cumulative NPV. The results of the algorithms showed the approximate answers were near optimum.