MiningMath

MiningMath

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Unlimited scenarios and decision trees for your strategic evaluations

Research

Author: Mima 257 views

PAPERS

2021 – PLANEJAMENTO DE LAVRA UTILIZAND SEQUENCIAMENTO DIRETO DE BLOCOS

Access here · Portuguese · ¹Jônatas Franco Campos da Mata, ¹Sílvia de Castro Martins, ²Saulo Sabino de Morais, ¹Alizeibek Saleimen Nader, ¹Douglas Batista Mazzinghy.

¹Universidade Federal de Minas Gerais (UFMG), ²BNA Mining Solutions

The Direct Block Scheduling (SDB) methodology brings innovations compared to the techniques of Lerchs and Grossmann (LG), within the scope of Strategic Mine Planning. The SDB applies an individual discount rate for each block depending on the time of extraction, while LG uses the initial premise of extracting all blocks at the same time. The present work makes three comparative scenarios of SDB through specific software, incorporating process recoveries and specific comminution energies as geometallurgical variables in a block model of an iron ore deposit. The NPV obtained by Scenario I, whose recoveries and specific energies were fixed, was 84,65 MUSD in 15 years, while Scenarios I and II returned, respectively, 79,38 MUSD in 16 years and 82,25 MUSD in 15 years.


Keywords
: Block model; Geometallurgy; Strategic Mine Planning; Direct Block Scheduling.

2019 – OPTIMUM PRODUCTION SCHEDULE FOR AN OPEN PIT MINE

Access here  · Turkish · ¹K. Hasözdemir 1, ¹S.G. Erçelebi

¹ İstanbul Teknik Üniversitesi, Maden Mühendisliği Bölümü

Nowadays, the strategic mine planning is become very crucial for the sustainability of mining investments because of the lack of high grade ore reserves. In this sense, the mine production planing requires solving a complex optimization problem in order to identify the production sequence of the mining blocks which is profitable after mining activities. In this work, a block model with the dimensions of x: 10m, y:10m, z:10m is used. The grades of the blocks are assigned by the krigging method, which is an interpolation method, according to the 3 dimensional semi-variogram analysis. After grade assignment, the economic values of the blocks are calculated. Then with the help of SimSched software which is programmed by mixed integer programming and other heuristic methods, the production plan is simulated while satisfying equipment and process plant capacity constraints, slope constraints, cut-off constraints. Then the optimum production plan is achieved.


Keywords:
Open pit mining, Long-term production plan, block model, schedule optimization

2019 – Environmental optimisation of mine scheduling through life cycle assessment integration
 
Access here · English · ¹ ³ Robert Pell, ¹ Laurens Tijselling, ¹ Luke W. Palmer, ¹ Hylke J. Glass, ² Xiaoyu Yan, ¹ ² Frances Wall, ³ Xianlai Zeng, ³ Jinhui Li
 

¹ Camborne School of Mines, University of Exeter Penryn Campus, Penryn, Cornwall, TR10 9FE, United Kingdom
² Environment and Sustainability Institute, University of Exeter Penryn Campus, Penryn, Cornwall, TR10 9FE, United Kingdom
³ Key Laboratory for Solid Waste Management and Environment Safety, School of Environment, Tsinghua University, Beijing, 100084, China

Life cycle assessments (LCA) are useful to quantify the environmental costs of mining projects, however the application of LCA is often a retrospective environmental measurement of operating mines. This paper presents a novel methodology of carrying out a LCA to generate life cycle impact assessment data that can form an environmental block model of a deposit. These spatially explicit data can then be used as a constraint within long-term mine scheduling simulations. The results indicate that significant reductions in global warming impact can be achieved at a small economic cost. For example using an environmental constraint it was possible to achieve 91.9% of the global warming impact whilst achieving 95.9% of the net present value compared to the baseline. Different constraints and economic scenarios are explored and multi-criteria decision analysis is carried out. This approach enables environmental considerations to be included in strategic mine planning. This is important because mining will continue to form an important part of our society for the foreseeable future. Integrating environmental considerations into the earliest stages of mine planning can assist in driving environmentally responsible raw material extraction.


Keywords:
Mining, Environmental, Life cycle assessment, Iron ore, Multi-objective optimisation.

2018 – Implementación del Software SimSched DBS para un yacimiento polimetálico modificando variables geométricas

Access here · Spanish · ¹ David Oliveiros-Sepúlveda, ² Eliana Hijuelos-Franco, ¹ Jenis Margoth Trespalacio-Torres, ² Giovanni Franco-Sepúlveda

¹ Grupo de Planeamento Minero , Giplamin , Faculdad de Minas, Universidad Nacional de Colombia
² Grupo de Planeamento Minero , Giplamin , Departamento de Materiales y Minerales, Faculdad de Minas, Universidad Nacional de Colombia

The following article intends to study the final pit of a hypothetical polymetallic deposit using the SimSched DBS software, based on a set of consecutive stages such as final pit with nested pits, phase design, operational sequence period by period, among others; this is done through the modification and analysis of geometric variables such as the slope angle, the vertical advance and the bottom of the pit. In addition, the close relationship between the variation of the Net Present Value (NPV) and the modification of the three geometric variables considered above is studied.


Keywords:
SimSched DBS; final pit; slope angle; optimal economic value; vertical advance; bottom of the pit; optimization; cumulative VPN.

2018 – Impact of the grade distribution on the final pit limit definition

Access here · English · ¹ Luiz Alberto Carvalho, ² Felipe Ribeiro Souza, ¹ Leonardo Soares Chaves, ¹ Beck Nader, ¹ Taís Renata Câmara, ² Vidal Félix Navarro Torres, ¹Roberto Galery

¹ Universidade Federal de Minas Gerais , ² Instituto Tecnológico Vale, ³ Universidade Federal Mato Grosso

Geologic modeling is an important step in determining the benefits and final pit dimensions for mining operations. Geostatistical models and distance-based functions are the main methods used to estimate the grade behavior. However, these two methods, despite their similar mean values, differ in spatial variability. The objective of this article is to prove, by comparing the two methodologies, that models with different spatial variability using the Lerchs-Grossmann algorithm will output subtly different final pit dimensions and scheduling. Furthermore, with the direct block schedule (DBS), these differences can be considerable. The tests compared the methodologies using the following three models: inverse distance (ID), ordinary kriging (OK) and turning bandssimulation (TBS). The results demonstrate that the Lerchs-Grossmann algorithm is only slightly sensitive to the spatial variability of the grade; however, DBS requires the model populations to be better defined because of its greater sensitivity to spatial variability.


Keywords:
Mine Planning, Geostatistics, Geologic Modeling, Direct Block Scheduling, Lerchs-Grossmann.

2018 – Direct block scheduling technology: Analysis of Avidity

Access here · English · ¹ Felipe Ribeiro Souza, ¹ Hudson Rodrigues Burgarelli, ¹ Alizeibek Saleimen Nader, ¹ Carlos Enrique Arroyo Ortiz, ¹ Leonardo Soares Chaves, ¹ Luiz Alberto Carvalho, ² Vidal Félix Navarro Torres

¹ Universidade Federal de Minas Gerais
² Instituto Tecnológico Vale

This study is focused on Direct Block Scheduling testing (Direct Multi-Period Scheduling methodology) which schedules mine production considering the correct discount factor of each mining block, resulting in the final pit. Each block is analyzed individually in order to define the best target period. This methodology presents an improvement of the classical methodology derived from Lerchs-Grossmann’s initial proposition improved by Whittle. This paper presents the differences between these methodologies, specially focused on the algorithms’ avidity. Avidity is classically de-fined by the voracious search algorithms, whereupon some of the most famous greedy algorithms are Branch and Bound, Brutal Force and Randomized. Strategies based on heuristics can accentuate the voracity of the optimizer system. The applied algorithm use simulated annealing combined with Tabu Search. The most avid algorithm can select the most profitable blocks in early periods, leading to higher present value in the first periods of mine operation. The application of discount factors to blocks on the Lerchs-Grossmann’s final pit has an accentuated effect with time, and this effect may make blocks scheduled for the end of the mine life unfeasible, representing a trend to a decrease in reported reserves.


Keywords:
mine planning, scheduling, avidity optimization, simulated annealing, tabu search.

2017 – Análisis del VPN en función de la tasa de descuento y el costo de remanejo implementando SIMSCHED DBS para una explotación minera a cielo abierto

Access here · Spanish · Carolina Navia-Vásquez, María Camila Monsalve-Hinestroza & Giovanni Franco-Sepúlveda

Grupo de Planeamiento Minero, Facultad de Minas, Universidad Nacional de Colombia, Medellín, Colombia.

The function of all software is to model situations that look like reality, in order to find the most viable conditions for developing a mining project, since in these what is sought is to increase revenue and reduce costs by making better decisions. In this industry investors seek to obtain the highest income in exploiting underground resources, with the aim of achieving return on investment. In this article the discount rate and the cost of rehandling of a mineral deposit hypothetical gold and copper is evaluated using the SIMSCHED DBS software. In turn a search for information, which can give clarity to the concepts with which you are working, is done. Based on the simulations performed with the two economic variables you can select the optimal net present value (NPV) for future flows.


Keywords:
Rehandling cost; discount rate; NPV; Simsched DBS.

2017 – SimSched Direct Block Scheduler: A new practical algorithm for the open pit mine production scheduling problem

Access here · English · Rodolfo Ota¹ ², Luis Martinez³, R&O Analytics

¹ MiningMath, Brazil
² Universidade Federal de Minas Gerais
³R&O Analytics, Austrália

Current practices in open pit mine planning normally challenges mine planners and mine managers to make different decisions at different stages before achieving the generation of the best long-term production scheduling for their projects. The objective of this thesis provides an in-depth coverage of a novel open pit mine optimization framework, called SimSched Direct Block Scheduler (SimSched DBS). This software allows for a more global optimization process in mine planning, where it includes the steps of the traditional practices in its own single optimization algorithm and provides the mine production scheduling straight from the block model.


Keywords:
long-term production scheduling, heuristics, SimSched Direct Block Scheduler, single step.

2017 – A Comparison of DBS and Nested Pit Stage Design as a Basis for Strategic Planning

Access here · English · Martin L. Smith², Lucas M. Nogueira¹

¹ Department of Mining Engineering (DEMIN)
² Minesmith Pty Ltd, Australia

Direct Block Scheduling ( DBS ) and standard nested pit optimization were used as two alternative starting points to define alternative mine planning scenarios. We contrast and compare the stage reserves produced by DBS and LG nested pits. Both sets of staged pit sequences are converted into detailed mine plans to produce a comprehensive comparision of the two approaches to pit optimization. Both methods produce similar reserves and value. Both reserves require intervention by an experienced engineer to produce a viable basis for staged reserves, but the imposition of additional geometric constraints in DBS yields a superior starting point. We conclude that DBS is a promising alternative to LGNP.

2017 – Mining sequence and mine capacity in open pit mining

Access here · English · Juan Camus , InnovaMine SpA, Chile

This paper challenges the current way the mine sequence and mine capacity are determined in practice in open pit mining. The former is usually determined by means of the Lerchs-Grossmann algorithm (LG) whereas the latter using a rule of thumb that involves mine equipment productivity and / or a preemptive bench sinking rate. The advent of more capable software and hardware has recently enabled the creation of more efficient mining applications to solve the mining sequence problem. But their theoretical results are risking to be labeled as unpractical if the mine capacity issue is not well understood.

2015 – A surface constrained stochastic mine production scheduling method and its application at a copper deposit

Access here · English · ¹Alexandre Marinho de Almeida, ²Roussos Dimitrakopoulos

¹COSMO – Stochastic Mine Planning Laboratory, Dept. of Mining and Materials Engineering
²McGill University, 3450 University St., Montreal, Quebec, H3A 2A7, Canada

This paper proposes a new stochastic integer programming (SIP) formulation based on surfaces, with a sequential implementation to address the optimization of life-of-mine production schedules for open pit mines with uncertain supplies of metal. The proposed formulation maximizes discounted cash flows and controls risk of deviation from production targets. The formulation using surfaces facilitates a sequential implementation, which was presented and compared using a small testing deposit. Results for the sequential approach were obtained more than 100 times faster and were identical to a single run of the SIP formulation. The application of the proposed approach to an existing deposit with 176,138 mining blocks and 25 mining periods demonstrates its computational efficiency.


Keywords:
mine production scheduling, geological uncertainty, surface, stochastic optimization, risk analysis

2015 – A Comparison of Conventional and Direct Block Scheduling Methods for Open Pit Mine Production Scheduling

Access here · English · ¹ Nelson Morales, ¹ Enrique Jélvez, ¹ Pierre Nancel, ² Alexandre Marinho, ² Octávio Guimarães

¹ Dpt. of Mining Engineering & AMTC, University of Chile, Santiago
² MiningMath Associates, Belo Horizonte, Brazil

Open pit mine production scheduling for long-term planning is a relevant and required task for any mining project or operation. Mining blocks must be scheduled for extraction over a set of years, and a destination must be assigned to each one of them. The goal is to maximize the Net Present Value of the project, subject to capacity and operational constraints. Traditionally, this task hasbeen performed either with the guidance of nested pits produced by the Lerchs-Grossmann algorithm (LG), considering pre-defined block destinations, or by the use the Direct Block Scheduling (DBS), in which individual blocks are selected (or not) for extraction and destinations are assigned at given periods of time. On the one hand, from the purely theoretical side, DBS methods should be superior to those based on LG, because they are designed to deal with more realistic considerations of the problem (like capacities, multiple products, etc.) while LG approaches are limited to slope constraints and a unique economic value as parameters. On the other hand, the practical one, LG-based methods have been at the advantage, because DBS methods require intensive computational power to be solved. Fortunately, in later years, the availability of new algorithms and technology has made DBS more competitive. New DBS algorithms based on Integer Programming and heuristics have arisen with reasonable processing times, and MineLib, a set of standard datasets for testing, has been published and made available for researchers and software developers. This paper presents two DBS algorithms and show, by means of MineLib, their competitiveness against the state-of-the-art algorithms commercially available. Furthermore, these algorithms are applied to a case study in order to see how the solutions obtained differ and improve on the traditional approach based on LG.

2015 – Traditional versus stochastic mine planning under material type and grade uncertainties

Access here · English · ¹ Alexandre Marinho, ² Dr. Luis Martinez Tipe

¹ MiningMath Associates, Belo Horizonte, Brazil
² Managing Director of ROMPEV Pty Ltd Indooroopilly, Australia

Long-term open pit mining production scheduling has been traditionally addressed with the assumption of perfect knowledge of the orebody model, given by a single geologic model filled with estimated mining block values. Material type and grade uncertainties are usually ignored misleading analysts and mine planners to make final operational and investment decisions. This paper shows how the inclusion of both rock type and grade uncertainties provide additional information about the project indicators behaviour, which should be accounted for when making final decisions. To achieve this, this paper considers a copper deposit with oxide and sulphide zones. Each zone has a given slope angle and a given density. The possible processing destinations are: a mill, an oxide leach and a sulphur leach processing plant, with respective non-linear recovery curves depending on grade. If oxide material is sent to the sulphur leach plant, or vice-versa, the recoveries are penalized. This orebody model is represented by 20 scenarios, in which each scenario represents one possible combination of material types and grades over the deposit. A direct block scheduling software is used herein for a comparison between traditional and stochastic mine planning for this deposit, considering optimized decisions on what to mine, when to mine and where to send. The optimizer maximizes the expected discounted cash flow of the project subject to physical and production constraints. The traditional scheduling considers the predominant material type for each block and the average grade over all scenarios. The stochastic scheduling considers the uncertainty in material types and copper grades, returning a schedule robust to all scenarios simultaneously. Comparisons show the importance of taking uncertainties into account in the definition of a long-term schedule with lower risk.


Keywords:
mine production scheduling, geological uncertainty, stochastic optimization, risk analysis

2015 – The impacts of slope angle approximations on open pit mining production scheduling

Access here · English · ¹ Filipe S. Beretta, ² Alexandre Marinho,

¹ Mining Engineer Consultant, SRK Consulting, Cardiff, UK
² MiningMath Associates, Belo Horizonte, Brazil

Open pit mining production scheduling requires slope angles to be defined as input to the engineering/optimization processing steps. The slope angles are approximated through appropriate parameters and methods, in an attempt to reproduce the safety requirements of an open pit mining operation. Different methods can result in considerably dissimilar results for the pit configuration. This paper presents the volatility of reported mineral reserves and cashflows to different slope angle approximation methods, when applied to open pit mining production scheduling. Two methods were revisited and parameters were changed to create a set of scenarios. The method based on blocks precedence, adopted in GEOVIA Whittle software, is examined, comparing the results for the variation of the ‘maximum number of levels’ parameter. The method based on mining surfaces, implemented in MiningMath SimSched software, is explored and compared with the previous results. The comparison between both methods shows the importance of the selection of the appropriate parameters and methods for each deposit. The ultimate pits produced by the blocks precedence method have shown a variation of up to 10.4% in reserves, with errors up to 7.8 degrees in slope angle approximations; against no variation and 0% error for the surface based method. For the mining schedule, using similar parameters for both methods, the discounted cashflow and production indicators differences are also analysed and reported herein.

2014 – The impacts of slope angle approximations on pit optimization

Access here · English · ¹ Filipe S. Beretta, ² Alexandre Marinho,

¹ Mining Engineer Consultant, SRK Consulting, Cardiff, UK
² MiningMath Associates, Belo Horizonte, Brazil

During the pit optimisation process, methods and parameters for slope angle approximations must be defined. This paper presents the sensitivity of the optimisation results to the method and parameters considered. The method based on blocks precedence, adopted in GEOVIA Whittle software, is examined, comparing the results for the variation of the ‘maximum number of levels’ parameter. The method based on mining surfaces, implemented in MiningMath SimSched software, is explored and compared with the previous results. The ultimate pits produced by the blocks precedence method have shown a variation of up to 10.4% in reserves and 2.8% in cashflow, with errors up to 7.8 degrees in slope angle approximations; against no variation and 0% error for the surface based method.


Keywords
: pit optimization; Whittle; SimSched.

2013 – Sequenciamento Direto de Blocos

Access here · Portuguese · ¹ Octávio Guimarães, ¹ Alexandre Marinho,

¹ MiningMath Associates, Belo Horizonte, Brazil

The purpose of the paper is to compare results of three technologies used for production scheduling as applied to open pit mining. In the first method, the mining sequence is directly optimised from the block model as a Mixed Integer Program (MIP). In the second method, the direct block scheduling is performed as a hybrid approach using MIP and heuristics. Results are compared using the widely accepted Lerchs-Grossman Nested Pit algorithm. The advantages and limitations of each method are compared by providing examples taken from a well-known Copper-Gold deposit. Direct block scheduling has proven to be an alternative with higher economic value, avoinding the steps of pit optimization, nested pits and cutoff grade optimization.


Keywords
: Direct block scheduling; mine planning; pit optimization; open pit.

2011 – Value creation in the mining business

Access here · English · ¹ Juan Camus

¹ Former Mining Industry Fellow at The University of Queensland, Australia and currently Managing Partner at InnovaMine, Chile

This paper challenges the deep-rooted notion that value creation in mining is all about production and costs. Instead, it puts forward that it mainly refers to the capacity of companies to continually increase the prospective mineral resources and transform them into economically mineable mineral reserves in the most effective and efficient way. To support this proposition, this study seeks to demonstrate that mining companies that excel in total shareholder return (TSR) over an entire economic cycle are those that also excel in expanding their reserves and production, here referred to as total reserves increment (TRI). The relationship between both variables is simple and revealing – company share price is to mineral reserves as dividends are to production. This match gives economic sense to the term ‘deposit’, which is used in mining parlance to refer to an ore body. Results obtained from a diverse group of 14 mining companies over the period 2000-2009 evince the previous hypothesis. There are two doubtful cases, but as the paper suggests these are transitional companies in the process of converting promising mineral resources into mineral reserves, which the market anticipates.

GRADUATION THESIS

2017 – Diseño de planificación minera a cielo aberto de un yacimento aurífero considerando la incertidumbre geológica

Access here · Spanish · ¹ Allan Guillermo Odeñana Rocafuerte

¹ Escuela Superior Politécnica del litoral, Facultad de Ingeniería en Ciencias de la Tierra, Ecuador

El yacimiento de estudio, es un diseminado aurífero que ha sido explotado de forma subterránea, por lo que, se ha mermado la posibilidad de una mayor extracción de sus reservas minerales. También, esta explotación subterránea ha afectado la estabilidad del macizo rocoso, generando accidentes y una condición de riesgo latente. Se tienen datos de muestras geoquímicas del yacimiento que se han tomado de forma espacialmente irregular, lo que dificulta la interpretación geológica del depósito mineral. La hipótesis es que el yacimiento debe ser explotado a cielo abierto. La metodología utilizada consiste en discretizar el yacimiento en un modelo de bloques y estimar las leyes de los bloques por Kriging. Luego se escoge y diseña el método de explotación. Después se planifica el programa de producción y calcula el VAN del proyecto. Se modela la incertidumbre geológica a través de 20 simulaciones estocásticas de las leyes, sintetizadas en un modelo de bloques, para luego realizar la planificación minera estocástica, es decir calcular el pit final óptimo, su programa de producción y el VAN del proyecto bajo incertidumbre. Los principales resultados son que el VAN determinado por un método determinístico tiene una probabilidad de cumplimiento menor a 0.046%. El VAN esperado considerando la incertidumbre es de 1063 (M$), es decir que es 8.74% mayor al VAN esperado por un método determinístico y tiene un 80% de probabilidad de ser alcanzado. La optimización estocástica es una metodología relativamente reciente que ha demostrado obtener resultados satisfactorios, maximizando el valor de los proyectos y minimizando el riesgo.


Keywords
: Planificación minera estocástica ; Minería a cielo abierto ; Programa de producción ; Incertidumbre geológica

2017 – Maximización de valor a través de la optimización del diseño de fases y plan de producción de una mina a tajo abierto

Access here · Spanish · ¹ Clider Niño Céspedes

¹ Pontificia Universidad Católica Del Perú, Facultad De Ciencias e Ingeniería

El presente trabajo de tesis corresponde a un estudio de rediseño de fases y optimización del plan de producción de una mina de oro a tajo abierto ubicada al norte del Perú. Es importante mencionar que la información publicada en esta tesis respecto al depósito y los resultados obtenidos de este estudio no corresponden necesariamente a la realidad. Previa a la explicación del caso de estudio, se describe información técnica de la mina respecto a temas relacionados a la geología y geotecnia, factores operativos, estructura de costos y una explicación teórica acerca del proceso de planificación minera a seguir a lo largo de la tesis.

Posteriormente, para el propósito principal de la tesis, se realizaron una serie de etapas estructuradas de la siguiente manera:

• Análisis de la información de entrada

• Solución del caso en estudio

• Análisis comparativo de resultados

• Conclusiones y recomendaciones

Estas etapas permitieron realizar la evaluación del caso inicial de los diseños de mina y el plan de producción para identificar posibles mejoras con el fin de maximizar el valor del proyecto en términos económicos y operativos. Luego de este análisis se planteó un nuevo caso de estudio que logre estos objetivos y que además satisfaga los requerimientos de corto plazo de la mina. Dicho caso fue ejecutado siguiendo una nueva metodología en planificación minera orientada a incrementar el valor de un yacimiento y optimizar los procesos de planificación minera tradicionales.

Finalmente, a través de un análisis comparativo de resultados entre el caso inicial y el nuevo caso de estudio se comprueba que se obtuvieron los resultados esperados en términos de valor y operatividad del nuevo plan de producción y diseño de mina elaborado.

2017 – Comparação entre métodos de cálculo de cava final: Lerchs Grossmann vs. Sequenciamento Direto de Blocos

Access here · Portuguese · ¹ Tiago Mozart Gonçalves Leite

¹ Centro Federal de Educação Tecnológica de Minas Gerais, Brazil

The study for delimitate the final pit of an open pit mine is a fundamental step for a mineral development. In that phase, it tries to define the quantity of overburden and ore that will be moved in the project, with the goal of maximizing the economic efficiency of the mineral company. Some time ago, this process of delimitating the mine pit was done by learning with the mistakes, but it was a slowly and imprecise process. In the current days, this job is done by the usage of software, where most of the well-known software in this area is based on the algorithm made by Lerchs & Grossmann in 1965. Nowadays the state of art for mining planning is based in the classic methodology where there is a pre-determined activities sequence: Determination of the final pit, generation of the pushbacks, block sequencing. This method determines the final pit by considering that all the blocks are mine at the same time. The evolution of the computers velocity and capacity has given new possibilities for this area. By that, the direct block sequencing is growing and becoming competitive at the market. This technique applies all the steps and solves the mining scheduling as one process, without the necessity of dividing it into independent steps. The given work has as goal the comparison of these two methods. For the comparison, it were used the software Micromine, which uses the Lerchs & Grossmann’s algorithm and the software Simsched, that appear with an optimal method for direct block sequencing. By the analysis of an unreal ore body, it was acquired an Net Present Value of 0.48% for the direct block sequencing method in relation of the Lerchs & Grossmann’s algorithm, therefore this results were more interesting in the economical view. Another observed factor, which leads in favor of the direct block sequencing method was that the fact that the exploitation of the ore body were made in a smaller time (19 years, against 25 years acquired with the L&G). It is important to emphasize that it were found an overburden movement of 62.12% bigger for the L&G than the direct block sequencing method.

 


Keywords
: mine planning, final pit, direct block sequencing, Lerchs-Grossmann algorithm.

MASTERS THESES

2016 – Stochastic optimization of strategic mine planning of a hypothetical copper deposit through a parameterizable algorithm

Access here · Spanish · ¹ José Mario Pareja Zapata

¹Universidad Nacional de Colombia, Medellín, Colombia

To perform a surface mine planning it is necessary to start from an initial evaluation of the mineral resource. The open pit schedule evaluation is a key step in the process of planning the extraction activities of a mining company. Traditional approaches applied to define the ultimate pit limit consider a single estimated model, which deviates from a real assessment of the mineral asset. Over the recent years, new approaches were proposed, so that the benefits of departing from deterministic world view, where every variable are static and modeled from an arithmetic average, to a stochastic evaluation which allows understanding the risk associated to the open pit long term mine planning. Exact optimization approaches were studied due the major roll of mine planning to financial analytics, however the implications associated with these methods are considered and a metaheuristic approach is proposed to solve the case of study.


Keywords
: Long term mine planning, Open pit scheduling, Stochastic optimization.

2016 – Cut-off Grade Optimisation for a Bimetallic Deposit: A Case Study of the Ruashi Mine Copper-Cobalt Deposit

Access here · English · ¹ Daniel Mugwagwa

¹ University of the Witwatersrand, Johannesburg

Cut-off grade optimisation is very crucial for any mining organisation. Material is classified into rock, ore or product. Grade is the ratio of the amount of product to the amount of ore in which it is contained. There grade of mineralised block can be expressed as grams per tonne (g/tonne), as a percentage (%), metal equivalent grade per tonne or dollar value per tonne. Cut-off grade is the grade that is used to distinguish between ore and waste during scheduling. The cut-off grade is the main driver of value in a mining operation. High cut-off grade results in fewer reserves. It is important to optimise the cut-off grade during the mine life in order to optimise the net present value. There are various stakeholders who derive benefits from a mining operation whose interest must be considered during cut-off grade optimisation. The scenarios investigated have shown that running a mine based on break-even cut-off grade does not optimise the net present value of an operation as given by the results for Ruashi Mining. It has also been shown that royalty does affect the cut-off grade for Ruashi Mining. The grade-tonnage curve is steeper at the beginning implying a small change in cut-off grade has a huge impact on the reserves. Cut-off grade optimisation in SimSched results in a steeply declining cut-off grade policy compared to NPVS. The optimisation in SimSched results in a highly accelerated mining rate and massive stockpiling. But SimSched gives a higher NPV compared to the current Ruashi life of mine schedule. This implies SimSched can be used to improve the NPV for Ruashi by producing an optimised cut-off grade policy.

2016 – Sequenciamento Direto de Blocos: Impactos, Limitações e Benefícios Para Aderência ao Planejamento de Lavra
 
Access here · Portuguese · ¹ Felipe Ribeiro Souza

¹ Universidade Federal De Minas Gerais, Brazil

Mining scheduling is an important mining planning procedure, which determines which material will be mined, in what quantity, and during which period. These variables are highly influenced by cash flow and can therefore lead to the success or failure of the undertaken. A classical methodology, initially proposed by Lerchs-Grossmann, defines the total amount of material mined without considering the correct discount factor and the operational restrictions of this process. To suppress the inconsistencies of this methodology, Direct Block Sequencing (SDB) proposes to execute the planning in a more efficient and precise manner, considering the main problems of the classical methodology: the discount rate and operational aspects are not present in the classical methodology. The SDB methodology is able to analyze each block individually and apply discount factor and operational constraints more assertively. This methodology is able, in a single step, to determine the sequencing since there is no need to determine final pit and pushbacks before the mining sequencing is established. The correct application of the discount rate is responsible for reducing the mineral reserves. The blocks mined in future times are settled to a correct discount factor that reduces their individual benefit function. In this way, the search for a better financial result promotes the choice of the richest blocks in order to contribute to the increase of the Net Present Value. The economic value grow is followed by operational constraints in order to determine a more assertive long- term scenario with direct block sequencing. The present dissertation proposes to elaborate a methodology of work in order to execute a more assertive mining plan considering the operational restrictions and the correct discount rate.

2013 – Surface Constrained Stochastic Life-of-Mine Production Scheduling

Access here · English · ¹ Alexandre Marinho de Almeida

¹ Department of Mining and Materials Engineering, McGill University , Montreal, Quebec, Canada.

The maximization of mining project discounted cash flows by defining the best sequence of extraction of underground materials requires understanding the availability of uncertain metal quantities throughout the deposit. This thesis proposes two versions of a stochastic integer programming formulation based on surfaces to address the optimization of life-of-mine production scheduling, whereby the supply of metal is uncertain and described by a set of equally probable simulated orebody models. The first version of the proposed formulation maximizes discounted cash flows, controls risk of deviating from production targets and is implemented sequentially, facilitating production scheduling for relatively large mineral deposits. Applications show practical intricacies and computational efficiency. The second variant extends the first to a two-stage stochastic integer programming formulation that manages the risk of deviating from production targets. The sequential implementation is considered first for pit space discretization and it is followed by the life-of-mine production scheduling at a relatively large gold deposit. The case studies show the computational efficiency and suitability of the method for realistic size mineral deposits, with production targets controlled, risk postponed to later stages of production and improvements in expected NPV, when compared to deterministic industry practices.

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Universidade Federal de Minas Gerais (UFMG)