A Stochastic Mine Planning and Production Scheduling Optimization Framework with Uncertain Metal Supply and Market Demand
The sustainable development and utilization of mineral resources and reserves is an area of critical importance to society given the fast growth and demand of new emerging economies and environmental and social concerns. Uncertainty, however, impacts sustainable mineral resource development, including the ability of ore bodies to supply raw materials, operational mining uncertainties, fluctuating market demand for raw materials and metals, commodity prices, and exchange rates.
Throughout the last decade, new technological advances in stochastic modelling, optimization and forecasting of mine planning and production performance have shown to simultaneously enhance production and return on investment. These advances shifted the paradigm in the field, showed initially counterintuitive outcomes that are now well understood, and outlined new areas of research needs. The old paradigm was based on estimating mineral reserves, optimizing mine planning, and production forecasting result in single, often biased and flawed forecasts. These flaws were largely due to the nonlinear propagation of errors associated with ore bodies throughout the chain of mining.
The new stochastic paradigm addresses these limits, and application of the stochastic framework increases net present value (NPV) of mine production schedules (20-30%). It also allows for stochastically optimal pit limits to be about 15% larger in total tonnage when compared to conventionally optimal pit limits, adding about another 10% NPV. Related technical developments also impact: (i) sustainable utilization of mineral resources; (ii) uncertainty quantification and risk management; (iii) social responsibility through improved financial performance; (iv) enhancement of production and product supply; (v) contribution to management of mine remediation; and (vii) objective, technically defendable decision-making.
Ongoing research efforts focus in particular on two interrelated topics, amongst others:
- Quantification of geological uncertainty / uncertainty in metal supply, including a new high-order modeling framework for spatial data defined based on measures of high-order complexity in spatial architectures, termed spatial cumulants. Cumulants are combinations of moments of statistical parameters that characterize non-Gaussian random fields. To date, research provides definitions, geological interpretations and implementations of high-order spatial cumulants that are used in the high-dimensional space of Legendre polynomials to stochastically simulate complex, non-Gaussian, nonlinear spatial phenomena. Advantages include the (a) absence of distributional assumptions and pre-/postprocessing steps, e.g., data normalization or training image (TI) filtering; (b) use of high-order relations in the data to the simulation process (data-driven, not TI-driven); (c) generation of complex spatial patterns reproducing any data distribution and variograms, and high-order spatial cumulants. The above is an alternative to the multiple point methods applied by our Stanford University colleagues, with additional advantages (data-driven, reconstructs consistently the lower-order spatial complexity in the data used, in addition to high- order). Research directions include the search of new methods for high-order simulation of categorical data (e.g., geology of mineral or petroleum deposits, ground water aquifers, sites for CO2 sequestration), as well as high-order simulations for spatially correlated attributes and principal cumulant decomposition methods.
All of these developments are critical in modeling the uncertainty in material types and metal content that are extracted from the ground, with particular emphasis on the spatial high-order connectivity of extreme values (high metal content). These models have significant impacts in mine production planning, scheduling and forecasting, from single mines to mineral supply chains.
- The development of global stochastic optimization techniques for mining complexes / mineral supply chains. These optimization techniques are a core aspect of mine design and production scheduling because they maximize the economic value generated by the production of ore and define a technical plan to be followed from the development of the mine to its closure. This planning optimization is a complex problem to address due to its large scale, the uncertainty in the key parameters involved (geological, mining, financial) and the absence of a method for global or simultaneous optimization of the individual elements of a mining complex or mineral supply chain. The past years, our research in global optimization of mining complexes is addressed through developing a new stochastic optimization framework that integrates multiple mines, multiple processing streams including blending stockpiles and waste dumps designed to meet quality specifications and minimize environmental impact and integrate waste management issues, and transportation methods. The ability to manage and simultaneously optimize all aspects of a mining complex leads to mine plans that not only minimize risk related to environmental impact and rehabilitation, but have previously demonstrated an increase of the economic value, reserves and life-of-mine forecast, thus contributing to the sustainable development of the non-renewable resource.
Stochastic integer programming has been a core framework in our stochastic optimization efforts. However, the scale of the scheduling and material flow through a mineral supply chain from mines products is very large and requires the development of efficient solution strategies for the proposed formulations which are sought through metaheuristics. For example, a hybrid approach integrating metaheuristics and linear programming permits to link the long-term production schedule with the short-term schedule, whereby the information gleaned from the solution of one can be used to improve the other, leading to a globally optimal and practical mine plans. Extensive testing, applications and benchmarking of the methods being developed are underway and the more promising approaches are being field tested at mine sites with collaborating companies from North to South America, and Africa to Australia.
For more information, see the related webinar available at the McGill web site.
For a short video with simple explanations, see the NSERC website.