http://cgm.cs.mcgill.ca/~avis/courses/567/roussos/EJOR2.pdf

A diversified Tabu search approach for the open-pit mine production scheduling problem with metal uncertainty

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.

Stochastic optimization for strategic mine planning: A decade of developments

Evaluating mine plans under uncertainty: Can the real options make a difference?

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 a risk of deviating from production targets over time. Comparison shows that the stochastically generated mine plan exhibits less risk in deviating from quality targets than the traditional mine planning approach based on a single interpolated orebody model.

Stochastic long-term production scheduling of iron ore deposits: Integrating joint multi-element geological uncertainty

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.

Stochastic Optimisation of Long-Term Production Scheduling for Open Pit Mines with a New Integer Programming Formulation

An economic argument is presented for the incorporation of quantitative modelling of the uncertainty of grade, tonnage and geology into open-pit design and planning. Two new implementations of conditional simulation—the generalized sequential Gaussian simulation and direct block simulation—are outlined. An optimization study of a typical disseminated, low-grade, epithermal, quartz breccia-type gold deposit is used to highlight the differences between the financial projections that may be obtained from a single orebody model and the range of outcomes produced when, for example, fifty deposit simulations are run. The effects on expectations of net present value, production cost per ounce, mill feed grade and ore tonnage are presented as examples and periods with a high risk of negative discounted cash flow are identified. Further integration of uncertainty into optimization algorithms will be needed to increase their efficacy.

C. T. Farrelly

Papers

Moving forward from traditional optimization: grade uncertainty and risk effects in open-pit design

I'd rather be approximately right than precisely wrong: Grade uncertainty, risk effects and decision making in open pit design