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

2021 ◽  
Author(s):  
Pritam Biswas ◽  
Rabindra Kumar Sinha ◽  
Phalguni Sen
Keyword(s):  
Dynamic Programming ◽  
Net Present Value ◽  
Real Life ◽  
Surface Mining ◽  
Life Time ◽  
Copper Deposit ◽  
Early Years ◽  
Open Pit ◽  
Present Value ◽  
Copper Mine

Abstract 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.

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

2021 ◽  
Author(s):  
Pritam Biswas ◽  
Rabindra Kumar Sinha ◽  
Phalguni Sen
Keyword(s):  
Dynamic Programming ◽  
Net Present Value ◽  
Surface Mining ◽  
Copper Deposit ◽  
Global Optimum ◽  
Open Pit ◽  
Prime Objective ◽  
Mining Complex ◽  
High Level ◽  
Optimum Solution

Abstract 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.

A Dynamic-Programming Based Model for Phase-Mining Optimization in Open-Pit Metal Mines

2013 ◽  
Vol 316-317 ◽  
pp. 896-901
Author(s):  
Qing Wang ◽  
Xiao Chuan Xu ◽  
Xiao Wei Gu
Keyword(s):  
Dynamic Programming ◽  
Net Present Value ◽  
Open Pit ◽  
Present Value ◽  
Dynamic Nature ◽  
Time And Space ◽  
Full Account ◽  
Metal Mines

Three important aspects of phase-mining must be optimized: the number of phases, the geometry and position of each phase-pit (including the ultimate pit), and the ore and waste quantities to be mined in each phase. A model is presented in this paper in which, a sequence of geologically optimum pits are first generated and then dynamically evaluated to simultaneously optimize the above three aspects, with the objective of maximizing the overall net present value. The model takes into full account of the dynamic nature of the problem with respect to both time and space, and is robust in accommodating different pit wall slopes and different bench heights.

scholarly journals Phase Planning for Open Pit Coal Mines through Nested Pit Generation and Dynamic Programming

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Xiaowei Gu ◽  
Qing Wang ◽  
Xiaochuan Xu ◽  
Xiaoqian Ma
Keyword(s):  
Dynamic Programming ◽  
Net Present Value ◽  
Open Pit ◽  
Coal Deposit ◽  
Present Value ◽  
Coal Seams ◽  
Column Model ◽  
Coal Deposits ◽  
Coal Rock

This paper presents a phase planning method specially designed for coal deposits with nearly horizontal, bedded coal seams. The geology of this type of deposit is modeled into a column model, instead of a block model, to avoid coal-rock mixing in blocks. A nested pit generation algorithm is developed for producing a series of nested, least-strip ratio pits with a column model as its input. The algorithm completely overcomes the troublesome gap problem. Taking the least-strip ratio pits as possible phase states, a dynamic programming formulation is proposed to simultaneously optimize the number of phases, the phase-pits, and the ultimate pit, with an objective of maximizing the net present value. The merits and capability of the proposed method are demonstrated through a case study on a large coal deposit.

A dynamic programming algorithm for optimization of uneven-aged forest stands

1994 ◽  
Vol 24 (9) ◽  
pp. 1758-1765 ◽  
Author(s):  
David J. Anderson ◽  
B. Bruce Bare
Keyword(s):  
Dynamic Programming ◽  
Interest Rates ◽  
Net Present Value ◽  
Initial Conditions ◽  
Dynamic Programming Algorithm ◽  
Basal Area ◽  
Management Problem ◽  
Present Value ◽  
Stand Management ◽  
The Impact

A deterministic dynamic programming formulation of the transition uneven-aged stand management problem is presented. Using a previously published northern hardwoods growth model, a forward recursive, discrete, two-state problem that maximizes the net present value of harvested trees at each stage is developed. State variables represent the total number of trees and the total basal area per acre. A neighborhood storage concept previously published is used to reduce the number of states considered at each stage. Two harvest allocation rules are used to assign the harvested basal area to individual diameter classes. Terminal end point conditions and stage to stage sustainability are not required. Results from four base runs of the model are presented and compared with previously published results. Each run produces significantly different optimal paths, with one showing a higher net present value than any previously published. Sensitivity runs illustrate the impact of changes in interest rates, width of neighborhood storage class, and initial conditions. Dynamic programming offers promise for analyzing uneven-aged stand management problems.

The Role of Economic Uncertainty on the Block Economic Value – a New Valuation Approach / Rola Czynnika Niepewności Przy Obliczaniu Wskaźnika Rentowności – Nowe Podejście

2012 ◽  
Vol 57 (4) ◽  
pp. 991-1014 ◽  
Author(s):  
H. Dehghani ◽  
M. Ataee-Pour
Keyword(s):  
Net Present Value ◽  
Economic Value ◽  
Operating Cost ◽  
Mine Planning ◽  
Open Pit ◽  
Economic Uncertainty ◽  
Present Value ◽  
Wrong Decision ◽  
Binomial Tree ◽  
Conventional Methods

Abstract The block economic value (BEV) is one of the most important parameters in mine evaluation. This parameter can affect significant factors such as mining sequence, final pit limit and net present value. Nowadays, the aim of open pit mine planning is to define optimum pit limits and an optimum life of mine production scheduling that maximizes the pit value under some technical and operational constraints. Therefore, it is necessary to calculate the block economic value at the first stage of the mine planning process, correctly. Unrealistic block economic value estimation may cause the mining project managers to make the wrong decision and thus may impose inexpiable losses to the project. The effective parameters such as metal price, operating cost, grade and so forth are always assumed certain in the conventional methods of BEV calculation. While, obviously, these parameters have uncertain nature. Therefore, usually, the conventional methods results are far from reality. In order to solve this problem, a new technique is used base on an invented binomial tree which is developed in this research. This method can calculate the BEV and project NPV under economic uncertainty. In this paper, the BEV and project NPV were initially determined using Whittle formula based on certain economic parameters and a multivariate binomial tree based on the economic uncertainties such as the metal price and cost uncertainties. Finally the results were compared. It is concluded that applying the metal price and cost uncertainties causes the calculated block economic value and net present value to be more realistic than certain conditions.

scholarly journals ANALISIS PENENTUAN KADAR BATAS OPTIMAL (OPTIMUM CUT-OFF GRADE) DENGAN METODE LANE: STUDI KASUS PENAMBANGAN EMAS BAWAH TANAH

2020 ◽  
Vol 1 (1) ◽  
pp. 1-8
Author(s):  
Sari Uly Uly Sibarani ◽  
Fadhila A Rosyid ◽  
Aryo P Wibowo ◽  
Lilik E Widodo ◽  
M Nur Heriawan
Keyword(s):  
Net Present Value ◽  
Underground Mining ◽  
Commodity Prices ◽  
Open Pit ◽  
Present Value ◽  
Open Pit Mines ◽  
Vein Type ◽  
Result Show ◽  
Cut And Fill ◽  
Mineral Reserves

ABSTRAKKonservasi mineral akan tercapai manakala semakin banyak cadangan mineral tertambang dan meninggalkan sesedikit mungkin material waste. Untuk mencapai hal tersebut salah satu cara yang dapat ditempuh adalah menentukan jumlah cadangan berdasarkan kadar batas yang optimal (optimum cut-off grade). Dalam penentuan optimum cut-off grade, model matematis yang dapat dipergunakan adalah model/persamaan Lane. Metode Lane akan memaksimalkan nilai Net Present Value (NPV) dengan mempertimbangkan 3 variabel, yaitu; variabel ekonomi (harga komoditas dan biaya), distribusi kadar pada endapan, dan kapasitas maksimum pada tahapan penambangan (mining, milling, and refinery). Model Lane biasa diterapkan dalam tambang terbuka, namun dalam penambangan bawah tanah sulit untuk diterapkan. Dalam peper ini akan dikaji penerapan Model Lane dalam penentuan optimum cut-off grade pada penambangan urat (vein) emas bawah tanah dengan metode cut-and-fill. Hasil simulasi menunjukkan nilai optimum cut-off grade yang dinamis dalam memaksimalkan NPV dan nilainya lebih besar dari break even cut-off grade.Kata Kunci: model Lane, optimum cut-off grade, tambang bawah tanah ABSTRACTMineral conservation will be obtained if more mineral reserves are extracted and leaves less waste as possible. One of the methods to achieve those condition is determining the total minable reserves based on the optimum cut-off grade. Optimum cut-off grade can be estimated using Lane Model. Lane Model will maximize the Net Present Value (NPV) by considering 3 variables, i.e; economic variables (commodity prices and costs), grade distribution of deposit, and maximum capacity of each stage of production (mining, milling, and refinery). Lane models are usually applied in open-pit mines, unfortunately it is difficult to apply for underground mining unless some there are some modifications. This paper will examine the application of the Lane Model in determining the optimum cut-off grade in underground gold mine using cut-and-fill method to extract vein type deposit. Simulation result show dynamic optimum cut-off grade which maximizing NPV and generally greater than the break-even cut-off grade.Key Words: Lane model, optimum cut-off grade, underground mine 

Risk Management Incorporated to Life-of-Mine Planning at Sossego Copper Mine, Carajás, Brazil

2014 ◽  
Vol 805 ◽  
pp. 263-271 ◽  
Author(s):  
Sandro Freitas ◽  
Benevides Aires ◽  
Giorgio de Tomi ◽  
Richardson Agra
Keyword(s):  
Decision Making ◽  
Production Scheduling ◽  
Real Life ◽  
Mine Planning ◽  
Open Pit ◽  
Copper Mine ◽  
Mining Sequence ◽  
Grade Uncertainty ◽  
The Impact ◽  
Production Plans

Open pit mine design and production scheduling deals with the quest for most profitable mining sequence over the life of a mine. The dynamics of mining ore and waste, and spatial grade uncertainty make predictions of the optimal mining sequence a challenging task. Valuation and related decision-making in surface mining require the assessment and management of orebody risk in the generation of a pit design and long term production scheduling. As the most profitable mining sequence over de life of a mine determines both economic outcome of a project and the technical plan to be followed from mine development to mine closure, the adverse effects of orebody risk on performance is critical and are documented in various studies. Ignoring such a consequential source of risk and uncertainty may lead to unrealistic production plans. This paper presented a set of procedures that enable mine planning engineers to carry out a series of analysis, which can be used to evaluate the sensitivity of incremental pit shells and pit designs to grade uncertainty. The results obtained from the analysis have shown to provide valuable information, which can be used to develop mining strategies that are risk resilient in relation to grade uncertainty. A real life application at Sossego copper mine ensure that such procedures are technically implementable, supporting decision-making as (a) in-fill drilling programs; (b) review of mining sequence; (c) identification of areas of upside potential and downside risk and (d) ore blending between mining areas in order to minimize the impact of high risk areas. The goal of this work is to provide an approach for clear risk analysis and management in mine planning cycle to various aspects of pit optimisation and design, resulting in more technically and economically sustainable life-of-mine production plans and mineral reserve depletion.

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