Optimal production strategy of bimetallic deposits under technical and economic uncertainties using stochastic chance-constrained programming (original) (raw)
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The Open Pit Mine Production Scheduling Problem (OPMPSP) studied in recent years is usually based on a single geological estimate of material to be excavated and processed over a number of decades. However techniques have now been developed to generate multiple stochastic geological estimates that more accurately describe the uncertain geology. While some attempts have been made to use such multiple estimates in mine production scheduling, none of these allow mining and processing decisions to flexibly adapt over time, in response to observation of the geological properties of the material mined. In this paper, we use multiple geological estimates in a mixed integer multistage stochastic programming approach, in which decisions made in later time periods can depend on observations of the geological properties of the material mined in earlier periods. Since the material mined in earlier periods is determined by our decisions, the information received about uncertain properties, and when that information is available, is decision-dependent. Thus we tackle the difficult case of stochastic programming with endogeneous uncertainty. We extend a successful mixed integer programming formulation of the OPMPSP to this stochastic case, and show that non-anticipativity can be modelled with linear constraints involving variables already present in the model. We extend this observation to the general class of endogenous stochastic programs, and exploit the special structure of our model to show that in some cases we can omit a significant proportion of these constraints. Using data supplied by our industry partner, (a multinational mining company), we show that this approach is reasonably tractable, and demonstrate the improvements that can be made to mine schedules through the explicit use of multiple geological estimates.
The Application of Stochastic Mine Production Scheduling in the Presence of Geological Uncertainty
Sustainability
The scheduling of open-pit mine production is a large-scale, mixed-integer linear programming problem that is computationally expensive. The purpose of this study is to create a computationally efficient algorithm for solving open-pit production scheduling problems with uncertain geological parameters. To demonstrate the effectiveness of the proposed research, a case study of an Indian iron ore mine is presented. Multiple realizations of the resource models were developed and integrated within the stochastic production scheduling framework to capture uncertainty and incorporate it into the mine plan. In this case study, two hybrid methods were developed to evaluate their performance. Model 1 is a combined branch and cut with the longest path, whereas Model 2 is a sequential parametric maximum flow and branch and cut. The results show that both methods produce similar materials, ore, metal, and risk profiles; however, Model 2 generates slightly more (4 percent) discounted cash flow f...
The production scheduling of open pit mines is an intricate, complex and difficult problem to address due to its large scale and the unavailability of a truly optimal net present value (NPV) solution, as well as the uncertainty in key parameters involved. These key factors are geological and mining, financial and environmental. Geological uncertainty is a major contributor in failing to meet production targets and the financial expectations of a project especially in the early stages of a project. Stochastic integer programming (SIP) models provide a framework for optimising mine production scheduling considering uncertainty. A specific SIP formulation is shown herein that generates the optimal production schedule using equally probable simulated orebody models as input, without averaging the related grades. The optimal production schedule is then the schedule that can produce the maximum achievable discounted total value from the project, given the available orebody uncertainty described through a set of stochastically simulated orebody models. The proposed SIP model allows the management of geological risk in terms of not meeting planned targets during actual operation, unlike the traditional scheduling methods that use a single orebody model and where risk is randomly distributed between production periods while there is no control over the magnitude of the risks on the schedule. Notably, the testing of the SIP formulation in two cases, a gold and a copper deposit, shows that the expected total NPV of the schedule using the SIP approach is significantly higher (10 and 25% respectively) than the traditional schedule developed using a single estimated orebody model.
Resources Policy, 2019
Over the last decade, geological uncertainty and its effects on long-term or strategic mine planning and methods for related risk management have been studied. However, the combined effect of geological and commodity price uncertainty has received relatively less attention in the technical literature. A research experiment that addresses both these sources of uncertainty is presented herein and accounts for their differences. In particular, while the current commodity price is known at the beginning of every new mining period, the geology, including the mineral grades, metal content, material types and so on, remain uncertain, even when additional information becomes available. The proposed method first uses a two-stage model to manage the geological uncertainty that leads to a scenario-independent extraction sequence. Based on different metal production targets, a pool of subsets of mining blocks is also precomputed for every period. Then, a stochastic dynamic programming algorithm is developed and employed to define the best policy in terms of metal production targets to follow, depending on the evolution of the related commodity price. This policy follows the scenario tree of the commodity price, as it is scenario-dependent (price only) with non-anticipativity constraints, which is similar to an operator that adapts to a fluctuating market. This new approach is tested through a case study that reveals the counter-intuitive combined effects of both sources of uncertainty. For instance, based on the previous evolution of the commodity price, the obtained policy suggests adaptations of the metal production target that go against common practices of mining operators.
Life of mine (LOM) production scheduling is a critically important part of open pit mining ventures and deals with the efficient management of cash flows in the order of hundreds of millions of dollars. A LOM production schedule determines the quantity and quality of ore and waste materials to be mined over time, so as to maximise the net present value (NPV) of the mine. Life of mine production scheduling is an intricate and complex problem to address and it is adversely affected by geological risk, which can, however, be accounted for and managed while constructing production schedules. In the present study, the LOM scheduling process of a disseminated copper deposit demonstrates the intricacies of a new scheduling approach based on the technique of simulated annealing and stochastically simulated representations of the copper orebody. The study documents the benefits of incorporating geological uncertainty in the mine scheduling process through the proposed approach. The stochastic approach is found to generate a LOM schedule with a NPV 26% higher than that of the conventional schedule. Risk analysis results show that the stochastic schedule has low chances to significantly deviate from targets; the probability that the conventional schedule will deviate from production targets is high. In addition, comparisons show that the conventional scheduling approach overestimates ore tonnages and underestimates the NPV of the mine design. The findings of this study suggest that LOM schedules that incorporate geological uncertainty lead to more informed investment decisions and improved mining practices.
Minerals, 2021
The simultaneous stochastic optimization of mining complexes optimizes various components of the related mineral value chain jointly while considering material supply (geological) uncertainty. As a result, the optimization process capitalizes on the synergies between the components of the system while not only quantifying and considering geological uncertainty, but also producing strategic mine plans, maximizing the net present value. This paper presents an application of simultaneous stochastic optimization at a large gold mining complex. The complex contains three open-pit mines, three stockpiles, a waste dump, and a processing facility. Material hardness management is integrated at the processing facility. The case study generated production schedules for each mineral deposit considered, as well as an overall assessment of the project and related forecasts. It resulted in an 18 year life-of-asset and identified the semi-autogenous grinder (SAG) mill as the bottleneck of the operation.
Stochastic Optimization for Strategic Mine Planning: A Decade of Developments
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 1 0% 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.
2018
Mining complexes are value chains where extracted material from different mines is transformed into sellable products through a set of processing streams. This value chain is governed by uncertainties in different aspects, from the pertinent geological attributes of the mineral deposits mined, to the different operational and processing components. Stochastic optimization formulations have been shown to maximize economic value and, at the same time, manage and reduce risk, thus providing reliable production plans and forecasts. However, related mine designs and production plans are static over the life of a mining complex and cannot include flexibility mechanisms to account for alternative, potential production and planning options. This paper presents a dynamic two-stage stochastic mixed integer non-linear programming formulation for modeling and optimizing a mining complex, including alternatives over capital expenditure investments and operational modes for different components o...
Mining Technology, 2007
The present paper attempts to model long term production scheduling problems by chance constrained binary integer programming in a stochastic environment. This stochastic model is set up to account for ore block grade uncertainty. The probability distribution function of grade in each block is used as a stochastic input to the optimisation model. This distribution function in each block should be determined using geostatistical simulation approach. The deterministic equivalent of proposed chance constrained model is then achieved which is the form of non-linear quadratic in binary variables. A confidence level at which it is desire that the uncertain constraints holds, is specified in each scheduling period. Rather than previous risk based model, this formulation will yield schedules with high chance of achieving planned production targets while maximises the expectation of net present value and minimises the variance function simultaneously. Using this method the grade uncertainty is integrated explicitly into the optimisation process.