Exploitation
Meisam Saleki; Reza Khaloo Kakaie; Mohammad Ataei; Ali Nouri Qarahasanlou
Abstract
One of the most critical designs in open-pit mining is the ultimate pit limit (UPL). The UPL is frequently computed initially through profit-maximizing algorithms like the Lerchs-Grossman (LG). Then, in order to optimize net present value (NPV), production planning is executed for the blocks that ...
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One of the most critical designs in open-pit mining is the ultimate pit limit (UPL). The UPL is frequently computed initially through profit-maximizing algorithms like the Lerchs-Grossman (LG). Then, in order to optimize net present value (NPV), production planning is executed for the blocks that fall within the designated pit limit. This paper presents a mathematical model of the UPL with NPV maximization, enabling simultaneous determination of the UPL and long-term production planning. Model behavior is nonlinear. Thus, in order to achieve model linearization, the model has been partitioned into two linear sub-problems. The procedure facilitates the model solution and the strategy by decreasing the number of decision variables. Naturally, the model is NP-Hard. As a result, in order to address the issue, the Dynamic Pit Tracker (DPT) heuristic algorithm was devised, accepting economic block models as input. A comparison is made between the economic values and positional weights of blocks throughout the steps in order to identify the most appropriate block. The outcomes of the mathematical model, LG, and Latorre-Golosinski (LAGO) algorithms were assessed in relation to the DPT on a two-dimensional block model. Comparative analysis revealed that the UPLs generated by these algorithms are consistent in this instance. Utilizing the new algorithm to determine UPL for a 3D block model revealed that the final pit profit matched LG UPL by 97.95%.
A. David Mwangi; Z. Jianhua; H. Gang; R. Muthui Kasomo; I. Mulalo Matidza
Abstract
The ultimate pit limit optimization (UPLO) serves as an important step in the mine planning process. Various approaches of maximum flow algorithms such as pseudo-flow and push-relabel have been used for pit optimization, and have given good results. The Boykov-Kolmogorov (BK) maximum flow algorithm has ...
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The ultimate pit limit optimization (UPLO) serves as an important step in the mine planning process. Various approaches of maximum flow algorithms such as pseudo-flow 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 push-relabel 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.
ebrahim elahi; Reza Kakaie; amir yusefi
Abstract
Ultimate limits of an open pit, which define its size and shape at the end of the mine’s life, is the pit with the highest profit value. A number of algorithms such as floating or moving cone method, floating cone method II and the corrected forms of this method, the Korobov algorithm and the corrected ...
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Ultimate limits of an open pit, which define its size and shape at the end of the mine’s life, is the pit with the highest profit value. A number of algorithms such as floating or moving cone method, floating cone method II and the corrected forms of this method, the Korobov algorithm and the corrected form of this method, dynamic programming and the Lerchs and Grossmann algorithm based on graph theory have been developed to find out the optimum final pit limits. Each of these methods has special advantages and disadvantages. Among these methods, the floating cone method is the simplest and fastest technique to determine optimum ultimate pit limits to which variable slope angle can be easily applied. In contrast, this method fails to find out optimum final pit limits for all the cases. Therefore, other techniques such as floating cone method II and the corrected forms of this method have been developed to overcome this shortcoming. Nevertheless, these methods are not always able to yield the true optimum pit. To overcome this problem, in this paper a new algorithm called floating cone method III has been introduced to determine optimum ultimate pit limits. The results show that this method is able to produce good outcome.
J. Gholamnejad; A.R. Mojahedfar
Abstract
The determination of the Ultimate Pit Limit (UPL) is the first step in the open pit mine planning process. In this stage
that parts of the mineral deposit that are economic to mine are determined. There are several mathematical, heuristic
and meta-heuristic algorithms to determine UPL. The optimization ...
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The determination of the Ultimate Pit Limit (UPL) is the first step in the open pit mine planning process. In this stage
that parts of the mineral deposit that are economic to mine are determined. There are several mathematical, heuristic
and meta-heuristic algorithms to determine UPL. The optimization criterion in these algorithms is maximization of the
total profit whilst satisfying the operational requirement of safe wall slopes. In this paper the concept of largest pit with
non- negative value is suggested. A mathematical model based on integer programming is then developed to deal with
this objective. This model was applied on an iron ore deposit. Results showed that obtained pit with this objective is
larger than that of obtained by using net profit maximization and contains more ore, whilst the total net profit of
ultimate pit is not negative. This strategy can also increase the life of mine which is in accordance to the sustainable
development principals.
