| Records |
| Author |
Armstrong, M.; Valencia, J.; Lagos, G.; Emery, X. |
| Title |
Constructing Branching Trees of Geostatistical Simulations |
Type |
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| Year |
2022 |
Publication |
Mathematical Geosciences |
Abbreviated Journal |
Math. Geosci. |
| Volume |
54 |
Issue |
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Pages |
711-743 |
| Keywords |
Mine planning; Multi-stage programming with recourse; Scenario reduction; Geological uncertainty; Adaptive optimisation |
| Abstract |
This paper proposes the use of multi-stage stochastic programming with recourse for optimised strategic open-pit mine planning. The key innovations are, firstly, that a branching tree of geostatistical simulations is developed to take account of uncertainty in ore grades, and secondly, scenario reduction techniques are applied to keep the trees to a manageable size. Our example shows that different mine plans would be optimal for the downside case when the deposit turns out to be of lower grade than expected compared to when it is of higher grade than expected. Our approach further provides th |
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1874-8961 |
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| Notes |
WOS:000725900700001 |
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UAI @ alexi.delcanto @ |
Serial |
1506 |
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| Author |
Espinoza, D.; Goycoolea, M.; Moreno, E.; Newman, A. |
| Title |
MineLib: a library of open pit mining problems |
Type |
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| Year |
2013 |
Publication |
Annals Of Operations Research |
Abbreviated Journal |
Ann. Oper. Res. |
| Volume |
206 |
Issue |
1 |
Pages |
93-114 |
| Keywords |
Mine scheduling; Mine planning; Open pit production scheduling; Surface mine production scheduling; Problem libraries; Open pit mining library |
| Abstract |
Similar to the mixed-integer programming library (MIPLIB), we present a library of publicly available test problem instances for three classical types of open pit mining problems: the ultimate pit limit problem and two variants of open pit production scheduling problems. The ultimate pit limit problem determines a set of notional three-dimensional blocks containing ore and/or waste material to extract to maximize value subject to geospatial precedence constraints. Open pit production scheduling problems seek to determine when, if ever, a block is extracted from an open pit mine. A typical objective is to maximize the net present value of the extracted ore; constraints include precedence and upper bounds on operational resource usage. Extensions of this problem can include (i) lower bounds on operational resource usage, (ii) the determination of whether a block is sent to a waste dump, i.e., discarded, or to a processing plant, i.e., to a facility that derives salable mineral from the block, (iii) average grade constraints at the processing plant, and (iv) inventories of extracted but unprocessed material. Although open pit mining problems have appeared in academic literature dating back to the 1960s, no standard representations exist, and there are no commonly available corresponding data sets. We describe some representative open pit mining problems, briefly mention related literature, and provide a library consisting of mathematical models and sets of instances, available on the Internet. We conclude with directions for use of this newly established mining library. The library serves not only as a suggestion of standard expressions of and available data for open pit mining problems, but also as encouragement for the development of increasingly sophisticated algorithms. |
| Address |
[Espinoza, Daniel] Univ Chile, Dept Ind Engn, Santiago Ctr, Santiago, Chile, Email: daespino@dii.uchile.cl; |
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Springer |
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English |
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0254-5330 |
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WOS:000320694000006 |
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| Call Number |
UAI @ eduardo.moreno @ |
Serial |
290 |
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| Author |
Lagos, T.; Armstrong, M.; Homem-de-Mello, T.; Lagos, G.; Saure, D. |
| Title |
A framework for adaptive open-pit mining planning under geological uncertainty |
Type |
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| Year |
2021 |
Publication |
Optimization And Engineering |
Abbreviated Journal |
Optim. Eng. |
| Volume |
72 |
Issue |
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Pages |
102086 |
| Keywords |
Mine planning; Geostatistics; Stochastic optimization; Adaptive algorithms; Iterative learning algorithm |
| Abstract |
Mine planning optimization aims at maximizing the profit obtained from extracting valuable ore. Beyond its theoretical complexity-the open-pit mining problem with capacity constraints reduces to a knapsack problem with precedence constraints, which is NP-hard-practical instances of the problem usually involve a large to very large number of decision variables, typically of the order of millions for large mines. Additionally, any comprehensive approach to mine planning ought to consider the underlying geostatistical uncertainty as only limited information obtained from drill hole samples of the mineral is initially available. In this regard, as blocks are extracted sequentially, information about the ore grades of blocks yet to be extracted changes based on the blocks that have already been mined. Thus, the problem lies in the class of multi-period large scale stochastic optimization problems with decision-dependent information uncertainty. Such problems are exceedingly hard to solve, so approximations are required. This paper presents an adaptive optimization scheme for multi-period production scheduling in open-pit mining under geological uncertainty that allows us to solve practical instances of the problem. Our approach is based on a rolling-horizon adaptive optimization framework that learns from new information that becomes available as blocks are mined. By considering the evolution of geostatistical uncertainty, the proposed optimization framework produces an operational policy that reduces the risk of the production schedule. Our numerical tests with mines of moderate sizes show that our rolling horizon adaptive policy gives consistently better results than a non-adaptive stochastic optimization formulation, for a range of realistic problem instances. |
| Address |
[Lagos, Tomas; Saure, Denis] Univ Chile, Dept Ind Engn, Santiago, Chile, Email: tito.hmello@uai.cl |
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Springer |
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English |
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Edition |
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| ISSN |
1389-4420 |
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| Notes |
WOS:000569001700001 |
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UAI @ alexi.delcanto @ |
Serial |
1244 |
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| Author |
Moreno, E.; Rezakhah, M.; Newman, A.; Ferreira, F. |
| Title |
Linear models for stockpiling in open-pit mine production scheduling problems |
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| Year |
2017 |
Publication |
European Journal Of Operational Research |
Abbreviated Journal |
Eur. J. Oper. Res. |
| Volume |
260 |
Issue |
1 |
Pages |
212-221 |
| Keywords |
OR in natural resources; Stockpiling; Linear and integer programming; Mine planning; Open pit mining |
| Abstract |
The open pit mine production scheduling (OPMPS) problem seeks to determine when, if ever, to extract each notional, three-dimensional block of ore and/or waste in a deposit and what to do with each, e.g., send it to a particular processing plant or to the waste dump. This scheduling model maximizes net present value subject to spatial precedence constraints, and resource capacities. Certain mines use stockpiles for blending different grades of extracted material, storing excess until processing capacity is available, or keeping low-grade ore for possible future processing. Common models assume that material in these stockpiles, or “buckets,” is theoretically immediately mixed and becomes homogeneous. We consider stockpiles as part of our open pit mine scheduling strategy, propose multiple models to solve the OPMPS problem, and compare the solution quality and tractability of these linear-integer and nonlinear-integer models. Numerical experiments show that our proposed models are tractable, and correspond to instances which can be solved in a few seconds up to a few minutes in contrast to previous nonlinear models that fail to solve. (C) 2016 Elsevier B.V. All rights reserved. |
| Address |
[Moreno, Eduardo; Ferreira, Felipe] Univ Adolfo Ibanez, Fac Sci & Engn, Avda Diagonal Torres 2700, Santiago, Chile, Email: eduardo.moreno@uai.cl; |
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Elsevier Science Bv |
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English |
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0377-2217 |
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| Notes |
WOS:000396952000018 |
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UAI @ eduardo.moreno @ |
Serial |
715 |
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| Author |
Reus, L.; Belbeze, M.; Feddersen, H.; Rubio, E. |
| Title |
Extraction Planning Under Capacity Uncertainty at the Chuquicamata Underground Mine |
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| Year |
2018 |
Publication |
Interfaces |
Abbreviated Journal |
Interfaces |
| Volume |
48 |
Issue |
6 |
Pages |
543-555 |
| Keywords |
underground mine extraction scheduling; operational uncertainty management; stochastic programming applications; long-term mine planning |
| Abstract |
We propose an extraction schedule for the Chuquicamata underground copper mine in Chile. The schedule maximizes profits while adhering to all operational and geomechanical requirements involved in proper removal of the material. We include extraction capacity uncertainties due to failure in equipment, specifically to the overland conveyor, which we find to be the most critical component in the extraction process. First we present the extraction plan based on a deterministic model, which does not assume uncertainty in the extraction capacity and represents the solution that the mine can implement without using the results of this study. Then we extend this model to a stochastic setting by generating different scenarios for capacity values in subsequent periods. We construct a multistage model that handles economic downside risk arising from this uncertainty by penalizing plans that deviate from an ex ante profit target in one or more scenarios. Simulation results show that a stochastic-based solution can achieve the same expected profits as the deterministic-based solution. However, the earnings of the stochastic-based solution average 5% more for scenarios in which earnings are below the 10th percentile. If we choose a target 2% below the expected profit obtained by the deterministic-based solution, this average increases from 5% to 9%. |
| Address |
[Reus, Lorenzo; Belbeze, Mathias; Feddersen, Hans] Adolfo Ibanez Univ, Dept Engn & Sci, Santiago 7910000, Chile, Email: lorenzo.reus@uai.cl; |
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Informs |
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English |
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0092-2102 |
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| Notes |
WOS:000454513500005 |
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UAI @ eduardo.moreno @ |
Serial |
967 |
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| Author |
Rezakhah, M.; Moreno, E.; Newman, A. |
| Title |
Practical performance of an open pit mine scheduling model considering blending and stockpiling |
Type |
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| Year |
2020 |
Publication |
Computers & Operations Research |
Abbreviated Journal |
Comput. Oper. Res. |
| Volume |
115 |
Issue |
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Pages |
12 pp |
| Keywords |
Stockpiling; Linear and integer programming; Mine planning; Open pit mining; Software |
| Abstract |
Open pit mine production scheduling (OPMPS) is a decision problem which seeks to maximize net present value (NPV) by determining the extraction time of each block of ore and/or waste in a deposit and the destination to which this block is sent, e.g., a processing plant or waste dump. Spatial precedence constraints are imposed, as are resource capacities. Stockpiles can be used to maintain low-grade ore for future processing, to store extracted material until processing capacity is available, and/or to blend material based on single or multiple block characteristics (i.e., metal grade and/or contaminant). We adapt an existing integer-linear program to an operational polymetallic (gold and copper) open pit mine, in which the stockpile is used to blend materials based on multiple block characteristics, and call it ((P) over cap (la)). We observe that the linear programming relaxation of our objective function is unimodal for different grade combinations (metals and contaminants) in the stockpile, which allows us to search systematically for an optimal grade combination while exploiting the linear structure of our optimization model. We compare the schedule of ((P) over cap (la)) with that produced by (P-ns) which does not consider stockpiling, and with ((P) over tilde (la)), which controls only the metal content in the stockpile and ignores the contaminant level at the mill and in the stockpile. Our proposed solution technique provides schedules for large instances in a few seconds up to a few minutes with significantly different stockpiling and material flow strategies depending on the model. We show that our model improves the NPV of the project while satisfying operational constraints. (C) 2019 Elsevier Ltd. All rights reserved. |
| Address |
[Rezakhah, Mojtaba] Tarbiat Modares Univ, Engn Dept, POB 14115411, Tehran, Iran, Email: m.rezakhah@modares.ac.ir; |
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Pergamon-Elsevier Science Ltd |
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English |
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Edition |
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0305-0548 |
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| Notes |
WOS:000514218600009 |
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| Call Number |
UAI @ eduardo.moreno @ |
Serial |
1161 |
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