Conventionally, mining industry relies on a deterministic view, where a unique mine plan is determined based on a single resource model. A major shortfall of this approach is the inability to assess the risk caused by...Conventionally, mining industry relies on a deterministic view, where a unique mine plan is determined based on a single resource model. A major shortfall of this approach is the inability to assess the risk caused by the well-known geological uncertainty, i.e. the in situ grade and tonnage variability of the mineral deposit. Despite some recent attempts in developing stochastic mine planning models which have demonstrated promising results, the industry still remains sceptical about this innovative idea. With respect to unbiased linear estimation, kriging is the most popular and reliable deterministic interpolation technique for resource estimation and it appears to remain its popularity in the near future. This paper presents a new systematic framework to quantify the risk of kriging-based mining projects due to the geological uncertainties. Firstly, conditional simulation is implemented to generate a series of equally-probable orebody realisations and these realisations are then compared with the kriged resource model to analyse its geological uncertainty. Secondly, a production schedule over the life of mine is determined based on the kriged resource model. Finally, risk profiles of that production schedule, namely ore and waste tonnage production, blending grade and Net Present Value （NPV）, are constructed using the orebody realisations. The proposed model was applied on a multi-element deposit and the result demonstrates that that the kriging-based mine plan is unlikely to meet the production targets. Especially, the kriging-based mine plan overestimated the expected NPV at a magnitude of 6.70% to 7.34% （135 M$ to 151 M$）. A new multivariate conditional simulation framework was also introduced in this paper to cope with the multivariate nature of the deposit. Although an iron ore deposit is used to prove the concepts, the method can easily be adapted to other kinds of mineral deposits, including surface coal mine.展开更多
Commodity prices have fallen sharply due to the global financial crisis. This has adversely affected the viability of some mining projects, including leading to the possibility of bankruptcy for some companies. These ...Commodity prices have fallen sharply due to the global financial crisis. This has adversely affected the viability of some mining projects, including leading to the possibility of bankruptcy for some companies. These price falls reflect uncertainties and risks associated with mining projects. In recent years, much work has been published related to the application of real options pricing theory to value life-of-mine plans in response to long term financial uncertainty and risk. However, there are uncertainties and risks associated with medium/short-term mining operations. Real options theory can also be applied to tactical decisions involving uncertainties and risks. This paper will investigate the application of real options in the mining industry and present a methodology developed at University of Queensland, Australia, for integrating real options into medium/short-term mine planning and production scheduling. A case study will demonstrate the validity and usefulness of the methodology and techniques developed.展开更多
This paper attempts to optimize optimal capacities, block routing and mine sequencing problems in a mining system. The solution approach is based on a heuristics and the mixed integer programming (MIP). Unlike previou...This paper attempts to optimize optimal capacities, block routing and mine sequencing problems in a mining system. The solution approach is based on a heuristics and the mixed integer programming (MIP). Unlike previous sequential solution approaches, the problems are herein solved at the same time. Furthermore, the proposed approach guarantees practical solutions because it considers ore material distribution within orebody. The paper has two main contributions: (a) the proposed approach generates production rates in a manner that the capacities are satisfied; (b) the proposed approach does not use pre-defined marginal cut-off grades. Thus, idle capacity problem is eliminated and different scheduling combinations are allowed. To see the performance of the approach proposed, a case study is carried out using a gold data. The schedule generated shows that the approach can determine optimal production rates, block destination and sequencing effectively.展开更多
This paper presents the development and implementation of an innovative mixed integer programming based mathematical model for an open pit mining operation with Grade Engineering framework.Grade Engineering comprises ...This paper presents the development and implementation of an innovative mixed integer programming based mathematical model for an open pit mining operation with Grade Engineering framework.Grade Engineering comprises a range of coarse-separation based pre-processing techniques that separate the desirable(i.e.high-grade)and undesirable(i.e.low-grade or uneconomic)materials and ensure the delivery of only selected quantity of high quality(or high-grade)material to energy,water,and cost-intensive processing plant.The model maximizes the net present value under a range of operational and processing constraints.Given that the proposed model is computationally complex,the authors employ a data preprocessing procedure and then evaluate the performance of the model at several practical instances using computation time,optimality gap,and the net present value as valid measures.In addition,a comparison of the proposed and traditional(without Grade Engineering)models reflects that the proposed model outperforms the traditional formulation.展开更多
Fluctuations in commodity prices should influence mining operations to continually update and adjust their mine plans in order to capture additional value under new market conditions. One of the adjustments is the cha...Fluctuations in commodity prices should influence mining operations to continually update and adjust their mine plans in order to capture additional value under new market conditions. One of the adjustments is the change in production sequencing. This paper seeks to present a method for quantifying the net present value(NPV) that may be directly attributed to the change in commodity prices. The evaluation is conducted across ten copper price scenarios. Discrete event simulation combined with mixed integer programming was used to attain a viable production strategy and to generate optimal mine plans. The analysis indicates that an increase in prices results in an increased in the NPV from$96.57M to $755.65M. In an environment where mining operations must be striving to gain as much value as possible from the rights to exploit a finite resource, it is not appropriate to keep operating under the same mine plan if commodity prices alter during the course of operations.展开更多
The ultimate pit may affect other aspects in the life of a mine such as economical, technical, environmental, and social aspects. What makes it even more complex is that most often there are many pits which are econom...The ultimate pit may affect other aspects in the life of a mine such as economical, technical, environmental, and social aspects. What makes it even more complex is that most often there are many pits which are economically minable. This calls for a heuristic approach to determine which of these pits is the ultimate pit. This study presents a means of selecting an ultimate pit during design operations of the Hebei Limestone mine. During optimization processes of the mine, many pit shells were created using Whittle Software. Normally, Whittle Software optimizes these processes and assigns a revenue factor of 1 for the ultimate pit. Unfortunately, the pit shells created did not satisfy the criteria with a revenue factor of 1 based on the parameters. As a result of this, statistical analysis was implemented to further understand the relationship, variability, and correlation of the pit shells created (data). Correlation Analysis, K-means++ Analysis, Principal Component Analysis, and Generalized Linear models were used in the analysis of the pit shells created. The results portray a salient relationship of the optimization variables. In addition, the proposed method was tested on Whittle Sample projects which satisfy the selection of ultimate pit selection with a revenue factor of 1. The results show that the proposed model produced almost the same results as the Whittle model with a revenue factor of 1 and was also able to determine the ultimate pit in cases which did not satisfy the Whittle selection criteria.展开更多
An optimal layout or three-dimensional spatial distribution of stopes guarantees the maximum profitability over life span of an underground mining operation.Thus,stope optimization is one of the key areas in undergrou...An optimal layout or three-dimensional spatial distribution of stopes guarantees the maximum profitability over life span of an underground mining operation.Thus,stope optimization is one of the key areas in underground mine planning practice.However,the computational complexity in developing an optimal stope layout has been a reason for limited availability of the algorithms offering solution to this problem.This article shares a new and efficient heuristic algorithm that considers a three-dimensional ore body model as an input,maximizes the economic value,and satisfies the physical mining and geotechnical constraints for generating an optimal stope layout.An implementation at a copper deposit demonstrates the applicability and robustness of the algorithm.A parallel processing based modification improving the performance of the original algorithm in terms of enormous computational time saving is also presented.展开更多
Underground mines require complex construction activities including the shaft, levels, raises, winzes and ore passes. In an underground mine based on stoping method, orebody part(s) maximizing profit should be determi...Underground mines require complex construction activities including the shaft, levels, raises, winzes and ore passes. In an underground mine based on stoping method, orebody part(s) maximizing profit should be determined. This process is called stope layout optimization (SLO) and implemented under site-specific geotechnical, operational and economic constraints. For practical purpose, the design obtained by SLO shows consecutive stopes in one path, which assists in defining the mining direction of these stopes. However, this direction may not accommodate the spatial distribution of the ore grade: if the orebody orientation and mining direction differ, the value of the mining operation may decrease. This paper proposes an approach whereby paths in the SLO are defined as decision variables to avoid the cost of mining in the wrong direction. Furthermore, in the genetic-based formulation, which accounts for orebody uncertainty, a robust cluster average design process is proposed to improve SLO’s performance regarding metal content. A case study in narrow gold vein deposit shows that the profit of an underground mining operation could be underestimated by 25%-48% if the algorithm ignores stope layout orientation.展开更多
To extract ore from open pit mines,the associated waste material must also be removed.In most mining operations,the amount of waste rock is greater than the amount of ore.Waste from the pits is usually disposed of in ...To extract ore from open pit mines,the associated waste material must also be removed.In most mining operations,the amount of waste rock is greater than the amount of ore.Waste from the pits is usually disposed of in piles,which results in environmental impacts,such as alterations in the natural landscape,possible contamination of soil and water,and the generation of dust and particulates.One way to reduce these environmental impacts and achieve a circular economy(CE)is to use waste rock to construct the pavement layers of mine roads.Another possibility would be to move only the amount of waste necessary to release the ore of interest;in addition to reducing costs,this approach would reduce the volume of waste disposed of in piles.In this study,to reduce the movement of this compact waste,a change in the planned slope is proposed,and the compact waste and surplus material in a long-term mining plan are evaluated.The new optimized geometries,which meet the requirements for road pavement material and remain stable,as indicated by 2D geotechnical finite element modeling,were incorporated into the mining plan of Pit A,an iron mining complex in northern Brazil.The new mining plan was further subjected to economic analysis,which revealed the variations in the tonnage of ore and waste rock(mostly fresh mafic),as well as the change in the net present value(NPV),compared with the original mining plan.The results indicated that the change in geometry led to a reduction of 4.42 Mt in fresh mafic movement.This reduction directly impacted the NPV of the mine plan,with an increase of US$6.88 million.展开更多
文摘Conventionally, mining industry relies on a deterministic view, where a unique mine plan is determined based on a single resource model. A major shortfall of this approach is the inability to assess the risk caused by the well-known geological uncertainty, i.e. the in situ grade and tonnage variability of the mineral deposit. Despite some recent attempts in developing stochastic mine planning models which have demonstrated promising results, the industry still remains sceptical about this innovative idea. With respect to unbiased linear estimation, kriging is the most popular and reliable deterministic interpolation technique for resource estimation and it appears to remain its popularity in the near future. This paper presents a new systematic framework to quantify the risk of kriging-based mining projects due to the geological uncertainties. Firstly, conditional simulation is implemented to generate a series of equally-probable orebody realisations and these realisations are then compared with the kriged resource model to analyse its geological uncertainty. Secondly, a production schedule over the life of mine is determined based on the kriged resource model. Finally, risk profiles of that production schedule, namely ore and waste tonnage production, blending grade and Net Present Value （NPV）, are constructed using the orebody realisations. The proposed model was applied on a multi-element deposit and the result demonstrates that that the kriging-based mine plan is unlikely to meet the production targets. Especially, the kriging-based mine plan overestimated the expected NPV at a magnitude of 6.70% to 7.34% （135 M$ to 151 M$）. A new multivariate conditional simulation framework was also introduced in this paper to cope with the multivariate nature of the deposit. Although an iron ore deposit is used to prove the concepts, the method can easily be adapted to other kinds of mineral deposits, including surface coal mine.
文摘Commodity prices have fallen sharply due to the global financial crisis. This has adversely affected the viability of some mining projects, including leading to the possibility of bankruptcy for some companies. These price falls reflect uncertainties and risks associated with mining projects. In recent years, much work has been published related to the application of real options pricing theory to value life-of-mine plans in response to long term financial uncertainty and risk. However, there are uncertainties and risks associated with medium/short-term mining operations. Real options theory can also be applied to tactical decisions involving uncertainties and risks. This paper will investigate the application of real options in the mining industry and present a methodology developed at University of Queensland, Australia, for integrating real options into medium/short-term mine planning and production scheduling. A case study will demonstrate the validity and usefulness of the methodology and techniques developed.
文摘This paper attempts to optimize optimal capacities, block routing and mine sequencing problems in a mining system. The solution approach is based on a heuristics and the mixed integer programming (MIP). Unlike previous sequential solution approaches, the problems are herein solved at the same time. Furthermore, the proposed approach guarantees practical solutions because it considers ore material distribution within orebody. The paper has two main contributions: (a) the proposed approach generates production rates in a manner that the capacities are satisfied; (b) the proposed approach does not use pre-defined marginal cut-off grades. Thus, idle capacity problem is eliminated and different scheduling combinations are allowed. To see the performance of the approach proposed, a case study is carried out using a gold data. The schedule generated shows that the approach can determine optimal production rates, block destination and sequencing effectively.
文摘This paper presents the development and implementation of an innovative mixed integer programming based mathematical model for an open pit mining operation with Grade Engineering framework.Grade Engineering comprises a range of coarse-separation based pre-processing techniques that separate the desirable(i.e.high-grade)and undesirable(i.e.low-grade or uneconomic)materials and ensure the delivery of only selected quantity of high quality(or high-grade)material to energy,water,and cost-intensive processing plant.The model maximizes the net present value under a range of operational and processing constraints.Given that the proposed model is computationally complex,the authors employ a data preprocessing procedure and then evaluate the performance of the model at several practical instances using computation time,optimality gap,and the net present value as valid measures.In addition,a comparison of the proposed and traditional(without Grade Engineering)models reflects that the proposed model outperforms the traditional formulation.
文摘Fluctuations in commodity prices should influence mining operations to continually update and adjust their mine plans in order to capture additional value under new market conditions. One of the adjustments is the change in production sequencing. This paper seeks to present a method for quantifying the net present value(NPV) that may be directly attributed to the change in commodity prices. The evaluation is conducted across ten copper price scenarios. Discrete event simulation combined with mixed integer programming was used to attain a viable production strategy and to generate optimal mine plans. The analysis indicates that an increase in prices results in an increased in the NPV from$96.57M to $755.65M. In an environment where mining operations must be striving to gain as much value as possible from the rights to exploit a finite resource, it is not appropriate to keep operating under the same mine plan if commodity prices alter during the course of operations.
文摘The ultimate pit may affect other aspects in the life of a mine such as economical, technical, environmental, and social aspects. What makes it even more complex is that most often there are many pits which are economically minable. This calls for a heuristic approach to determine which of these pits is the ultimate pit. This study presents a means of selecting an ultimate pit during design operations of the Hebei Limestone mine. During optimization processes of the mine, many pit shells were created using Whittle Software. Normally, Whittle Software optimizes these processes and assigns a revenue factor of 1 for the ultimate pit. Unfortunately, the pit shells created did not satisfy the criteria with a revenue factor of 1 based on the parameters. As a result of this, statistical analysis was implemented to further understand the relationship, variability, and correlation of the pit shells created (data). Correlation Analysis, K-means++ Analysis, Principal Component Analysis, and Generalized Linear models were used in the analysis of the pit shells created. The results portray a salient relationship of the optimization variables. In addition, the proposed method was tested on Whittle Sample projects which satisfy the selection of ultimate pit selection with a revenue factor of 1. The results show that the proposed model produced almost the same results as the Whittle model with a revenue factor of 1 and was also able to determine the ultimate pit in cases which did not satisfy the Whittle selection criteria.
文摘An optimal layout or three-dimensional spatial distribution of stopes guarantees the maximum profitability over life span of an underground mining operation.Thus,stope optimization is one of the key areas in underground mine planning practice.However,the computational complexity in developing an optimal stope layout has been a reason for limited availability of the algorithms offering solution to this problem.This article shares a new and efficient heuristic algorithm that considers a three-dimensional ore body model as an input,maximizes the economic value,and satisfies the physical mining and geotechnical constraints for generating an optimal stope layout.An implementation at a copper deposit demonstrates the applicability and robustness of the algorithm.A parallel processing based modification improving the performance of the original algorithm in terms of enormous computational time saving is also presented.
基金Project(488262-15)supported by the Natural Sciences and Engineering Research Council of Canada
文摘Underground mines require complex construction activities including the shaft, levels, raises, winzes and ore passes. In an underground mine based on stoping method, orebody part(s) maximizing profit should be determined. This process is called stope layout optimization (SLO) and implemented under site-specific geotechnical, operational and economic constraints. For practical purpose, the design obtained by SLO shows consecutive stopes in one path, which assists in defining the mining direction of these stopes. However, this direction may not accommodate the spatial distribution of the ore grade: if the orebody orientation and mining direction differ, the value of the mining operation may decrease. This paper proposes an approach whereby paths in the SLO are defined as decision variables to avoid the cost of mining in the wrong direction. Furthermore, in the genetic-based formulation, which accounts for orebody uncertainty, a robust cluster average design process is proposed to improve SLO’s performance regarding metal content. A case study in narrow gold vein deposit shows that the profit of an underground mining operation could be underestimated by 25%-48% if the algorithm ignores stope layout orientation.
文摘To extract ore from open pit mines,the associated waste material must also be removed.In most mining operations,the amount of waste rock is greater than the amount of ore.Waste from the pits is usually disposed of in piles,which results in environmental impacts,such as alterations in the natural landscape,possible contamination of soil and water,and the generation of dust and particulates.One way to reduce these environmental impacts and achieve a circular economy(CE)is to use waste rock to construct the pavement layers of mine roads.Another possibility would be to move only the amount of waste necessary to release the ore of interest;in addition to reducing costs,this approach would reduce the volume of waste disposed of in piles.In this study,to reduce the movement of this compact waste,a change in the planned slope is proposed,and the compact waste and surplus material in a long-term mining plan are evaluated.The new optimized geometries,which meet the requirements for road pavement material and remain stable,as indicated by 2D geotechnical finite element modeling,were incorporated into the mining plan of Pit A,an iron mining complex in northern Brazil.The new mining plan was further subjected to economic analysis,which revealed the variations in the tonnage of ore and waste rock(mostly fresh mafic),as well as the change in the net present value(NPV),compared with the original mining plan.The results indicated that the change in geometry led to a reduction of 4.42 Mt in fresh mafic movement.This reduction directly impacted the NPV of the mine plan,with an increase of US$6.88 million.
