SummaryOpen pit design and production scheduling considering the commodity price uncertainty is one of the important issues in the field of open pit mining, so that mine design and planning regardless of price uncertainty leads to erroneous assessments and non-operational production scheduling, which itself increases the investment risk. The amount of reserve that can be extracted and the location of surface facilities directly depends on the Final pit limit. In this paper, a mathematical algorithm based on Monte Carlo Simulation and Lerch and Grossman algorithm is presented, which is able to calculate the expected value of blocks based on the metal price history and estimating its distribution function and get the most likely Final pit limit. This pit can be the basis of long-term mine production planning as well as a criterion for locating surface facilities. IntroductionThe aim of the planning process for an open pit mine is usually to find optimum annual schedules that will give the highest Net Present Value (NPV). The primary input of this procedure is an economic block model, which includes a set of mining blocks representing the ore body and the surrounding rock. Net economic value is assigned to each block based on the revenue of recoverable metal content in a given block and subtracting all the operating costs, comprising mining, processing, refining, and selling costs. An economic evaluation of each block requires the estimation of ore tonnage and grade of mining blocks as well as some economic parameters such as metal prices and operation costs. In the current pit design approaches, the block economic values are calculated using a fixed known value. In this paper, using the metal prices in the past as well as the Monte Carlo simulation method, the most probable ultimate pit is obtained. Methodology and ApproachesIn this article, the price distribution function of the metal price (copper) was obtained using the metal price history. Then 100 prices were simulated using Monte Carlo simulation and the expected value of each block was obtained using these simulated values of other fixed technical and economic parameters. Finally, by using these values and using the NPV Scheduler software, a single optimal pit was obtained. Results and ConclusionsIn this article, the expected value of the blocks was obtained using the Monte Carlo simulation method, and then the optimal pit, which is actually the most probable pit, was obtained. Because the price history of the metal is considered in the design process, the obtained pit has little sensitivity to the changes in the price of the metal in the future.

Miduk in one of the largest copper ore reserves in Iran that is situated in the north west of Kerman province. It consititues approximately 157 million tons of ore with an average grade of 85%. One of the most important elements of the open pit planning is the determination of the Final pit limits. The simulation method (positive floating cone) is a commonly used method for this purpose in which the users design by grade blocks. In this presentation, geostatistic methods have been described and their application in open pit mine planning discussed. Furthermore, computer programs of CSMINE and VARIOC have then been explained and parameters required for the application of the software programs obtained. Finally, The optimum design of the pit is determined by using two sets of real data and applying the above computer programs. The recommended pit will produce appropriate ore for the ore dressing plant with maximum average and the highest amount of economic gain mind.

So far a large number of algorithms have been developed for optimisation of ultimate pit limits, most of which follow deterministic rules. In this paper a new algorithm is introduced, which follows a probabilistic logic using Markov chains. The algorithm is implemented on a transition matrix that correspond the 2D conventional economic block model of the orebody. Probability of mining a block is proportional to the profit it may produce. Applying this algorithm, probability of mining each block is obtained and Finally the optimum pit is defined as the pit, which provides with the highest probability of mining. A 2D analysis of the problem is discussed in this paper; however, it is not difficult to expand the problem to 3D cases.

In this paper, the flashlight (FL) algorithm, which is categorized as a heuristic method, has been suggested to determine the ultimate pit limit (UPL). In order to apply the suggested algorithm and other common algorithms, such as the dynamic programming, the Korobov, and the floating cone, and to validate the capability of the proposed method, the ultimate pit limit was determined in a cross-section of the Korkora reserve, which is located in Kurdistan province, northwestern of Iran and consists of 3080 blocks. The comparison of the FL algorithm and other methods revealed that same as high accuracy dynamic programming methods, the proposed algorithm could find the optimum value, while the Korobov and the floating cone algorithms failed to determine the optimum limit.

To design an open pit mine, geological operations must be conducted, followed by the preparation of a three-dimensional model and mineral block model. The ultimate pit limit can be determined through accurate methods and artificial intelligence techniques. The problem of determining the ultimate pit limit is considered to be NP-hard, making it challenging to solve. While exact methods provide better and optimal results, they may require significant time to answer the problem due to the large number of blocks involved. In such cases, it is more suitable to use collective algorithms or a planned approach to determine the Final range. Optimizing the determination of the ultimate pit limit is similar to other optimization problems that can be addressed using logical algorithms in MATLAB software. In this study, Keshtel algorithm, implemented in MATLAB, is utilized to optimize the Final range. Initially, Keshtel algorithm is employed to solve the problem. Subsequently, the Songun copper mine is chosen as a case study for the two-dimensional and three-dimensional implementation, and the results of determining the ultimate pit limit are compared with both Keshtel algorithm and NPV Scheduler software. The findings reveal that Keshtel algorithm, used to determine the Final limits of the Songun copper mine, differs by only 0.47% compared to the NPV Scheduler software. Moreover, the comparison of Keshtel algorithm with the results of Lerch Grossman in determining the two-dimensional Final range, as well as the comparison with NPV Scheduler software in three-dimensional problems, demonstrates its efficiency in solving these issues effectively.

In open-pit mine planning, the design of the most profitable ultimate pit limit is a prerequisite to developing a feasible mining sequence. Currently, the design of an ultimate pit is achieved through a computer program in most mining companies. The extraction of minerals in open mining methods needs a lot of capital investment, which may take several decades. Before the extraction, the pit limit, which influences the stripping ratio, damp locations, ore processing site and access routes, should be designed. So far, a large number of algorithms have been developed to optimize the pit limits. These algorithms are categorized into two groups: heuristic and rigorous. In this paper, a new approach is presented to optimize the pit limit based on Dijkstra’ s algorithm which is based on mathematical relations. This algorithm was implemented on a 2D economic graph model and can find the true optimal solution. The results were compared with those from the dynamic programming (DP) algorithm. This algorithm showed to have less time complexity compared to the dynamic programming algorithm and to be easier to write dynamic computer programs.

Various methods have been proposed to determine the ultimate pit limits. Artificial intelligence-based methods such as heuristic genetic algorithms, ants and colony competition algorithms. Artificial bee colony (ABC) algorithm is one of the most powerful heuristic algorithms inspired by the social life of bees. In this paper, a hypothetical example of the life of bees is primarily described to find the source with the highest amount of nectar by this algorithm. Then, a method based on the bee algorithm is proposed to determine the ultimate pit limit, and to examine its performance, a two-dimensional example is described step by step. In this example, it was found that in cases where the moving cone can not find the optimal ultimate pit limit, the ABC method is well suited for introducing solution. Then, this algorithm was used to determine the ultimate limits of Sungun Copper mine pit with a number of 120*100*45 blocks. To validate the proposed algorithm, the graph theory and moving cone techniques were used. Results showed that the profit obtained by ABC algorithm is just 1. 6% less than that of graph theory algorithm, which is a rigorous technique and entails finding the true optimum. Meanwhile, the ABC algorithm provides 12. 3% more profit when compared to heuristic moving cone algorithm.

The primary aim of this study was to define the Final pit boundaries utilizing the maximum flow Pseudoflow method in an open-pit mining context. Our methodology encompassed exploratory data analysis (EDA), establishing geomechanical and economic factors, and assessing the Final pit. The study was conducted using Python 3.11 and SGeMS 3.0. We discovered that our block model comprised 480,000 blocks of 10x10x10 m dimensions. We generated 20 pits with revenue factors between 0.1 to 2, increasing by increments of 0.1. The Study indicated that pit 20 was optimal, with an estimated NPV of 17855 MUSD, extracting 212 million tons of ore and 58 million tons of waste rock, achieving a stripping ratio based on block model and market conditions, and is subject to change with further block sequencing analysis. Nevertheless, pit 20 emerged as the most advantageous when considering economic feasibility, given its high estimated NPV and favorable stripping ratio.

The ultimate pit limit optimization (UPLO) serves as an important step in the mine planning process. Various approaches of maximum flow algorithms such as pseudoflow and push-relabel have been used for pit optimization, and have given good results. The Boykov-Kolmogorov (BK) maximum flow algorithm has been used in solving the computer vision problems and has given great practical results but it has never been applied in UPLO. In this work, we formulate and use the BK maximum flow algorithm and the push-relabel maximum flow algorithm in MATLAB Boost Graph Library within the MATLAB software in order to perform UPLO in two case studies. Comparing both case studies for the BK maximum flow algorithm and pushrelabel maximum flow algorithm gives the same maximum pit values but the BK maximum flow algorithm reduces the time consumed by 12% in the first case and 16% in the second case. This successful application of the BK maximum flow algorithm shows that it can also be used in UPLO.