JMS, Vol. 47, No. 2, 2011 (Special Issue)

CHIEF EDITOR’S FOREWORD

Special Issue on Strategic Mine Planning
Victor Oparin
Corresponding Member of the Russian Academy of Sciences
JMS Chief Editor
Institute of Mining
Siberian Branch, Russian Academy of Sciences
Novosibirsk, Russia

Dear Reader of the Journal!

It is an intention of the Journal Editorial Board to make the regular basis Special Issues of Journal of Mining Science to be devoted to the most significant and important achievements in the worldwide science and experience, annually presented and discussed at various international forums and meetings on mining, both in Russia and abroad.

Introduction at first hand to state-of-the-art progress and topical problem handling in the area of global mineral resource development will enable our Dear Reader to self-confidently navigate the «ocean» of information, concerning development strategy in mining countries all over the world, in the context of their singularity, and in terms of fixing specific practical targets in mining industry.

The drive power for the industrial development strategy in any country, the mineral wealth extraction is now at the level hardly imaginable barely a hundred years ago. Transnational streams of crude minerals and final products thicken and strengthen, and it is unthinkable to ignore and overlook the world market business environment.

Evidently, mining transfer to greater depths, apart from higher investment to maintain the extraction and treatment processes, is certainly going with ever growing risk caused by the catastrophic ground pressure.

In these days already, the international mining science is responsible for the future mining technology and machinery to be in use in the conditions of constraints imposed by Nature and under the incremental risk as a result of a Man’s industrial activity. These risk factors and constraints remain almost incognizable to natural philosophers.

The Interior of the Earth is comparable to the Interplanetary Space. The research into the Earth’s Interior complex structure, laws and behavior is a vital scientific field worldwide, which needs financial and administrative backing so that we are not to face the yet more elevated risk in mining in days to come!

As mining science and engineering professional throughout the world together with Professor Roussos Dimitrakopoulos in the course of our meeting at the International Symposium on «Orebody Modelling and Strategic Mine Planning: Old and New Dimensions in Changing World» (16 — 18 March 2009, Perth, Western Australia), the idea of having this Special Issue of the Journal of Mining Science was initiated. This would only be possible through the concernment and team effort between world leaders in the field of economics and stochastic modeling. By the way, such Special Issues may become a sort of analytical reviews of developments in the World Wide Mining Science.

The final article, which was not presented at the Orebody Modelling and Strategic Mine Planning Symposium in Australia, will, in my opinion, contribute to the precious selection of this Special Issue thanks to the courtesy of Professor Roussos Dimitrakopoulos. I appreciate much his effort and feel hopeful you will too, Dear Reader.

GUEST EDITOR’S FOREWORD

Special Issue on Strategic Mine Planning
Roussos Dimitrakopoulos
COSMO Stochastic Mine Planning Laboratory
McGill University
Montreal, Canada

It is a privilege to introduce this special issue of the Journal of Mining Science dedicated to the topic of Strategic Mine Planning under Uncertainty. This is arguably the backbone of the mining industry and represents a technically and scientifically intricate, complex and critically important part of mining ventures. In an ever-changing world, the sustainable development and utilization of mineral and energy resources needed to ensure global demand and supply of raw materials, metals and energy, is a critical problem that highlights the importance and role of Strategic Mine Planning.

Education underpins the transfer and acceptance of new technologies and concepts to both the current and next generation of mining researchers, academics and professionals. This special issue presents several related topics, and serves as an update to those in the field, as well as stress the critical importance to the mining profession of new leading-edge technologies that quantify uncertainty and manage risk in decision-making on a global scale. This uncertainty stems from both the uncertain supply of metal and future market demand. Given the high risk/high reward nature of mining and the current global economic environment, this issue highlights (i) new «leading-edge» technologies that add substantial value to mining assets, as well as mineral production, and (ii) knowledge dissemination related to these technologies in a rapidly changing world.

This issue comprises 12 articles covering several interrelated topics. The first set of papers start with an overview of a new stochastic mine planning paradigm, «Stochastic optimization for strategic mine planning» by the Guest Editor, followed by «leading-edge» industry practices by Rocchi et al. entitled «Sequence optimization technologies: Application to longwall coal mining». Zuckerberg et al. then discuss the «Optimization of life-of-mine production scheduling at a bauxite mine» as a new state-of-the-art optimization method based on mixed integer programming which is used at the industrial scale for life-of-mine planning. These articles are in a sense complemented by the paper entitled «A geology-based joint conditional simulation of a lateritic nickel deposit for quantification of risk in grade-tonnage curves and resource categorization» by Lopes et al. who unveil a general approach to quantifying geological uncertainty that, when available, can be used in mine planning.

Optimization solutions to typical key open pit mine production parameters are then discussed in, «Integrated open pit pushback selection and production capacity optimization» by Elkington and Durham , followed by a risk based approach in the paper «Accounting for joint ore supply, metal price and exchange rate uncertainties in mine design» by Abdel Sabour. The following paper then presents an intriguing application based on a novel combination of optimization and simulation entitled «Modeling the mining supply chain from mine to port» by Bodon et al., and it is followed by «A new methodology for flexible mine design» by Groeneveld and Topal.

The next set of articles are introduced with «Direct net present value open pit optimization with probabilistic models» by Richmond, who examines an extension for risk based concepts and approaches. This is followed by «A risk analysis based framework for strategic mine planning and design» by Godoy which outlines a key element of stochastic mine planning, and by «Optimal mining practice in strategic planning» which discusses King’s review of the interrelated components of strategic planning, sparse and uncertain information, limits of concepts, good practices and the enormous value of strategic planning. The issue concludes with «Hubbert’s theory and the ultimate coal production in the Kuznetsk coal basin» by Oparin and Ordin.

It is appropriate to stress that versions of most of the contributions in this issue were presented at an international symposium entitled «Orebody Modelling and Strategic Mine Planning,» held in March 2009, Perth, Australia, organized by the Australasian Institute of Mining and Metallurgy (AusIMM). The papers from this conference appear in the volume «Advances in Orebody Modelling and Strategic Mine Planning — I: Old and New Dimensions in a Changing World,» Spectrum Series Volume 17, AusIMM, Melbourne, which is available through the Institute for mining academics and professionals interested in this topic.

It is appropriate for me to thank the AusIMM and its staff for their collaboration, as well as acknowledge the substantial encouragement and support of leading-edge research in new stochastic modeling and optimization technologies for risk quantification and management in context of strategic mine planning by: AngloGold Ashanti, Barrick Gold, BHP Billiton, De Beers, Newmont Mining and Vale. Their relentless encouragement towards education and publication of new research results, particularly in the context of social responsibility, are also a major factor contributing to the production of this special issue.

Last but not least, I would like to thank Victor Oparin, Editor-in-Chief of this Journal, Leonid Nazarov, Associate Editor, and Inna Fadeeva of the Editorial and Translation Department for leadership and the opportunity they provided, as well as their hard work and support in producing this special issue.

STRATEGIC MINE PLANNING UNDER UNCERTAINTY

STOCHASTIC OPTIMIZATION FOR STRATEGIC MINE PLANNING: A DECADE OF DEVELOPMENTS
R. Dimitrakopoulos

Conventional approaches to estimating reserves, optimizing mine planning, and production forecasting result in single, and 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 optimization. These elements provide an extended mathematical framework that allows modeling 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 (i) can be about 15% larger in terms of total tonnage when compared to the conventional optimal pit limits, while (ii) adding about 10% of net present value to that reported above for stochastic production scheduling within the conventionally optimal pit limits. Results suggest a potential new contribution to the sustainable utilization of natural resources.

Mine planning, stochastic optimization, geological uncertainty, simulated annealing, production scheduling

REFERENCES
1. J. Whittle, «A decade of open pit mine planning and optimisation — the craft of turning algorithms into packages,» in: APCOM’99 Computer Applications in the Minerals Industries 28th International Symposium, Colorado School of Mines, Golden (1999).
2. M. David, Handbook of Applied Advanced Geostatistical Ore Reserve Estimation, Elsevier Science Publishers, Amsterdam (1988).
3. R. Dimitrakopoulos, C. T. Farrelly, and M. Godoy, «Moving forward from traditional optimization: grade uncertainty and risk effects in open-pit design,» Transactions of the Institution of Mining and Metallurgy, Section A: Mining Technology, 111 (2002).
4. A. G. Journel, «Modelling uncertainty: some conceptual thoughts,» in: Geostatistics for the Next Century, R. Dimitrakopoulos (Ed.), Kluwer Academic Publishers, Dordrecht (1994).
5. M. Kent, R. Peattie, and V. Chamberlain, «Incorporating grade uncertainty in the decision to expand the main pit at the Navachab gold mine, Namibia, through the use of stochastic simulation», The Australasian Institute of Mining and Metallurgy, Spectrum Series, 14 (2007).
6. M. C. Godoy and R. Dimitrakopoulos, «A risk analysis based framework for strategic mine planning and design — Method and application,» Journal of Mining Science, No. 2 (2011).
7. M. C. Godoy and R. Dimitrakopoulos, «Managing risk and waste mining in long-term production scheduling,» SME Transactions, 316 (2004).
8. H. Mustapha and R. Dimitrakopoulos, «High-order stochastic simulations for complex non-Gaussian and non-linear geological patterns,» Mathematical Geosciences, 42, No. 5 (2010).
9. S. A. Abdel Sabour and R. Dimitrakopoulos, «Accounting for joint ore supply, metal price and exchange rate uncertainties in mine design,» Journal of Mining Science, No. 2 (2011).
10. C. Meagher, S. A. Abdel Sabour, and R. Dimitrakopoulos, «Pushback design of open pit mines under geological and market uncertainties,» The Australasian Institute of Mining and Metallurgy, Spectrum Series No. 17 (2010).
11. R. Dimitrakopoulos, H. Mustapha, and E. Gloaguen, «High-order statistics of spatial random fields: Exploring spatial cumulants for modelling complex, non-Gaussian and non-linear phenomena,» Mathematical Geosciences, 42, No. 1 (2010).
12. B. D. Ripley, Stochastic Simulations, J. Wiley & Sons, New York (1987).
13. A. M. Law and W. D. Kelton, Simulation Modeling and Analysis, McGraw-Hill Higher Education, Singapore (1999).
14. R. Dimitrakopoulos and X. Luo, «Generalized sequential Gaussian simulation on group size and screen-effect approximations for large field simulations,» Mathematical Geology, 36 (2004).
15. H. Mustapha and R. Dimitrakopoulos «Generalized Laguerre expansions of multivariate probability densities with moments,» Computers & Mathematics with Applications, 60, No. 7 (2010).
16. A. Leite and R. Dimitrakopoulos, «A stochastic optimization model for open pit mine planning: Application and risk analysis at a copper deposit,» Transactions of the Institution of Mining and Metallurgy: Mining Technology, 116, No. 3 (2007).
17. F. Albor Consquega and R. Dimitrakopoulos, «Stochastic mine design optimization based on simulated annealing: Pit limits, production schedules, multiple orebody scenarios and sensitivity analysis,» Transactions of the Institution of Mining and Metallurgy: Mining Technology, 118, No. 2 (2009).
18. S. Ramazan and R. Dimitrakopoulos, «Stochastic optimisation of long-term production scheduling for open pit mines with a new integer programming formulation,» The Australasian Institute of Mining and Metallurgy, Spectrum Series, 14 (2007).
19. S. Ramazan and R. Dimitrakopoulos, «Production scheduling with uncertain supply — A new solution to the open pit mining,» COSMO Research Report, No. 2, McGill University, Montreal (2008).
20. M. Menabde, G. Froyland, P. Stone, and G. Yeates, «Mining schedule optimisation for conditionally simulated orebodies,» The Australasian Institute of Mining and Metallurgy, Spectrum Series, 14 (2007).
21. A. Leite and R. Dimitrakopoulos, «Production scheduling under metal uncertainty — Application of stochastic mathematical programming at an open pit copper mine and comparison to conventional scheduling,» The Australasian Institute of Mining and Metallurgy, Spectrum Series, 17 (2010).
22. S. Geman and D. Geman, «Stochastic relaxation, Gibbs distribution, and the Bayesian restoration of images,» IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-6, 6 (1984).
23. H. Lerchs and I. F. Grossmann, «Optimum design of open pit mines,» CIM Bulletin, Canadian Institute of Mining and Metallurgy, 58 (1965).
24. R. Dimitrakopoulos and S. Ramazan, «Stochastic integer programming for optimizing long term production schedules of open pit mines: methods, application and value of stochastic solutions,» Transactions of the Institution of Mining and Metallurgy, Section A: Mining Technology, 117, No. 4 (2008).
25. R. Dimitrakopoulos and S. Ramazan, «Uncertainty based production scheduling in open pit mining,» SME Transactions, 316 (2004).

SEQUENCE OPTIMIZATION IN LONGWALL COAL MINING
L. Rocchi, P. Carter, and P. Stone

BHP Billiton’s Illawarra Coal operates several longwall coal extraction systems in the Bulli and Wongawilli coal seams in the Southern Coalfields of the Sydney Basin, Australia. IC has applied a proprietary mixed integer linear programming open pit strategic mine planning tool called Blasor to rapidly evaluate, for a number of longwall mining domains, the jointly optimal underground development strategy and mining sequences necessary. For each development scenario, the Blasor optimizer maximizes the discounted operating cash flow as the objective function, subject to mining, processing, and transportation capacity constraints and product blend constraints. When applied to the underground longwall domain sequence optimization problem, Blasor evaluates a set of carefully considered scenarios, each describing a feasible underground development and transport strategy. In this application, Blasor plays the role of a fair valuation tool for each major scenario, by determining the most valuable extraction schedule for each development scenario. This establishes a basis for comparing the economic merits of competing scenarios that are structurally different.

Longwall mining, sequence optimization, economic evaluation, mixed integer programming

REFERENCES
1. M. Menabde, P. Stone, B. Law, and B. Baird, «Blasor — A generalized strategic mine planning optimization tool,» in: 2007 SME Annual Meeting, Society of Mining Engineers (2007).

OPTIMAL LIFE-OF-MINE SCHEDULING FOR. A. BAUXITE MINE
M. Zuckerberg, J. van der Riet, W. Malajczuk, and P. Stone

This paper describes a new optimized life-of-mine planning software tool called Bodor (Boddington Optimizer), developed for BHP Billiton’s Boddington Bauxite mine in south Western Australia. Bodor minimizes pre-tax net present cost (capital and operational) over a specified mine life, and is applied to a mine model consisting of bauxite pods pre-designed to a fixed cut-off grade, directly feeding a refinery with bauxite that meets grade and throughput targets in each period over the life-of-mine. Bodor has been very successful in its application to the Boddington mining operation, producing a new life-of-asset mine plan which delivers a significant reduction in net present cost. This value add is achieved primarily through a better timing of ore-body exploitation which optimally trades-off lower haulage costs against some capital costs that are brought forward. A core aspect of Bodor’s utility lies in managing various complex environmental constraints in determining the optimal extraction schedule.

Bauxite mining, planning optimization, environmental constraints, extraction schedule, truck fleet

REFERENCES
1. ILOG CPLEX v10, ILOG Inc, http://www.ilog.com/products/cplex/ (2007).

RISK QUANTIFICATION IN GRADE-TONNAGE CURVES AND RESOURCE CATEGORIZATION IN. A. LATERITIC NICKEL DEPOSIT USING GEOLOGICALLY CONSTRAINED JOINT CONDITIONAL SIMULATION
J. A. Lopes, C. F. Rosas, J. B. Fernandes, and G. A. Vanzela

The risk quantification in grade-tonnage curves is critical for capital investment in mining projects. Geostatistical simulations for orebodies can be used to obtain grade-tonnage curves, and determine uncertainty and risk assessments. Applying these in multi-element deposits can be a difficult practice, as the related attributes using the traditional co-simulation approaches require intensive computational work and may be impractical for use in the mineral industry. This paper presents the risk assessment for integrating grade-tonnage curves and resources categorization for lateritic nickel deposits in the central region of Brazil, by joint simulation of multiple correlated variables of interest: Ni, MgO and SiO₂. The joint simulation of these variables is based on Minimum/Maximum Autocorrelation Factors (MAF). Based on this approach, the resources are categorized honoring Ni joint simulated results by applying the 15 % rule, where it is considered there will be a statistical error < 15%, with 90% of a confidence interval per production period.

Grade-tonnage curves, lateritic nickel min/max autocorrelation factors, resource categorization, risk

REFERENCES
1. V. C. Deutsch and A. G. Journel, GSLIB: Geostatisitcal Software Library and User’s Guide, 2nd Edition, Oxford University Press, New York (1998).
2. G. W. Verly, «Sequencial Gaussian co-simulation: A simulation method integrating several types of information,» in: Geostatistics, Kluwer Academic Publishers, Dordrecht. Ed: A Soares, 5 (1993).
3. P. Goovaerts, Geostatistics for Natural Resources Evaluation, Oxford University Press, New York (1998).
4. J. P. Chiles and P. Delfiner, Geostatistics Modeling Spatial Uncertainty, John Wiley and Sons, New York (1999).
5. A. S. Almeida and A. G. Journel, «Joint simulation of multiple variables with a Markov-type coregionalization model,» Mathematical Geology, 26 (1994).
6. M. David, Handbook of Applied Advanced Geostatistical Ore Reserve Estimation, Elsevier, Amsterdam (1988).
7. A. J. Desbarats and R. Dimitrakopoulos, «Geostatistical simulation of regionalized pore-size distribution using min/max autocorrelation factors,» Mathematical Geology, 32 (2000).
8. P. Switzer, and A. A. Green, «Min/max autocorrelation factors for multivariate special imagery,» Technical Report 6, Stanford University, Department of Statistics (1984).
9. A. Boucher, and R. Dimitrakopoulos, «A new efficient joint simulation framework and application in a multivariable deposit,» Orebody Modelling and Strategic Mining Planning, Spectrum Series, 14, 2nd Edition, the AuSIMM, Melbourne (2007).
10. A. Boucher, and R. Dimitrakopoulos, «Block simulation of multiple correlated variables,» Mathematical Geosciences, 41 (2010).
11. R. Dimitrakopoulos, and M. B. Fonseca, «Assessing risk in grade-tonnage curves in a complex copper deposit, northern Brazil, based on an efficient joint simulation of multiple correlated variables,» in: Application of Computers and Operations Research in the Minerals Industries, South African Institute of Mining and Metallurgy (2003).
12. C. Dohm, «Quantifiable mineral resource classification: A logical approach,» in: Geostatistics Banff — Book Series Quantitative Geology and Geostatistics, Springer, 2 (2004).
13. R. Dimitrakopoulos and X. Luo, «Generalized sequential Gaussian simulation on group size and screen-effect approximations for large field simulations,» Mathematical Geology, 36 (2003).

INTEGRATED OPEN PIT PUSHBACK SELECTION AND PRODUCTION CAPACITY OPTIMIZATION
T. Elkington and R. Durham

Strategic mine planning for open pits has now evolved to the simultaneous optimization of a number of decisions and this leads to the consideration of additional solutions, with the potential to add value to planning and reduce manual data transfer time. Unlike previous efforts, this paper outlines a method for simultaneously optimizing mining and processing capacities, including intermediate and ultimate pushback selection, with the determination of scheduling, cut-off grade, and stockpiling to maximize net present value.

Mine optimization, mixed integer programming, open pit scheduling, cut-off grade, production rates

REFERENCES
1. T. Johnson, «Optimum open pit production scheduling,» PhD Thesis, University of California, Berkeley, USA (1968).
2. M. Gershon, «Optimal mine production scheduling: Evaluation of large-scale mathematical programming approaches,» Int. J. Mining Engineering, 1 (1983).
3. S. Ramazan and R. Dimitrakopoulos, «Recent applications of operations research in open pit mining,» SME Transactions, 314 (2004).
4. L. Caccetta and S. Hill, «An application of branch and cut to open pit mine scheduling,» J. Global Optimization, 27 (2003).
5. H. Lerchs and I. Grossman, «Optimum design of open pit mines,» Transactions of the CIM, 68 (1965).
6. J. Whittle and L. Rozman, «Open pit design in the 90’s,» in: Proceedings of Mining Industry Optimisation Conference, Australasian Institute of Mining and Metallurgy, Sydney (1991).
7. S. Ramazan and R. Dimitrakopoulos, «Stochastic optimization of long term production scheduling for open pit mines with a new integer programming formulation,» in: Orebody Modelling and Strategic Mine Planning, Spectrum Series, 14, 2nd Edition The Australasian Institute of Mining and Metallurgy (2007).
8. P. Stone, G. Froyland, M. Menabde, B. Law, R. Pasyar, and P. Monkhouse, «Blasor — Blended iron ore mine planning optimisation at Yandi,» in: Orebody Modelling and Strategic Mine Planning, Spectrum Series, 14, 2nd Edition The Australasian Institute of Mining and Metallurgy (2007).
9. S. Ramazan, «The new fundamental tree algorithm for production scheduling of open pit mines,» Eur. J. Operational Research, 177 (2007).
10. K. Lane, The Economic Definition of Ore: Cut-Off Grades in Theory and Practice, Mining Journal Books, London (1988).
11. B. King, «Optimal mine scheduling policies,» PhD Thesis, University of London, London (2000).
12. S. Hoerger, J. Bachmann, K. Criss, and E. Shortridge, «Long term mine and process scheduling at Newmont’s Nevada Operations,» in: Twenty-Eighth International Symposium on the Application of Computers and Operations Research in the Mineral Industry, Colorado School of Mines, Golden (1999).
13. M. Menabde, G. Froyland, P. Stone, and G. Yeates, «Mining schedule optimisation for conditionally simulated orebodies,» in: Orebody Modelling and Strategic Mine Planning, Spectrum Series, 14, 2nd Edition, Australasian Institute of Mining and Metallurgy, Melbourne (2007).
14. T. Elkington and R. Durham, «Open pit optimisation — Modelling time and opportunity costs,» Transactions of the Institution of Mining and Metallurgy, Section A: Mining Technology, 118 (2009).
15. R. Dimitrakopoulos, C. Farrelly, and M. Godoy, «Moving forward from traditional optimization: Grade uncertainty and risk effects in open-pit design,» Transactions of the Institution of Mining and Metallurgy, Section A: Mining Technology, 111 (2002).
16. R. Dimitrakopoulos and S. Ramazan, «Uncertainty-based production scheduling in open pit mining,» SME Transactions, 316 (2004).
17. M. Godoy and R. Dimitrakopoulos, «Managing risk and waste mining in long-term production scheduling of open-pit mines,» SME Transactions, 316 (2004).
18. S. Ramazan and R. Dimitrakopoulos, «Traditional and new MIP models for production scheduling with in-situ grade variability,» Int. J. Surface Mining, Reclamation and Environment, 18 (2004).
19. A. Leite and R. Dimitrakopoulos, «Stochastic optimisation model for open pit mine planning: Application and risk analysis at copper deposit,» Transactions of the Institution of Mining and Metallurgy, Section A: Mining Technology, 116 (2007).
20. A. Boucher and R. Dimitrakopoulos, «Block-support simulation of multiple correlated variables,» Mathematical Geosciences, 41 (2009).
21. R. Dimitrakopoulos and S. Abdel Sabour, «Evaluating mine plans under uncertainty: Can the real options make a difference?» Resources Policy, 32 (2007).
22. H. Taylor, Valuation and Feasibility Studies, Mineral Industry Costs, J. Hoskins and W. Green (Eds.), Northwest Mining Association, Washington (1978).
23. E. Topal, «Early start and late start algorithms to improve the solution time for long-term underground mine production scheduling,» J. Southern African Institute of Mining and Metallurgy, 108 (2008).

INCORPORATING GEOLOGICAL AND MARKET UNCERTAINTIES AND OPERATIONAL FLEXIBILITY INTO OPEN PIT MINE DESIGN
S. A. Abdel Sabour and R. Dimitrakopoulos

This work outlines a procedure for integrating uncertainty and operational flexibility into open pit mine design selection. A multi-criteria design ranking system based on advanced uncertainty and financial modeling techniques such as Monte Carlo simulation and real options is proposed. A case study at a copper mine is provided.

Mine design, economic evaluation, real options, Monte Carlo simulation

REFERENCES
1. J. Whittle, «Beyond optimization in open pit design,» in: Canadian Conference on Computer Applications in the Mineral Industries, Balkema, Rotterdam (1988).
2. S. Ramazan, «The new fundamental tree algorithm for production scheduling of open pit mines,» European Journal of Operations Research, 177 (2007).
3. R. Dimitrakopoulos and S. Ramazan, «Stochastic integer programming for optimizing long-term production schedules of open pit mines: Methods, application and value of stochastic solutions,» IMM Transactions, Mining Technology, 117 (2008).
4. M. W. A. Asad, «Multi-period quarry production planning through sequencing techniques and sequencing algorithm,» Journal of Mining Science, 44 (2008).
5. M. Zuckerberg, J. van der Riet, W. Malajczuk, and P. Stone, «Optimization of life-of-mine production scheduling at a Bauxite mine,» Journal of Mining Science, 47 (2011).
6. M. Vallee, «Mineral resource + engineering, economic and legal feasibility = ore reserve,» CIM Bulletin, 93 (2000).
7. R. Dimitrakopoulos, C. T. Farrelly, and M. Godoy, «Moving forward from traditional optimisation: grade uncertainty and risk effects in open pit design,» in: Transactions of the Institute of Mining and Metallurgy, Section A: Mining Technology, 111 (2002).
8. M. C. Godoy and R. Dimitrakopoulos, «Managing risk and waste mining in long-term production scheduling,» SME Transactions, 316 (2004).
9. A. Leite and R. Dimitrakopoulos, «A stochastic optimization model for open pit mine planning: Application and risk analysis at a copper deposit,» in: Transactions of the Institute of Mining and Metallurgy, Section A: Mining Technology, 116 (2007).
10. R. Dimitrakopoulos, L. S. Martinez, and S. Ramazan, «A maximum upside/minimum downside approach to the traditional optimization of open pit mine design,» Journal of Mining Science, 43 (2007).
11. R. Dimitrakopoulos and N. Grieco, «Stope design and geological uncertainty: Quantification of risk in conventional designs and a probabilistic alternative,» Journal of Mining Science, 45 (2009).
12. M. Godoy and R. Dimitrakopoulos, «A risk analysis based framework for strategic mine planning and design method and application,» Journal of Mining Science, 47 (2011).
13. P. H. L. Monkhouse and G. Yeates, «Beyond naive optimization,» in: Orebody Modelling and Strategic Mine Planning, Spectrum Series, 14, The Australian Institute of Mining and Metallurgy (2005).
14. L. T. Miller and C. S. Park, «Decision making under uncertainty-real options to the rescue?» The Engineering Economist, 47, No 2 (2002).
15. A.Moel and P. Tufano, «When are real options exercised? An empirical study of mine closings,» Review Financial Studies, 15, No. 1 (2002).
16. M. Samis, G. A. Davis, D. Laughton, and R. Poulin, «Valuing uncertain asset cash flows when there are no options: A real options approach,» Resources Policy, 30 (2006).
17. M. E. Slade, «Valuing managerial flexibility: an application of real option theory to mining investments,» Journal of Environmental Economics and Management, 41 (2001).
18. A. Boucher and R. Dimitrakopoulos, «Block-support simulation of multiple correlated variables,» Mathematical Geosciences, 41 (2009).
19. C. Scheidt and J. Caers, «Representing spatial uncertainty using distances and kernels,» Mathematical Geosciences, 41 (2009).
20. E. S. Schwartz, «The stochastic behaviour of commodity prices: implications for valuation and hedging,» Journal of Finance, 52 (1997).
21. F. A. Longstaff and E. S. Schwartz, «Valuing American options by simulation: a simple least-squares approach,» The Review of Financial Studies, 14 (2001).
22. S. A. Abdel Sabour and R. Poulin, «Valuing real capital investments using the least-squares Monte Carlo method,» The Engineering Economist, 51 (2006).
23. R. Dimitrakopoulos and S. A. Abdel Sabour, «Evaluating mine plans under uncertainty: Can the real options make a difference?» Resources Policy, 32 (2007).
24. S. A. Abdel Sabour, R. Dimitrakopoulos, and M. Kumral, «Mine plan selection under uncertainty,» Mining Technology: IMM Transactions Section A, 117, No. 2 (2008).
25. C. Meagher, S. A. Abdel Sabour, and R. Dimitrakopoulos, «Pushback design of open pit mines under geological and market uncertainties,» in: Orebody Modelling and Strategic Mine Planning, Perth, WA (2009).
26. J. Whittle, «A decade of open pit mine planning and optimization — The craft of turning algorithms into packages,» in: APCOM’99 Computer Applications in the Minerals Industries 28th International Symposium, Colorado School of Mines, Golden (1999).

MODELING THE MINING SUPPLY CHAIN FROM MINE TO PORT: A COMBINED OPTIMIZATION AND SIMULATION APPROACH
P. Bodon, C. Fricke, T. Sandeman, and C. Stanford

This paper describes a method for modeling a complex export supply chain using a combination of optimization and Discrete Event Simulation techniques to enable capacity analysis and evaluation of expansion options. A description of the modeling process is presented along with a case study of a successful implementation of the approach to analyze the export supply chain of PT Kaltim Prima Coal in Indonesia.

Mining supply chain modeling, discrete event simulation, optimization

REFERENCES
1. Y. Chang and H. Makatsoris, «Supply chain modeling using simulation,» International Journal of Simulation, 2, No. 1 (2001).
2. N. Anderson and G. W. Evans, «Determination of operating policies for a barge transportation system through simulation and optimization modeling,» in: Proceedings of the 2008 Winter Simulation Conference (2008).
3. B. P. Zeigler, H. Praehofer, and T. G. Kim, Theory of Modeling and Simulation, Academic Press (2000).
4. W. L. Winston, Operations Research: Applications and Algorithms, Duxbury Press (1987).
5. W. Hustrulid and M. Kuchta, Open Pit Mine Planning & Design, Taylor & Francis (2006).
6. L. A. Wolsey, Integer Programming, Wiley-Interscience (1998).
7. L. Schrage, Optimization Modeling with Lingo, LINDO Systems (2000).

FLEXIBLE OPEN-PIT MINE DESIGN UNDER UNCERTAINTY
B. Groeneveld and E. Topal

The risk associated with a mining project comes from the uncertainties involved in the industry. Mining companies endeavouring to maximize their return for shareholders make important strategic decisions which take years or even decades to «play out». However, many mining companies feel comfortable with point estimates of all project parameters but realize that no parameter value is known with certainty. A model that incorporates uncertainties and is able to adapt will help deliver a design with a better risk-return profile. In this paper, a new methodology is developed in order to have a design that is flexible and able to adapt with change. Following recent research on decision making methods in mine planning, this paper develops a mixed integer programming model that determines the optimal design for simulated stochastic parameters. The paper shows how to incorporate optionality (flexibility) in relation to mine, stockpile, plant and capacity constraint options. Obtained results are promising and are helping decision makers to think in terms of value, risk and frequency of execution.

Real options, robust design, uncertainty, flexibility, stochastic simulation, mine design

REFERENCES
1. E. Topal, «Evaluation of a mining project using discounted cash flow analysis, decision tree analysis, Monte Carlo simulation and real options using an example,» International Journal of Mining and Mineral Engineering, 1, No. 1 (2008).
2. P. A. Dowd, «Risk in minerals industry projects: perception, analysis and management,» Transactions of the Institute of Mining and Metallurgy, 106, No. A (1997).
3. R. Dimitrakopoulos, L. S. Martinez, and S. Ramazan, «A maximum upside/minimum downside approach to the traditional optimization of open pit mine design,» Journal of Mining Science, 43 (2007).
4. T. Elkington and R. Durham «Integrated open pit pushback selection and production capacity optimization,» Journal of Mining Science, 47, No. 2 (2011).
5. H. Mustapha and R. Dimitrakopoulos «High-order stochastic simulations for complex non-Gaussian and non-linear geological patterns,» Mathematical Geosciences, 42, No. 5 (2010).
6. A. Boucher and R. Dimitrakopoulos, «Block-support simulation of multiple correlated variables,» Mathematical Geosciences, 41 (2009).
7. M. Godoy and R. Dimitrakopoulos, «Managing risk and waste mining in long-term production scheduling,» SME Transactions, 316 (2004).
8. A. Leite, and R. Dimitrakopoulos, «A stochastic optimization model for open pit mine planning: Application and risk analysis at a copper deposit,» in: Mining Technology, Transactions of the Institute of Materials, Minerals and Mining, 116, No. 3 (2007).
9. S. Ramazan and R. Dimitrakopoulos «Stochastic optimization of long term production scheduling for open pit mines with a new integer programming formulation,» in: Orebody Modelling and Strategic Mine Planning, Spectrum Series AusIMM, 2nd Edition (2007).
10. A. Leite and R. Dimitrakopoulos, «Production scheduling under metal uncertainty-application of stochastic mathematical programming at an open pit copper mine and comparison to conventional scheduling,» in: Orebody Modelling and Strategic Mine Planning, Spectrum Series AusIMM, 2nd Edition (2009).
11. C. Meagher, S. A. A. Sabour, and R. Dimitrakopoulos, «Pushback design of open pit mines under geological and market uncertainties,» in: Orebody Modelling and Strategic Mine Planning, Spectrum Series AusIMM, 2nd Edition (2009).
12. R. de Neufville, S. Scholtes, and T. Wang, «Real options by spreadsheet: parking garage case example,» Journal of Infrastructure Systems, 12, No. 2 (2005).
13. R. de Neufville, «Analysis methodology for the design of complex systems in uncertain environment: Application to mining industry,» (unpublished) Engineering Systems Division, Massachusetts Institute of Technology (2006).
14. T. Wang and R. de Neufville, «Real options «in» projects,» in: Proceedings of the 9th Real Options Annual International Conference, Paris (2005).
15. T. Wang and R. de Neufville, «Identification of real options «in» projects,» in: Proceedings of the 16th Annual International Symposium of the International Council on Systems Engineering, Orlando (2006).
16. M. Cardin «Facing reality: Design and management of flexible engineering systems,» Masters (unpublished), Engineering System Divisions, Massachusetts Institute of Technology (2007).
17. M. A. Cardin, R.de Neufville, and V. Kazakidis, «A process to improve expected value of mining operations,» in: Mining Technology, Transactions of the Institute of Materials, Minerals and Mining, 117, No. 2 (2008).
18. B. Groeneveld, E. Topal, and B. Leenders, «A new methodology for flexible mine design,» in: Proceedings of the International Symposium on Orebody Modelling and Strategic Mine Planning, Perth (2009).
19. R. Dimitrakopoulos and S. A. Abdel Sabour, «Evaluating mine plans under uncertainty: Can the real options make a difference?» Resources Policy, 32, No. 3 (2007).
20. G. A. C. Lima and S. B. Suslick, «Estimating the volatility of mining projects considering price and operating cost uncertainties,» Resources Policy, No. 3 (2006).
21. C. Morley, V. Snowden, and D. Day, «Financial impact of resource/reserve uncertainty,» The Journal of the South African Institute of Mining and Metallurgy, No. 6 (1999).

EVALUATING CAPITAL INVESTMENT TIMING WITH STOCHASTIC MODELING OF TIME-DEPENDENT VARIABLES IN OPEN PIT OPTIMIZATION
A. Richmond

A new approach to optimizing the timing of capital investment in open pit mines is suggested and demonstrated in an application at a large copper deposit. The approach considers explicitly the uncertain nature of the commodity price cycle and operating costs that can be modelled via stochastic simulation techniques. The stochastic models of prices and costs are fed directly into either a set of nested pits or a direct net present value (NPV) optimization algorithm. This avoids divorcing the delineation of an open mine’s pit limit from calculating the related NPV that is common in traditional approaches.

Optimisation, economic evaluation, stochastic simulation, mining schedules

REFERENCES
1. H. Lerchs and I. F. Grossman, «Optimum design of open pit mines,» Bulletin of Canadian Institute of Mining, 58 (1965).
2. T. B. Johnson, «Optimum open pit mine production scheduling» PhD Thesis, University of California Berkeley (1968).
3. D. S. Hochbaum and A. Chan, «Performance analysis and best implementations of old and new algorithms for the open-pit mining problem,» Operations Research, 48 (2000).
4. L. Caccetta and S. P. Hill, «An application of branch and cut to open pit mine scheduling,» Journal of Global Optimization, 27 (2003).
5. S. Ramazan, «The new fundamental tree algorithm for production scheduling of open pit mines,» European Journal of Operations Research, 177 (2007).
6. P. H. L. Monkhouse and G. Yeates, «Beyond naive optimization,» Orebody Modelling and Strategic Mine Planning, AusIMM Spectrum Series, 14 (2007).
7. P. Stone, G. Froyland, M. Menabde et al., «Blended iron-ore mine planning optimization at Yandi Western Australia,» in: AusIMM Spectrum Series, 14 (2007).
8. A. J. Richmond and J. E. Beasley, «An iterative construction heuristic for the ore selection problem,» Journal of Heuristics, 10.2 (2004).
9. M. Menabde, P. Stone, B. Law, and B. Baird, «A generalized strategic mine planning optimization tool,» in: SME Annual Meeting and Exhibit (2007).
10. R. Dimitrakopoulos and S. A. A. Sabour, «Evaluating mine plans under uncertainty: Can the real options make a difference?» Resources Policy, 32 (2007).
11. M. Menabde, G. Froyland, P. Stone, and G. A. Yeates, in: Orebody Modelling and Strategic Mine Planning, The Australasian Institute of Mining and Metallurgy, Melbourne, Australia (2007).
12. S. Ramazan and R. Dimitrakopoulos, «Stochastic optimisation of long-term production scheduling for open pit mines with a new integer programming formulation,» in: Orebody Modelling and Strategic Mine Planning, 2nd Edition (2007).
13. A. Leite and R. Dimitrakopoulos, «A stochastic optimization model for open pit mine planning: Application and risk analysis at a copper deposit,» in: Transactions of the Institute of Mining and Metallurgy, Section A: Mining Technology, 116 (2007).
14. M. C. Godoy and R. Dimitrakopoulos, «Managing risk and waste mining in long-term production scheduling,» SME Transactions, 316 (2004).
15. P. J. Ravenscroft, «Risk analysis for mine scheduling by conditional simulation,» in: Transactions of the Institute of Mining and Metallurgy, Section A: Mining Technology, 101 (1992).
16. A. J. Richmond, «Integrating multiple simulations and mining dilution in open pit optimisation algorithms,» in: Orebody Modelling and Strategic Mine Planning Conference (2004).
17. A. Boucher and R. Dimitrikopoulos, «Block-support simulation of multiple correlated variables,» Mathematical Geosciences, 42, No. 2 (2009).
18. H. Mustapha and R. Dimitrikapoulos, «High-order stochastic simulations for complex non-Gaussian and non-linear geological patterns,» Mathematical Geosciences, 42, No. 5 (2010).
19. J. Wu, T. Zhang, and A. Journel, «Fast FILTERSIM simulation with score-based distance,» Mathematical Geosciences, 40, No. 7 (2010).
20. C. Scheidt and J. Caers, «Spatial uncertainty using distances and kernels,» Mathematical Geosciences, 41 (2009).
21. P. A. Dowd and A. H. Onur, «Open pit optimization. Part 1: Optimal open-pit design,» in: Transactions of the Institute of Mining and Metallurgy, Section A: Mining Technology, 102 (1993).
22. A. J. Richmond, «Direct NPV open pit optimisation with probabilistic models,» in: Orebody Modelling and Strategic Mine Planning Conference (2009).
23. M. Lemieux, «Moving cone optimizing algorithm: Computer Methods for the 80’s,» in: SME of AIMMPE (1979).
24. M. Godoy, The Effective Management of Geological Risk in Long-Term Production Scheduling of Open Pit Mines, University of Queensland (2002).

A RISK QUANTIFICATION FRAMEWORK FOR STRATEGIC MINE PLANNING: METHOD AND APPLICATION
M. Godoy and R. Dimitrakopoulos

Quantification, assessment and management of orebody uncertainty is critical to strategic mine planning. A method consisting of a series of steps for uncertainty quantification and risk assessment in pit design optimization is outlined here. Multiple simulated scenarios of an orebody’s grade distribution are processed through an established pit optimization approach to produce a distribution of possible outcomes in terms of key project indicators. These indicators are then assessed to support mine planning decisions.

Open pit mine design, grade risk analysis, upside potential, downside risk

REFERENCES
1. M. David, Handbook of Applied Advanced Geostatistical Ore Reserve Estimation, Elsevier Science Publishers (1988).
2. R. Dimitrakopoulos, C. T. Farrelly, and M. Godoy, «Moving forward from traditional optimization: Grade uncertainty and risk effects in open-pit design,» Transactions of the Institution of Mining and Metallurgy, Section A: Mining Technology, 111 (2002).
3. A. G. Journel, «Computer imaging in the minerals industry — Beyond mere aesthetics,» in: APCOM’92 Computer Applications in the Minerals Industries 23rd International Symposium (1992).
4. P. J. Ravenscroft, «Risk analysis for mine scheduling by conditional simulation,» Transactions of the Institution of Mining and Metallurgy, Section A: Mining Technology, 101 (1992).
5. R. Dimitrakopoulos, «Conditional simulation algorithms for modelling orebody uncertainty in open pit optimisation,» International Journal of Surface Mining, Reclamation and Environment, 12 (1998).
6. R. Dimitrakopoulos, L. Martinez, and S. Ramazan, «A maximum upside / minimum downside approach to the traditional optimization of open pit mine design,» Journal of Mining Science, 43 (2007).
7. M. Kent, R. Peattie, and V. Chamberlain, «Incorporating grade uncertainty in the decision to expand the main pit at the Navachab gold mine, Namibia, through the use of stochastic simulation,» " in: The Australasian Institute of Mining and Metallurgy, Spectrum Series, 14 (2007).
8. P. A. Dowd and A. H. Onur, «Open pit optimization — part 1: optimal open-pit design,» Transactions of the Institute of Mining and Metallurgy, Section A: Mining Technology, 102 (1993).
9. P. A. Dowd, «Risk in minerals projects: analysis, perception and management,» Transactions of the Institution of Mining and Metallurgy, Section A: Mining Technology, 106 (1997).
10. H. Mustapha and R. Dimitrakopoulos, «High-order stochastic simulations for complex non-Gaussian and non-linear geological patterns,» Mathematical Geoscience, 42, No. 5 (2010).
11. J. Wu, T. Zhang, and A. Journel, «Fast FILTERSIM simulation with score-based distance,» Mathematical Geosciences, 40, No. 7 (2010).
12. C. Scheidt and J. Caers, «Spatial Uncertainty Using Distances and Kernels,» Mathematical Geosciences, 41 (2009).
13. H. Lerchs and I. F. Grossmann, «Optimum design of open pit mines,» CIM Bulletin, Canadian Institute of Mining and Metallurgy, 58 (1965).
14. J. Whittle, «A decade of open pit mine planning and optimization — The craft of turning algorithms into packages,» in: APCOM’99 Computer Applications in the Minerals Industries 28th International Symposium (1999).

OPTIMAL MINING PRACTICE IN STRATEGIC PLANNING
B. King

In recent years, the mining industry has become more aware of the benefits of strategic planning as a cost-effective means of improving project value. As the quality of our assumptions improves, the quality of our results also improves, enabling us to make better decisions and improve the value of the finite mining resources. Though universities and software companies strive to provide better algorithms and integrate these in their software tools, mining companies are still faced with very limited options and capability in this field. Engineers charged with the responsibility of undertaking strategic planning for large mining companies often need to make significant compromises in undertaking the tasks. A core thread throughout this paper is the role of skilled people in realising the potential of a project. The paper aims to highlight some of the dangers for the engineers working in this field and provide some sound principles to help them maximise the value of the limited resources we have been entrusted with.

Strategic planning, optimization, economic evaluation

REFERENCES
1. B. M. King, «Optimal mining principles,» in: AusIMM Orebody Modelling and Strategic Mine Planning Proceedings, Perth (2009).
2. H. Lerchs and I. F. Grossman, «Optimum design of open-pit mines,» in: Transactions of CIM, LXVIII, pp. 17–24 (1965).
3. R. A. Brealey and S. C. Myers, Principles of Corporate Finance, 6th edition, Irwin McGraw-Hill (2000).
4. R. Wooller, «Optimising multiple operating policies for exploiting complex resources — An overview of the COMET Scheduler,» in: Orebody Modelling and Strategic Mine Planning, AusIMM Spectrum Series, 14, 2nd Edition, Melbourne (2007).

HUBBERT’S THEORY AND THE ULTIMATE COAL PRODUCTION IN TEMRS OF THE KUZNETSK COAL BASIN
V. N. Oparin and A. A. Ordin

The paper addresses Hubbert’s theory and its applicability to coal production dynamics in terms of the Kuznetsk Coal Basin (Kuzbass). The authors describe and validate the evaluation procedure for ultimate coal production using the lag modeling and the law of ultimate mineral mining efficiency decline, and present preliminary estimates of the ultimate coal production in Kuzbass based on the maximum NPV criterion in the dynamical unconstrained optimization problem.

Hubbert’s theory, asymptote, logistic curve, ultimate coal production, optimization, mine design capacity, NPV

REFERENCES
1. M. King Hubbert, «Nuclear energy and the fossil fuels,» in: Spring Meeting of the Southern District, American Petroleum Institute, San Antonio, Texas (1956).
2. P. F. Verhulst, «Notice sur la loi que la population poursuit dans son accroissement,» Correspondance Math?matique et Physique, 10 (1838).
3. L. I. Lopatnikov, Economic and Mathematical Dictionary [in Russian], Nauka, Moscow (1993).
4. http://www.inopressa.ru/nytimes/2010/09/30/15:56:00/coal.
5. A. A. Ordin, Dynamic Optimization Models of a Mine’s Design Capacity [in Russian], IGD SO RAN, Novosibirsk (1991).
6. A. A. Ordin and V. I. Klishin, Lag Models toward Optimizing Mining Process Variables [in Russian], Nauka, Novosibirsk (2009).
7. M. V. Kurlenya and V. N. Oparin, «Decreasing limiting efficiency of mining economic mineral deposits,» Journal of Mining Science, No. 4 (1998).
8. A. A. Ordin, «Assessment of ultimate ore production in Kuzbass based on the lag modeling,» in: Proceedings of the 12th Conference «Russia’s Energy Preparedness: New Approaches to the Coal Industry Growth» [in Russian], Kemerovo (2010).
9. V. V. Kosov, V. N. Livshits, A. G. Shakhnazarov et al., Investment Efficiency Evaluation Guidelines [in Russian], Ekonomika, Moscow (2000).
10. Yu. E. Kaputin, Information Technologies and the Economic Appraisal of Mining Projects [in Russian], Nedra, Saint Petersburg (2008).
11. P. Z. Zvyagin, Fixing the Capacities and Life Periods for Mines [in Russian], Gosgortekhizdat, Moscow (1962).
12. V. N. Oparin, A. D. Sashurin, G. I. Kulakov et al., Contemporary Geodynamics in the Upper Lithosphere: Sources, Parameters and Impact [in Russian], SO RAN, Novosibirsk (2008).
13. V. N. Oparin, S. N. Bataev, A. A. Malovichko et al., Seismic-Deformation Monitoring Methods and Equipment for Mining-Induced Earthquakes and Rock Bursts [in Russian], 1, SO RAN (2009).
14. V. N. Oparin, S. N. Bataev, A. A. Malovichko et al., Seismic-Deformation Monitoring Methods and Equipment for Mining-Induced Earthquakes and Rock Bursts [in Russian], 2, SO RAN (2010).
15. R. Dimitrakopoulos, «Orebody modelling and strategic mine planning: Old and new dimensions in a changing world,» in: Proceedings of the 2009 International Symposium, Aus IMM, Perth, Western Australia (2009).

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