Exploitation
Javad Lotfi Godarzi; Ahmad Reza Sayadi; Amin Mousavi; Micah Nehring
Abstract
The production rate and cut-off grade are two critical variables in the design and planning of open-pit mines. Generally, the production rate depends on the reserve amount, which is influenced by the cut-off grade. Additionally, the cut-off grade is affected by the production cost, which is influenced ...
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The production rate and cut-off grade are two critical variables in the design and planning of open-pit mines. Generally, the production rate depends on the reserve amount, which is influenced by the cut-off grade. Additionally, the cut-off grade is affected by the production cost, which is influenced by the production rate and product price. A conventional approach optimizes each variable individually, and neglects the trade-off between production rate and cut-off grade, leading to a sub-optimal solution. This work aimed to address the simultaneous optimization of the production rate and cut-off grade and provided a novel solution for this problem. In this context, a non-linear mathematical model was developed. The Particle Swarm Optimization (PSO) algorithm was used due to the model's non-linear nature and the continuous decision variables. Implementing the model for a typical copper mine showed that the suggested model resulted in a concurrent optimization of production rate and cut-off grade. The maximum NPV of 1.153 billion dollars occurred at a production rate of 15.66 Mt/y, and a cut-off grade of 0.64%. Additionally, a sensitivity analysis was conducted for key factors such as product price, discount rate, and maximum capital cost.
Exploitation
Elham Lotfi; Javad Gholamnejad; Mehdi Najafi; Mohammad Sadegh Zamani
Abstract
In the context of open pit mining operations, long-term production scheduling faces significant challenges due to inherent uncertainties, particularly in commodity prices. Traditional mathematical models often adopt a single-point estimation strategy for commodity price, leading to suboptimal mine plans ...
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In the context of open pit mining operations, long-term production scheduling faces significant challenges due to inherent uncertainties, particularly in commodity prices. Traditional mathematical models often adopt a single-point estimation strategy for commodity price, leading to suboptimal mine plans and missed production targets. The simultaneous effect of commodity price uncertainty on the cut-off grade and long-term production scheduling is less considered. This paper introduces a novel model for optimizing open pit mine long-term production scheduling under commodity price uncertainty considering a dynamic cut-off grade strategy, based on a two-stage Stochastic Production Programming (SPP) framework. The presented model seeks to identify optimal mining block sequences, maximizing total discounted cash flow while penalizing deviations from production targets. To illustrate the model's efficiency, it was implemented in a copper mine. First, the Geometric Brownian Motion (GBM) model is used to quantify the future commodity price. Then, both deterministic and SPP models were solved using GAMS software. The results showed that the practical NPV obtained from the SPP model is approximately 3% higher than the DPP model, while all constraints are satisfied.
Exploitation
M. Jamshidi; M. Osanloo
Abstract
The block economic value (BEV) of a single-metal deposit is calculated based on the metal content and the related costs. The common methods available for calculating BEV are just based upon the profitable elements, and the effects of undesirable elements on BEV are not considered. However, in multi-element ...
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The block economic value (BEV) of a single-metal deposit is calculated based on the metal content and the related costs. The common methods available for calculating BEV are just based upon the profitable elements, and the effects of undesirable elements on BEV are not considered. However, in multi-element deposits, the effects of other elements existing in the blocks on BEV should be considered with the purpose of optimizing the blending. These elements and blending methods have considerable effects on the quality of the final product. In this paper, a new approach is introduced to determine BEV in multi-element deposit with two types of profitable and penalty elements by considering the effect of blending on BEV. Consequently, the ultimate pit limits (UPLs) will be determined based on these conditions. The developed model is tested in the Gol-e-Gohar No.2 iron-ore mine, and the mine UPLs is determined. The results obtained showed that the mineable reserve of the pit increased by 3% when the effects of both types of elements are considered. In order to investigate the effect of grade uncertainty on BEV, twenty realizations of the ore block are generated using the sequential Gaussian simulation approach. The UPLs of all the realizations are determined using the developed BEV-calculation method, and the pit limits with different probabilities of occurrence are determined. The total mineable reserve varied between 20,380 and 46,410 million tons. The exploitation of mine should start with the smallest pit (100% probability). The largest pit should be considered as a guide for surface-facility locating.