Determination of optimum cut-off grade of an open-pit metalliferous deposit under various limiting conditions using a linearly advancing algorithm derived from dynamic programming

Biswas, Pritam; Sinha, Rabindra Kumar; Sen, Phalguni; Rajpurohit, Sohan Singh

doi:10.1016/j.resourpol.2020.101594

Cited by 9 publications

(5 citation statements)

References 14 publications

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“…Dynamic programming (DP) has been widely used in mining projects to make optimal decisions considering geological and commodity price uncertainty (Rimélé et al, 2020;M. F. Del Castillo Ali, et al (2024) & Dimitrakopoulos, 2019Biswas et al, 2020;Inthavongsa et al, 2016). DP transforms complex decision-making problems into interconnected subproblems, allowing efficient optimization in the face of uncertainties.…”

Section: Decision Making With Dynamic Programmingmentioning

confidence: 99%

Strategic Integration of Real Options for Enhanced Valuation and Optimization in Mining Project Planning under Uncertainty: A Comprehensive Review

Ali,

Rafique

2024

IJPM

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Purpose: In the contemporary landscape of mining projects, the imperative to navigate through periods of uncertainty has driven the exploration of alternative strategic tools rooted in project flexibility. Real options have emerged as a pivotal strategic approach, offering the means to adapt and refine mining projects under unpredictable conditions Materials and Methods: This paper provides a comprehensive review and discussion on the strategic application of real options for optimizing mining project planning in the face of uncertainty. Organized into four sections, the paper begins with a general introduction to real options in Section one, delving into their strategic and technical classifications. Section two critically examines and reviews the indispensable role of real options in the realms of mining investment and project planning. The third section is dedicated to an in-depth discussion of the strategic tools inherent in real options, specifically focusing on their valuation and optimization aspects within mining project planning. The final section provides a discussion and conclusion on the strategic application of real options for optimizing mining project planning under uncertainty. Findings: The review identifies that real options offer valuable strategic flexibility in addressing uncertainties inherent in mining project planning. Through a detailed examination of their application, it becomes evident that real options can enhance decision-making processes and improve project outcomes by allowing for adaptive responses to changing conditions. Implications to Theory, Practice, and Policy: The strategic integration of real options into mining project planning presents significant implications for theory, practice, and policy. Theoretical implications include advancing understanding of decision-making under uncertainty and the role of flexibility in strategic planning. In practice, the adoption of real options can lead to improved project outcomes, increased resilience to market fluctuations, and enhanced risk management strategies. From a policy perspective, recognizing the value of real options may inform regulatory frameworks and promote the adoption of flexible planning approaches within the mining industry, ultimately contributing to sustainable development and resource management.

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Section: Decision Making With Dynamic Programmingmentioning

confidence: 99%

Strategic Integration of Real Options for Enhanced Valuation and Optimization in Mining Project Planning under Uncertainty: A Comprehensive Review

Ali,

Rafique

2024

IJPM

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“…This method fails to give a satisfactory answer when the projects need different levels of investment and with a different economic life of the projects. However, a few authors have also advocated that the theory of 𝐶𝑂𝐺 optimization supports the ultimate objective of a mining operation through maximization of 𝑁𝑃𝑉 [43][44][45]. Ahmadi and Bazzazi [46] proposed that choosing the optimal 𝐶𝑂𝐺 maximizes the 𝑁𝑃𝑉 and the total profit of the project.…”

Section: Dehghani and Bogdanovicmentioning

confidence: 99%

“…𝐶𝐹 (𝛼,𝛽) = { 𝑆𝑃 (𝛼,𝛽) × 𝑄 𝑐 (𝛼,𝛽) × ḡ (𝛼,𝛽) × 𝑌 𝑐 (𝛼,𝛽) × 𝑌 𝑟 (𝛼,𝛽) -∑𝛷 (𝑀 (𝛼,𝛽) , 𝐶 (𝛼,𝛽) , 𝑅 (𝛼,𝛽) ) − ∑𝜉 (𝑀 (𝛼,𝛽), 𝐶 (𝛼,𝛽), 𝑅 (𝛼,𝛽) -𝐴𝐶 (𝛼,𝛽) -𝐷 (𝛼,𝛽) } (1-𝑇𝑅 (𝛼,𝛽)) ) + 𝐷 (𝛼,𝛽) (43) The objective function is to maximize the 𝑁𝑃𝑉 for the whole deposit over the whole Mine life (𝑛). It is the cumulative summation of all the cash flows (𝐶𝐹 0 , 𝐶𝐹 1 , 𝐶𝐹 2 … 𝐶𝐹 𝑛 ), where 𝐶𝐹 0 is the capital invested having a fixed discount rate of '𝜕′ up to 𝑛 𝑡ℎ year given by equation (44) .…”

Section: Stage -Iiimentioning

confidence: 99%

A sequentially advancing algorithm based on multi-value dynamic programming for the cut-off grade optimization in open-pit metalliferous deposits

Biswas

Sinha

Sen

2021

Preprint

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In techno-economic concern, cut-off grade (COG) optimization is the key for efficient mineral liquidation from the huge metalliferous surface mining sector. In this paper, a sequentially advancing algorithm based on exact multi-value dynamic programming (MDP) has been developed to determine the optimum COG of an open-pit metalliferous deposit. The proposed COG optimization algorithm aims to overcome the limitations of straightforward classical techniques in determining the optimum COG. This discrete COG-MDP model is the first of its kind and has the novelty of dealing with the simulation of eight dynamic possibilities to achieve the maximal Net Present Value (NPV). A high-level programming language (Python) has been used to develop the computer model to deal with the complexity of handling a minimum of 500 series of dynamic variables with a precision value of 0.01% in grade bins. This model can generate results in polynomial-time from the complex mine, mill, and smelter and refinery system corresponding to various limiting conditions. The prime objective considered in the model is to optimize the COG of a metalliferous deposit. The model validation has been done using a real-life case study of an open-pit copper mine in India (Malanjkhand Copper Mine, HCL), considering the fixed yearly output of the mining, milling, and smelting and refining. In this study, the optimum COG for the Malanjkhand copper deposit has been found to be (0.33%, 0.23%, 0.52%, 0.26%, 0.27%, 0.22%, 0.24%) with a maximum NPV of ₹ (12204, 14653, 16948, 14609, 21454, 26717, 38821) million corresponding to various scenarios. The findings also show that the present value of net cash-flow grows in the early years, peaks at a specified mid-life time, and then drops as the reserve is depleted. The present value gradually hits zero after the project’s life cycle, confirming the typical pattern of other mining firms.

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“…Ahmadi optimized the 𝐶𝑂𝐺 based on Lane's theory to maximize the 𝑁𝑃𝑉 using MATLAB. The optimum 𝐶𝑂𝐺 is the grade that maximizes the chosen objective function, usually the 𝑁𝑃𝑉 (Asad & Topal, 2011;Biswas et al, 2020). Various researchers (Ahmadi & Shahabi, 2018;Bascetin & Nieto, 2007;Qingfei Wang et al, 2010) have given several algorithms to determine optimum 𝐶𝑂𝐺.…”

Section: Literature Reviewmentioning

confidence: 99%

“…The value of 𝑄 𝑐 (𝛼,𝛽) and 𝑄 𝑟 (𝛼,𝛽) are calculated using equations ( 36) and ( 37). The selection of the optimal 𝐶𝑂𝐺 is followed by a multi-staged sequential decision problem (Li & Yang, 2012;Biswas et al, 2020) with the output from each state feeding as an input for the following stages. Each stage has multiple different states correlated with it, as illustrated in Fig.…”

Section: 𝑺𝒕𝒂𝒈𝒆 -𝑰𝑰mentioning

confidence: 99%

A new global optimum solution model based on multi-value dynamic programming for the cut-off grade optimization in a surface mining complex

Biswas

Sinha

Sen

2021

Preprint

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In techno-economic concern, cut-off grade (COG) optimization is the key for efficient mineral liquidation from thehuge metalliferous surface mining sector. In this paper, a sequentially advancing algorithm based on discretemulti-value dynamic programming (MDP) has been developed to calculate the global optimum COG of alarge-scale open-pit metalliferous deposit. The proposed COG optimization algorithm aims to overcome thelimitations of straightforward classical techniques in determining the optimum COG. This discrete COG-MDPmodel is the first of its kind and has the novelty of dealing with the simulation of eight dynamic possibilities toachieve the maximal global Net Present Value (NPV). A high-level programming language (Python) has been usedto develop the computer model to deal with the complexity of handling a minimum of 500 series of dynamicvariables. This model can generate results in polynomial-time from the complex of mining, milling, and smeltingand refining system corresponding to various limiting conditions. The prime objective considered in the model isto optimize the COG of a metalliferous deposit. A working open-pit copper mining complex from India has beenused to validate the model. In this study, the optimum COG for the Malanjkhand copper deposit has been found tobe (0.33%, 0.23%, 0.52%, 0.26%, 0.27%, 0.22%, 0.24%) with a maximum NPV of ₹ (12204, 14653, 16948, 14609,21454, 26717, 38821) million corresponding to various scenarios. The findings also show that the present valuegradually hits zero after the project’s life cycle, confirming the typical pattern of other mining firms.

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Determination of optimum cut-off grade of an open-pit metalliferous deposit under various limiting conditions using a linearly advancing algorithm derived from dynamic programming

Cited by 9 publications

References 14 publications

Strategic Integration of Real Options for Enhanced Valuation and Optimization in Mining Project Planning under Uncertainty: A Comprehensive Review

Strategic Integration of Real Options for Enhanced Valuation and Optimization in Mining Project Planning under Uncertainty: A Comprehensive Review

A sequentially advancing algorithm based on multi-value dynamic programming for the cut-off grade optimization in open-pit metalliferous deposits

A new global optimum solution model based on multi-value dynamic programming for the cut-off grade optimization in a surface mining complex

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