Advances in Applied Strategic Mine Planning

Most practitioners would regard the maximising of the net present value (NPV) of a mine by changing mining schedules, push-backs, cut-off grades, ultimate pit shells and stockpile rules and procedures as encompassing current best practice in mine planning. This optimisation is typically carried out for a single set of assumptions about:orebody tonnes and grade,processing methods and costs,maximum sales volumes in the case of bulk commodities,commodity prices, anddiscount rates.About the only thing we can be sure of is that the assumptions on all these factors will be wrong, yet we continue to naïvely optimise our mine plan. This paper argues that this approach is inherently flawed. Recognising that our assumptions will be wrong, and that our actions can alter over time as new information is made available, means that the mine plan that is ‘optimal’ under a single set of assumptions may well be suboptimal in the real and uncertain world.

Picture yourself responsible for the exploitation of a world class deposit, creating staggering quantities of products for global consumption over decades, employing thousands of people, about to spend billions of dollars on infrastructure and you are going to design this project. Should it be surface or underground (or both), how big should the processing plants be, what technology should be utilised, what happens if more resources are found or the price forecast changes? This paper aims to help guide engineers faced with the prospect of determining optimal mining policies for large projects. It draws on experiences at some of the largest mining projects and mining companies in the world, including the Bingham Canyon Mine (USA), Freeport (Irian Jaya), Escondida (Chile), Chuquicamata (Chile), Hamersley Iron (Australia), Ekati Diamond Mine (Canada) and several Hunter Valley coal mines (Australia). The paper outlines some important areas to put in place before starting, principles to guide the planning process and suggestions for finding additional value.

The Global Optimiser used by Whittle Consulting has gone through three major versions to date. The first was based on the Milawa optimisation algorithm; it worked, but had many shortcomings. The second, known internally as ProberA, had a different approach to optimisation in that it used a series of random starting points and found the nearest local NPV maximum to each. It did this a sufficient number of times to give us some confidence that the best result found was close to optimal. ProberB was an enhanced version of ProberA, with the ability to handle a wider range of constraints, particularly with regard to limits on the differences in depth between adjacent areas of a pit. ProberB has been used successfully for some time now. It has produced excellent Life of Project schedules for a wide range of very large mining complexes. However, like any piece of software, it has its limitations. For example, it only copes directly with three steps—mining, processing, and blending.It is possible to ‘fool’ the program into handling other steps, but only by using mental and mathematical gymnastics. This paper reviews the mechanisms behind the Prober series and describes the plans for the next version—ProberC.

A new mine planning optimisation software tool called Blasor has been developed and implemented at BHP Billiton’s Yandi Joint Venture operation in the Pilbara. Blasor is specifically configured for designing and optimising the long-term pit development plan for the multi-pit blended-ore operation at Yandi. It is used for optimal design of the ultimate pits and the mining phases contained within those pits. In designing the mining phases, Blasor ensures that all market tonnage, grade and impurity constraints are observed whilst maximising the nett discounted cash flow (DCF) of the joint venture operation.

Many factors including data scarcity, volume support effects, information effect, accessibility and pervasive uncertainty, make the early prediction of recoverable reserves a challenge that cannot be addressed by mere estimation or interpolation algorithms. There is the illusion that as long as one uses the ‘best’ estimation algorithm based on quality data and sound geological interpretation, one would provide the best possible evaluation.

Quantification of risk is important to the management team of any rapidly expanding mining operation. Examples of areas of concern are the likelihood of not achieving project targets, the impact of a planned drilling program on uncertainty and the change in the risk profile due to a change in the mining sequence. Recent advances in conditional simulation and the practical use of such models have provided the opportunity to more fully characterise mineral deposits and to develop empirical estimates of the recoverable resources and ore reserves. This allows meaningful quantification of risk (and upside potential) associated with various components of a mining project. This paper presents an approach referred to herein as ‘simulation of the chain of mining’ to model the grade control and mining process. Future grade control sampling, mining selectivity and other issues that impact on the final recoverable tonnes and grades are incorporated. The application of this approach to Escondida, a large-scale open pit copper mining operation in Chile, provided a definitive way to assess the expected risk of a number of alternative development strategies on operational performance of the project. This approach is gaining acceptance as one of the most important steps in developing short-term mining models. The concepts developed here also have implications for assessing the ore that will be recovered from ore reserves during mining.

Assessment and management of orebody uncertainty is critical to strategic mine planning. This paper presents an approach that consists of a series of procedures for risk assessment in pit optimisation and design. Multiple block grade simulations are processed in Whittle Software to produce a distribution of possible outcomes in terms of net present value. Examples from an open pit mine are used to illustrate the practical application of the methodology.

Traditionally the process of mine development, pit design and long-term scheduling is based on a single deterministic orebody model built by the interpolation of drill hole data using some form of spatial interpolation procedure, e.g. kriging. Typical steps in mine design would include the determination of the ultimate pit, the development of a number of mining phases (pushbacks) and then the development of a life-of-mine schedule. All of these steps would have the aim of maximising the mine’s net present value (NPV), along with meeting numerous other business and physical constraints. There are a number of software packages commercially available and widely used in the mining industry that deal with some or all of these issues. The methods employed by all of these packages treat the process described above in a strictly deterministic way. In reality, given the sparse drill hole data, there is usually significant and variable uncertainty associated with a single or unique deterministic block model. This uncertainty is not captured or used in the planning process. This paper describes work undertaken by the Exploration and Mining Technology Group within BHP Billiton to develop a new mathematical algorithm for mine optimisation under orebody uncertainty. This uncertainty is expressed as a number of conditionally simulated orebody models. This optimisation algorithm is implemented in a new software package. The software uses a number of proprietary algorithms along with the commercially available mixed integer-programming package ILOG CPLEX. The development targets all phases of mine optimisation, including the NPV optimal block extraction sequence, pushback design, and simultaneous cut-off grade and mining schedule optimisation.

Conventional approaches to estimating reserves, optimising mine planning and production forecasting result in single, often biased, forecasts. This is largely due to the non-linear propagation of errors in understanding orebodies throughout the chain of mining. A new mine planning paradigm is considered herein, integrating two elements: stochastic simulation and stochastic optimisation. These elements provide an extended mathematical framework that allows modelling and direct integration of orebody uncertainty to mine design, production planning, and valuation of mining projects and operations. This stochastic framework increases the value of production schedules by 25%. Case studies also show that stochastic optimal pit limits:can be about 15% larger in terms of total tonnage when compared to the conventional optimal pit limits, whileadding about 10% of net present value (NPV) to that reported above for stochastic production scheduling within the conventionally optimal pit limits.Results suggest a potential new contribution to the sustainable utilisation of natural resources.

The value of a mining project is based upon a quantitative model of material of value in the ground, a block model of the deposit, and a schedule for extracting this material including relevant revenues and costs. The schedule usually attempts to maximise the net present value (NPV) of the project over the life of the mine. Frequently, a block model is the result of a smooth interpolation, such as kriging, of data collected from holes drilled throughout the orebody. More drill holes will lead to greater certainty in the contents of block models and from these ‘more accurate’ block models, schedules of greater ultimate value may be realised. We discuss how conditional simulations can assist with rigorously valuing the trade-off between the cost of extra drilling and the schedules of greater value that may be constructed from the resultant block models of greater accuracy.

Conventional approaches to optimising open pit mine design and production scheduling are based on a single estimated orebody model, which does not account for geological variability. Conditional simulation can be employed to quantitatively address the resulting grade uncertainty. Multiple simulated orebody models provide a suitable input for stochastic integer programming (SIP), a type of mathematical programming that generates the optimal result for a defined set of objectives under uncertainty. In the case of production scheduling, the objectives are to maximise the total net present value (NPV) and to minimise unsatisfied demand for processed ore. Using a set of multiple simulated orebody models as input into an SIP model allows for the integration of in situ deposit variability and uncertainty directly into the production scheduling optimisation process.

Meeting production targets in terms of ore quantity and quality is critical for a successful mining operation. In situ grade variability and uncertainty about the spatial distribution of ore and quality parameter cause both deviations from production targets and general financial deficits. A stochastic integer programming formulation (SIP) is developed herein to integrate geological uncertainty described by sets of equally possible scenarios of the unknown orebody. The SIP formulation accounts not only for discounted cashflows and deviations from production targets, discounts geological risk, while accounting for practical mining. Application at an iron ore deposit in Western Australia shows the ability of the approach to control risk of deviating from production targets over time. Comparison shows that the stochastically generated mine plan exhibits less risk in deviating from quality targets that the traditional mine planning approach based on a single interpolated orebody model.

A new multistage stochastic mine production scheduling approach is developed and tested in a large operating gold mine. The proposed approach takes short-scale orebody information in the form of grade control data into account. As simulated orebodies used in stochastic long-term mine planning are based on sparse exploration data and while grade control data are unavailable at the time of production scheduling, the short-scale information is first simulated stochastically and then serves as input to the optimisation process. Stage 1 of the approach generates high density future grade control data for incorporation into the production scheduling process based on sequential co-simulation and pseudo cross-variograms between exploration data and grade control in previously mined out parts of a deposit. In Stage 2, the technique of conditional simulation by successive residuals enables pre-existing simulated orebody models to be updated using the simulated future grade control information. Stage is based on a stochastic programming mine scheduling formulation that handles multiple simulated orebody models from Stage 2 and accommodates both maximising Net Present Value (NPV) and minimising deviations from production targets. Stage 4 includes quantification of risk in the produced schedules generated, comparison of schedules and reporting. The application at a large operating gold mine demonstrates that the proposed approach is practical and adds value to the operation. The approach is shown to deliver additional ore (3.6 Mt more) and metal (2.6 million grams) which matches the mined reconciliations and results in a cumulative NPV which is on average A$7.7 M higher than that of a stochastic schedule without the simulated grade control data and substantially higher (about 30%) compared to the NPV from the actual schedule of the mine.

Uncertainty and risk are invariably embedded in every mining project. Mining companies endeavouring to maximise their return for shareholders make important strategic decisions which take years or even decades to ‘play out’. Therefore, developing a model that analyses the potential payoff of a decision based on current fixed assumptions is severely flawed. A model that incorporates uncertainty and is able to adapt, almost certainly will help deliver a design with a better risk-return profile. In this paper, a new approach is developed in order to have a design that is flexible and able to adapt with change. This is achieved by developing a mixed integer programming model that determines the optimal design for simulated stochastic parameters. This research has incorporated optionality (flexibility) in relation to mining, stockpiling, processing plant and port capacity. The results are promising and are helping decision makers to think in terms of value, risk and frequency of execution.

Traditional implementations of open pit optimisation algorithms are designed simply to find a set of nested open pit limits that maximise the undiscounted financial pay-off for a series of commodity prices using a single ‘estimated’ orebody model. Then, the maximum Net Present Value (NPV) open pit limit is derived by considering alternate (usually only best and worst-case) mining schedules for each open pit limit. Divorcing the open pit limit delineation from the NPV calculation in this two-step approach does not guarantee that an optimal NPV open pit solution will be found. A new open pit optimisation algorithm that considers the mining schedule is proposed. As a consequence, it can also account explicitly for commodity price cycles and uncertainty that can be modelled by stochastic simulation techniques. This state-of-the-art algorithm integrates Monte Carlo-based simulation and heuristic optimisation techniques into a global system that directly provides NPV optimal pit outlines. This new approach to open pit optimisation is demonstrated for a large copper deposit using multiple orebody models.

A method that optimizes mining complexes which are comprised of multiple processing destinations, open pits and underground operations is presented. Mining, blending, processing and transportation decision variables are simultaneously optimized while accounting for geological uncertainty. The method uses a simulated annealing algorithm at different decision levels in order to generate a stochastic-based extraction sequence and processing policies. A case study shows its ability to generate a higher NPV while facing a reduced amount of risk when compared to traditional optimization methods.

An export supply chain, beginning with the extraction of ore from a pit and ending with the loading of this ore onto vessels at a port, is a key component of many mining operations. These supply chains are comprised of a number of complex subsystems such as mining, ore processing, transportation, stockyard management and vessel loading. Typically, the operation and performance of each of these subsystems is analysed in isolation, with little consideration of their interaction with upstream and downstream subsystems. In reality, stochastic and dynamic influences that affect one of these subsystems will have flow on effects for all other subsystems in the supply chain. Hence, evaluation of the performance of the total integrated system needs to capture the interaction of these subsystems. Discrete Event Simulation (DES) has proved to be a powerful tool in modelling supply chains, capturing the system dynamics and interactions, and evaluating the overall performance of the integrated system. The primary objective of mining export supply chains is typically to maximise production capacity, i.e. tonnes of ore loaded onto vessels at the port. In some mining operations, the extracted ore is blended into a variety of products with differing characteristics before being exported. This can be the case for ores such as coal, iron and manganese. In these operations, an additional objective, in the form of achieving a predetermined quality of material on the vessels, is equally important as a measure of system performance as production capacity. The objective of delivering a certain quality of product often conflicts directly with the objective of maximising production capacity, resulting in an increased level of complexity within the supply chain. In these supply chains, the decision-making process of planning the movement and blending of ore through the system is paramount to the overall system performance. Capturing this complex planning process in a DES modelling language is possible, but proves to be a very difficult and time-consuming task. Since planning problems are often modelled and solved using an optimisation framework, an alternative approach is to decouple the decision-making process from the simulation model, develop a stand alone optimisation model for it, and then integrate the two to create a holistic model of the supply chain. This paper describes the approach taken and presents a case study of a successful implementation on the export supply chain of PT Kaltim Prima Coal (KPC) in Indonesia.

Mining companies seek to mine, route and process ore to make the most efficient use of capital equipment during the life of the mine. The situation analysed in this paper relates to optimisation of medium-term production strategy for a group of mines and metallurgical plants. Typical operations under this scenario involve mining of crude ore from shafts and/or open pits; transportation of ore to the milling plants, run-of-mine stockpiles and leach-pads. The concentrate from the mill(s) is sent to the smelters and refineries, from where the finished metal is sent to the markets. If one assumes that the grade of run-of-mine ore varies according to source and that the milling plants are designed to handle different types of ore, plus the fact that mines and plants may separate by considerable distances, optimisation of the production plan becomes imperative. Most of the publications dealing with the subject of mine production planning are limited to mine scheduling optimisation and do not include metallurgical plants. However, the nature of the problem requires the application of a model that incorporates all the elements of the mineral production system. The methodology outlined in this paper is based on a Network Linear Programming formulation of the production-planning problem for a mining and metallurgical complex. Network LP models are particularly useful in analysing production-distribution type systems such as the one involving a group of mines and metallurgical plants. The problem is formulated using the theory of dual-primal relationships in linear programming. The solution algorithm finds the minimum cost of production and distribution, hence the optimal production and material routing plan for a group of mines and metallurgical plants. The graphs of optimality conditions for each arc in the network could be exploited as a tool for strategic mine planning. The advantages of this formulation are outlined and its application is demonstrated using a hypothetical situation involving an integrated mining and metallurgical complex, specifically six mines, five concentrators, three smelter and two copper refineries. A computer program called Linear Integer Discrete Optimiser (LINDO) is used to solve the network linear programming model. This program allows the user to quickly input an LP formulation, solve it and perform ‘what if’ type analyses.

This paper presents an iterative Net Present Value (NPV) maximization method to determine the optimum surface to underground transition depth for an ore body to be mined by multiple open pits and an underground mine. The determination of transition depth from open pit to underground mining is based on global production scheduling optimization of open pit and underground mines using Mixed Integer Linear Programing (MILP). The method is applied to a case study coming from a gold mining complex with six open pits and a large underground mine using long hole open stoping. The results indicate potential improvements of the NPV of global operations when compared to the traditional techniques based on independently optimized open pit first, followed by the underground mining.

Dynamic market and operating conditions coupled with an environment in which multiple objectives and trade-offs are common, pose major challenges for planners and schedulers working in any mining entity. Many mining companies recognise the need to shift from a siloed mining-focused push model to an integrated value chain, demand-driven approach but there are still fundamental barriers in business process and the supporting technology preventing a consideration of end-to-end optimality. This paper presents some elements of experiences working with companies to adopt such advanced approaches. In addition to algorithmic elements, an approach to phased and gradual deployment of progressively more sophisticated optimisation models is described. From a practical software adoption perspective, it is believed that this last concern is also of primary importance. Next generation approaches to the optimisation of complex bulk commodity demand chains; namely iron ore and coal are presented, with case studies in the world’s largest integrated operations in Western Australia and Queensland from the raw material mined through to market. Utilising accurate simulation models supported by metaheuristic optimisation techniques, a range of ways to engineer a dynamic decision support framework that can adapt and change with the inevitable changes in commodity markets is explored. Objectives such as total revenue, margin, cost, NPV, throughput, asset utilisation, contractual penalties and bonuses, and energy consumption can be managed simultaneously across the mine, plant, logistics network, port operation, shipping and sales domains.

Prior to the acquisition of data from production drilling and grade control sampling, the spatial density of data is usually insufficient to properly address issues related to short-scale variability. Grade interpolation, whether conducted through ordinary kriging or other linear or non-linear regression techniques, usually suffers from significant over-smoothing or conditional bias. Four examples presented in this paper show that conditional simulations provide a viable and powerful alternative in assessing the sensitivity of key variables that are critical to the decisions made prior to moving forward with significant capital expenditures. These variables include the selection of the most appropriate mining method and mining equipment, the optimum cut-off strategy and the short-term variability constraints on process plant feed. The results also demonstrate that conditional simulations can be used to assess the risk associated with many of the technical aspects of the project and its financial performance.

Development of mineral resources is based on a spatial model of the orebody that is only partly known from exploration drilling and associated geological interpretations. As a result, orebody models generated from the available information are uncertain and may require the use of stochastic or geostatistical simulation techniques. Multiple-point methods have been developed for petroleum reservoir modelling enabling reproduction of complex geological geometries for ore bodies. This paper considers a multiple-point approach to capture the uncertainty of the lithological model at the Yandi channel iron ore deposit, Western Australia. Performance characteristics of the method for the application are discussed. It is shown that the lithological model uncertainty translates into considerable grade-tonnage uncertainty and variability that is now quantitatively expressed.

The application of conditional simulation techniques for modelling orebodies requires efficient algorithms, particularly due to the large number of grid nodes required, often in order of tens of millions. In this paper, two new efficient conditional simulation methods are reviewed: the generalised sequential Gaussian simulation (GSGS) and the direct block simulation (DBSIM). Both methods gain computational efficiency by simulating groups of nodes simultaneously, using a local neighbourhood as the conditioning data set. The relationship between the group and local neighbourhood sizes used is found to be important to both the accuracy of results and processing efficiency, and it is assessed numerically through a measure of the loss of accuracy. Practical aspects of the GSGS are demonstrated and assessed in a case study at a porphyry copper deposit. Computational efficiency is demonstrated in the case study involving orebody models with up to 14,000,000 grid nodes, where the method is up to 20 times faster than the well-established sequential Gaussian simulation. At the same time, GSGS maintains a high level of accuracy. The practical aspects of DBSIM are demonstrated in simulating the same copper deposit in a comparable way to GSGS. In the case study, the computational efficiency of DBSIM is marginally better than GSGS; however, there are two major improvements. First, the application of DBSIM results in a substantial reduction of storage requirements and leads to improved data management. Second, the validation of the reproduction of variogram models is performed at the block support scale, which leads to a substantially more efficient variogram validation process than at the point support scale. Both methods, GSGS and DBSIM, provide efficient and reliable tools for practitioners to assess geological uncertainty in large mining applications.

To speed up multivariate geostatistical simulation it is common to transform the set of attributes into spatially uncorrelated factors that can be simulated independently. The main method in recent years has been minimum/maximum autocorrelation factors, either based on the coefficient matrices of a two structure linear model of coregionalisation (LMC) or on a pair of experimental covariance matrices. In both cases there is an underlying assumption that the covariance structure of the data set can be adequately modelled using a two structure LMC. We consider an extension that removes the restriction imposed by this assumption by using the experimental matrices for a larger set of lags. The method relies on an iterative algorithm that approximately diagonalises a set of symmetric matrices, and is referred to as the Alternating Columns-Diagonal Centres method. We use the Jura data set to evaluate the extent to which factors obtained from each method are spatially decorrelated and to assess the effect of the transformation method on the simulated attributes.

This paper provides an assessment of the current challenges in strategic mine planning and design and suggested approaches for addressing them. The specific challenges covered are: (1)Realistic quantification of downstream processes applied to orebody models to provide an integrated approach to mine design and optimisation.(2)Modelling, estimation and simulation of geometallurgical variables and their integration into resource and reserve estimation and mine planning.(3)Modelling, estimation and simulation of new variables for new forms of mining—deep mining, particularly block caving, and solution mining.(4)Flexibility in planning and design to manage risk and minimise its impact.(5)IT infrastructure and platforms for rapid on-line data collection, storage, access and processing.Most of these challenges require new types of data, variables, modelling and estimation methods. Foremost among the new types of variables and data are geometallurgical and dynamic rock mass characterisation variables. New types of data and data collection include rapid generation of very large amounts of on-line sensor data and the consequent need for rapid processing and modelling of these data. This paper outlines the challenges and strategies in each of these areas and uses examples of models and outputs to illustrate approaches and potential solutions.

The full potential of geostatistical simulation as a tool for planning, designing and optimising production is only realised when it is integrated within the entire design and production cycle. In the planning and design stages this involves the simulation of components of the production cycle that depend on (simulated) grades and geology. In the production stage it involves integration with the mining method and the type and use of equipment. This paper explores the general concepts of integrated geostatistical simulation and illustrates them with particular reference to blast design, equipment selection and the associated quantification of ore loss, ore dilution and the ability to select ore on various scales. The critical component of most metalliferous open pit mining operations is ore selection, i.e. the minimisation of ore loss and ore dilution during extraction. In general, extraction comprises drilling, blasting and loading, all of which are planned and designed on the basis of uncertain models of geology and grade. The application describes the integration of geostatistically simulated grade, geological and geomechanical models with blast modelling to provide a link between the estimated in situ characteristics of the orebody and the locations of the same (displaced) characteristics following the blast. This approach provides a means of evaluating different types of selection and thereby enables planners to optimise the selection process in terms of blast design, type and size of loading equipment, maximisation of ore recovery and minimisation of ore loss and dilution. This conversion of the in situ/block model resource to a realistically recoverable reserve may, in many instances, be the most significant source of uncertainty in reserve estimation.

Geometallurgical modelling of an orebody provides benefits to a mine by gaining a better understanding of the ore characteristics and how these affect the performance of the concentrator. With this knowledge, plant operating conditions can be adjusted to optimise throughput and recovery in advance of the arrival of particular ore types. Therefore it is extremely important that the origin of the ore being processed is known as accurately as possible. Depending on the homogeneity of the ore characteristics, reliance on assumptions about stockpile residence times, scheduling and material handling can render the best geometallurgical models useless. The solution adopted at Kittilä was to utilise Metso SmartTags™ and in-house expertise to develop a system that continuously and accurately links geotechnical and lab data from the mine to the performance of the plant. This application presented several unique opportunities and challenges. For example, this was the first installation of a SmartTag™ system for geometallurgical modelling in an underground mine. Challenges included the fact that the system installation is routinely subjected to temperatures below −20 ℃. The system was installed and commissioned in early 2013 and has been operating continuously since. Kittilä has begun to see the benefits of the system with an increased understanding of how different ores are processed in the concentrator. Other advantages include the ability to alert operators about the arrival of difficult ores and a better understanding of their ore handling systems. This paper describes the installation and use of the system at Kittilä, and details some of the geometallurgical relationships that have been developed using the data collected so far.

The Ban Houayxai Mine (BHX) is a relatively low grade, low cost, open pit gold-silver deposit in Laos operated by Phu Bia Mining, a subsidiary of PanAust. Ore production rate is 4.5Mt pa with direct tipping to a SAB mill with a carbon in leach process plant. Approximately 100,000 oz of gold is produced per annum. The operation is located in mountainous terrain with minimal ROM stockpiling are which results is limited capacity for blending from stockpile with the mill instead reliant upon direct feed ex-pit. Since commissioning in 2012, the plant has seen significant variation in milling rates due to variability in the feed properties of the oxide, transition and primary ores. As part of an ongoing continuous improvement program, an integrated approach was initiated focussing on maintaining and enhancing production in the future as the proportion of harder primary ore increases with focus on direct blending from the loading face using the ore properties and blast fragmentation to maintain mill throughput. This approach was based on the concept of physical assets management, commencing with improving information and knowledge of the condition of the ore body through modelling the characteristics, variability and performance of the feed for processes relevant to throughput. These models are used to support both mine and process plant production planning. The key ore feed characteristics and parameters modelled for the life of mine are blastability index (BI), powder factor, crushability or impact resistance (A*b) and grindability (BWi). These predictive spatial models were based on the data from diamond drill holes used in resource definition and geotechnical drilling programs by integrating geotechnical, geological, geochemical and metallurgical data. Although, at the early stages of implementation, the models are being utilised for ore blending decisions, to provide guidance and support for budgeting, long term mine planning, blast design for mill feed and providing the mill with an expectation of performance.

In order to quantify the uncertainty in the grade estimate for the Sadiola deep sulfide prefeasibility project, a conditional simulation model was generated using the direct block simulation methodology. Compared to conventional sequential Gaussian simulation, the direct block simulation algorithm produced a reliable model in significantly less time, lending its application to a production environment. Through application of a mining transfer function, risk pits were generated for comparison with the deep sulfide prefeasibility pit. The results of this study revealed that the prefeasibility pit is optimal at the applied gold price and cost parameters, and that the risk of not achieving the project grade profile is low. Should the gold price increase, or the operating costs of the project decrease significantly, the deep sulfide reserve tonnage would realise significant upside potential. Probability and uncertainty analysis revealed that the greatest risk to the project is the confidence in the footwall grade estimate. At a drill spacing of 50 m × 50 m and a sample interval of 1 m, the probability of the footwall grade exceeding the economic cut-off of 2.0 g/t is low, while the uncertainty in the grade estimate is high. Although significantly lower in grade than the main zone, which is the primary economic driver of the project, the footwall mineralisation is important in terms of reducing stripping ratio and delivering ore tonnes to optimise the treatment schedule. This zone is therefore a focus area for further drilling.

The use of conditional simulation to characterize mine plan uncertainty is gaining more use for assessment of risk in mining projects. While the development of grade uncertainty profiles is relatively straightforward and can be validated using standard geostatistical techniques, the addition of geological uncertainty to evaluate total risk remains problematic. Some of the problems associated with geological uncertainty methods include the clustering of data in favourable geologic units, difficulty in training image definition, and the inability to address change of support issues for categorical variables. Despite these obstacles the importance of geological uncertainty as a contributor to total uncertainty has prompted Newmont to explore and evaluate the use of various techniques (and combinations of techniques) on different deposit types. Two orogenic deposits of different geological complexity were selected for the study: Subika, a shear zone hosted deposit and Merian, a deposit containing gold mineralisation associated with quartz vein zones and stockwork within which are found higher-grade quartz breccia zones. Newmont trialed various categorical simulation approaches to determine the applicability of these methods for each deposit type and the effect of parameter choice on the width of the uncertainty interval. Some of the techniques that were trialed include Multiple Point Statistics (MPS) methods, Sequential Indicator Simulation using local probabilities (SIS-lvm) as well as variations of these methodologies. Goals of this study included: (1) an understanding of which techniques may work best in which deposit types, (2) an understanding of the intricacies of each method, (3) and an understanding of the effect each method used has on total uncertainty analysis. This paper presents a comparison of the various techniques and makes recommendations for their use in uncertainty analysis.

Research in the field of cut-off grade optimisation has shown a relationship between cut-off grade, project life and Net Present Value. Lane’s theory demonstrates that cut-off grades can be optimised in order to maximise project profitability. Although the theory forms the basis for many open pit mining projects, application of the theory in underground mining remains limited to-date. The main reason for this is the complex interaction between all processes in underground mine planning which makes it difficult to apply Lane’s mathematical optimisation approach. Recently a new Stope Optimiser product was released. The AMS Stope Optimiser automates the design of underground stopes at user defined cut-off grades and allows for rapid evaluation of mine designs at different cut-off grades. Using this software, an optimisation approach was developed and validated on an underground gold deposit in northern Sweden. Potential project NPV increased by approximately 30% when using this new approach. Spatial grade uncertainty in mineral resources was identified to be a major risk in underground stope design. The optimisation approach was further extended to account for grade risk using estimated and stochastic simulated resource models. The resulting optimisation process accounts for grade risk early in the design process and reduces the risk of a stope not meeting the cut-off grade with subsequent financial loss.

Classifications of mining methods date back to the 1960s and use the following criteria: type and size of a mineral deposit, mined-out space support, state of a working excavation, type of a face, roof support, etc. Since that time mobile mining machinery has appreciably advanced, and some mining methods have lost their importance. Mobile mining equipment is effective in definite mining methods: in open mined-out space, mining with backfill and combined schemes. The transition to deep mining inevitably results in the sharply worsened technical and geomechanical conditions, and some well-established techniques for safe mining at rock burst hazardous deposits can not be considered self-sufficient. This paper puts forward a classification of deep mining methods, considering rock pressure control. The classification involves three classes: mining with backfill, mining with caving of overlying rocks and combined mining with backfill and caving.

Decisions in the mining industry are made in the presence of uncertainty whether it is in the form of technical, financial or environmental risk. In recent years, the main focus of uncertainty has been the mineral resource. Methods for assessing and quantifying grade risk in open pit operations has lead to the ability to forecast problems and improve the design and planning process by integrating this risk. This paper successfully implements these risk-based methods in an underground stoping environment using data from Kidd Creek Mine, Ontario, Canada. Risk is quantified in terms of the uncertainty a conventional stope design has in contained ore tonnes, grade and economic potential. A mathematical formulation optimising the size, location and number of stopes in the presence of uncertainty is introduced and applied. The implementation of different geostatistical simulation methods to the optimisation formulation is discussed briefly and observations made.

The Callie underground mine, located in the Tanami Desert in the Northern Territory, includes two parallel declines accessing a large orebody extending some two kilometres below the surface. One of several ideas considered in strategic mine planning is to incorporate a vertical hoisting shaft and an orepass as an alternative to trucking material to the surface along the declines. In this work, we use network optimisation techniques to investigate the feasibility of the proposed system, and to mathematically determine the optimum positions and geometry of the shaft, orepass and surrounding infrastructure. We propose a modelling procedure taking aspects from a mathematical problem, called the Fermat-Weber problem, which asks for a point minimising the sum of weighted distances to a given set of points. We describe the implementation of the procedure into a computer program for solving the problem iteratively, and present results over a range of infrastructure and haulage costs, decline gradients and life-of-mine (LOM) schedules.

To date, the scheduling and access design of an underground mine have only been considered as two separate optimisation problems. First, access to the mine is designed and then the scheduling is completed. One drawback of this approach is that the costs of access construction fail to be reflected in the Net Present Value (NPV) calculation. In this paper, designing the access and scheduling its construction are formulated as a single optimisation problem. The underground mine access construction process can be classified according to the number of faces being developed concurrently. An underground mine with a single decline branching at a junction point into two declines is considered. After construction reaches the junction, the two faces of the decline can be constructed sequentially or concurrently. This paper proposes an efficient algorithm for optimally locating a junction point to maximise the NPV where two faces are being developed concurrently. The NPV is defined by taking the locations of ore bodies and their values, decline construction costs, decline development rate and discount rate into account. The variation of the NPV and the optimal locations of the junction point for one and two concurrent development faces for a range of discount rates are discussed and compared. The proposed algorithm is applied in a simulated case study based on hypothetical values for an underground mine.

A long-term production schedule for the LabMag iron ore deposit in northern Quebec, Canada is derived using stochastic integer programming. The optimization formulation maximizes the schedule’s net present value, while simultaneously managing the risk of deviations in production tonnages and qualities by considering stochastic simulations of the orebody instead of a single deterministic model. The formulation also smooths and minimizes haul truck requirements and ensures that as mining progresses, space is created within the mined out pit for the return of waste material.

As open-pit mining of a deposit deepens, the cost of extraction may increase up to a threshold where transitioning to mining through underground methods is more profitable. This paper provides an approach to identify an optimal depth at which a mine should transition from open-pit to underground mining. The value of a set of candidate transition depths is investigated by optimizing the production schedules for each depth’s unique open-pit and underground operations. By considering the sum of the open-pit and underground mining portion’s value along with the cost of transitioning corresponding to each candidate transition depth, the optimal transition depth can be identified. The optimization model presented is based on a stochastic integer program that integrates geological uncertainty. As an input, the stochastic integer program utilizes a set of several stochastic simulations that represent equally probable scenarios of the mineral resource. This group of simulations describes the uncertainty in the deposit while the optimizer aims to maximize value based on discounted profits of both the open-pit and underground components of the deposit.

This paper proposes a new multi-resource multi-stage scheduling problem for optimising the open-pit drilling, blasting and excavating operations under equipment capacity constraints. The flow process is analysed based on the real-life data from an Australian iron ore mine site. The objective of the model is to maximise the throughput and minimise the total idle times of equipment at each stage. The following comprehensive mining attributes and constraints have been considered: types of equipment; operating capacities of equipment; ready times of equipment; speeds of equipment; block-sequence-dependent movement times of equipment; equipment-assignment-dependent operation times of blocks; distances between each pair of blocks; due windows of blocks; material properties of blocks; swell factors of blocks; and slope requirements of blocks. It is formulated by mixed integer programming and solved by ILOG-CPLEX optimiser. The proposed model is validated with extensive computational experiments to improve mine production efficiency at the operational level. The model also provides an intelligent decision support tool to account for the availability and usage of equipment units for drilling, blasting and excavating stages.

A mine landform progression plan can provide a clear outlook of the entire mining operation. To produce such an output requires detailed placement schedule of the mined material, including the volume (or tonnage) and the allocated dumping location. However, current practise mainly focuses on the ore production, over-simplifying the waste material scheduling. As a result, a rock dump is often treated as a single point in long term planning, making it difficult to predict the progression pattern over the life of mine. Without such a guidance, it is almost impossible to carry out progressive rehabilitation of the waste rock dumps. The lack of dumping schedule could cause delay in development construction, i.e., tailing storage facility (TSF) and ROM-pad. Other downstream effect due to the over-simplification is inaccurate estimation of required truck hours, which could have huge financial impact on the operation. In this paper, mixed integer programming (MIP) models of different objective functions, i.e., maximise truck productivity by minimising the overall haulage distance, minimise required truck deviation between adjacent years, and a hybrid between the two objectives, are utilised to generate the long term optimum rock placement schedules under the criteria of satisfying site specific conditions. All three MIP models are implemented in a large scale open pit mine. The numerical solutions from the models forms three different rock placement schedules, based on which, the yearly truck requirements are easily calculated and compared. The graphical results show the three corresponding landform progression patterns over the life of mine, providing the optimised long term forecast of the operation.

One of the main steps during the decision-making process of long-term mine planning is the definition of the optimal sequence of extraction, which usually is synonymous of maximizing the discounted cash flow of the project subjected to several constraints arising from aspects of technical, physical, and economic limits. The Open-Pit Mine Production Scheduling (OPMPS) comprises several intricacies related to its size and uncertainty of input parameters. Due to its complexity and prohibitive size, traditional mine planning usually relies on heuristic or metaheuristic methodologies which are able to provide good solutions in a reasonable amount of time. However, most of the uncertainty that surrounds the mining complex is ignored leading to non-realistic results. In this paper, a new heuristic approach is explored in order to solve a stochastic version of the OPMPS problem accounting for geological uncertainty in terms of metal content, multiple processing streams, and stockpiling option. The methodology involves generating an initial solution by solving a series of sub-problems and this initial solution is improved using a network-flow based algorithm. The algorithm was applied to a relatively large gold deposit with more than 119 thousands blocks. Results have shown that the methodology is promising to deal with large-size mine instances in reasonable time.

One of the primary objectives when optimising a mining complex is to maximise its value for the primary stakeholders. In order to achieve this objective, it is necessary to holistically optimise all aspects of the mining complex, including decisions of when to extract materials from the available sources, how to blend or stockpile these materials, and how to best use the available processing streams to satisfy customer demand. Existing methods for global, or holistic, optimisation ignore the compounded effects that risk has on the performance of a mining complex. Over the past decade, several stochastic optimisation approaches have been proposed to integrate various forms of uncertainty into the open pit mine design and production scheduling. These methods, however, are limited in their ability to simultaneously optimise the production schedules for the portfolio of mines, material destination policies, the use of the available processing streams and the various products that are produced at each location of the mining complex. This paper aims to discuss a new method for the global optimisation of open pit mining complexes with geological uncertainty. The proposed generalised methodology is capable of modelling and holistically optimising mining complexes, including aspects related to production scheduling, blending, stockpiling and non-linear interactions that often occur in practice, but are over-simplified in existing models. Two case studies are discussed to highlight the need for these complex, stochastic optimisers. First, a case study for a nickel laterite blending operation highlights the need to integrate geological uncertainty into the optimisation in order to ensure product quality constraints are respected. Second, a case study for a copper-gold mining complex highlights the added value when simultaneously optimising the production schedule and the stockpiling and treatment of extracted materials.

The flow of information and consequently the decision making along the chain of mining from exploration to beneficiation typically occurs in a discontinuous fashion over long time spans. In addition, due to the uncertain nature of the knowledge about the deposit and its inherent spatial distribution of material characteristics actual production performance in terms of produced ore grades and quantity and extraction process efficiency often deviate from expectations. Reconciliation exercises to adjust mineral reserve models and planning assumptions are performed with timely lags of weeks, months or even years. With the development of modern Information and Communication Technology over the last decade, literally a flood of data about different aspects of the production process is available in a real-time manner. For example, sensor technology enables online characterisation of geochemical, mineralogical and physical material characteristics on conveyor belts or at working faces. The ability to utilise the value of this additional information and feed it back into reserve block models and planning assumptions opens up new opportunities to continuously control the decisions made in production planning to increase resource recovery and process efficiency. This leads to a change in paradigm from a discontinuous to a near real-time reserve reconciliation and model updating, which calls for suitable modelling and optimisation methodologies to quantify prior knowledge in the reserve model, to process and integrate information from different sensor-sources and accuracy, back propagate the gain in information into reserve models and efficiently optimise operational decisions real-time. This contribution introduces the concept of an integrated closed-loop framework for Real-Time Reserve management (RTRM) incorporating sensor based material characterisation, geostatistical modelling under uncertainty, modern data assimilation methods for a sequential model updating and mining system simulation and optimisation. The effectiveness of the framework and the value added will be demonstrated in an illustrative case study.

Geometallurgical parameters are descriptions of the mineralogy and microstructure of the ore determining its mineralogical and microstructural characteristics. From a conditional geostatistical simulation of such properties, a processing model can compute recovery, equipment usage, processing costs, and thus the monetary value for mining and processing a block with certain processing parameters. The output can be used for optimising mining sequences or finding optimal processing parameters by solving the corresponding stochastic optimisation problem. The approach requires two properties of the simulation not provided by established geostatistical techniques: (1)Many relevant geometallurgical parameters are from non-Euclidean statistical scales such as (mineral) compositions, (grain size) distribution, (grain) geometry, and (stratigraphic type) categorical which might produce nonsensical values (for example, negative proportions, negative facies probabilities, planar grains) when simulated with standard geostatistical techniques.(2)Due to the nonlinearity of processing, the entire conditional distribution of the geometallurgical parameters is relevant, not only its mean and variance. The geostatistical simulation needs to reproduce the joint conditional distributions of all the geometallurgical parameters.The multi-point conditional geostatistical simulation technique discussed here allows for jointly simulating dependent spatial variables from various sample spaces. The technique combines an infill simulation, similar to the one used in multi-point geostatistics (MPS), with a new form of distributional regression to estimate conditional distributions of arbitrary scales from different information sources, including training images, training models and observed data. The distributional regression is based on a generalisation of logistic regression and is related to both Bayesian Maximum Entropy (BME) geostatistics and high order cumulants. The method ensures that simulated data reside in the set of possible values and honour the characteristics of the joint distribution to be reproduced. The computational effort is substantial, but affordable for a useful application with standard problems: from processing-aware block value prediction and block processing optimisation as shown in the test application to a mathematically completely defined simulated model situation with a complex processing model.

Earth sciences and engineering phenomena such as geologic units, grade content and other properties of a mineral deposit, as well as attributes of other natural phenomena, represent complex geological systems distributed in space. Their spatial distributions are currently predicted from finite measurements and second-order spatial statistical models, which are limiting, as geological systems are highly complex, non-Gaussian and exhibit non-linear patterns of spatial connectivity. Non-linear and non-Gaussian high-order geostatistics is a new area of research based on higher-order spatial connectivity measures and spatial cumulants. Key elements of a high-order spatial stochastic modelling framework are developed herein, starting with the definitions of high-order spatial statistics and, more specifically, the definition and properties of spatial cumulants, and the inference and interpretation of high-order anisotropic cumulants. Spatial cumulants are shown to capture the directional multiple-point periodicity and spatial architecture of geological processes. It is further shown that only a subset of all the cumulant templates has to be computed to characterize complex spatial patterns. The second key element of high-order geostatistics is the simulation of complex mineral deposits using a nonparametric Legendre series approximation with coefficient calculated in terms of spatial cumulants. Examples show that the approach works very well.

A two-stage stochastic mixed integer non-linear program is formulated for a mining complex to optimize strategic and tactical plans. The objective is to find the near optimal decisions for a mineral supply chain in the context with uncertainties in both ore supply and the commodity market (price and demand). The endogenous spot price in the commodity market and long-term sales contracts are considered in the formulation of the mining complex’s optimization model and an ad hoc heuristic is developed to deal with the throughput- and head-grade-dependent recovery rate in processing plants. Numerical results indicate that the proposed heuristic is effective and efficient in numerical tests. Based on the proposed model and heuristic, a long-term contract design strategy is proposed for making decisions on the contract price and strategic investments. A shadow price based method is also proposed to evaluate the existing mining schedule.