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Author (up) Armstrong, M.; Valencia, J.; Lagos, G.; Emery, X.
Title Constructing Branching Trees of Geostatistical Simulations Type
Year 2022 Publication Mathematical Geosciences Abbreviated Journal Math. Geosci.
Volume Early Access Issue Pages
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
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1874-8961 ISBN Medium
Area Expedition Conference
Notes WOS:000725900700001 Approved
Call Number UAI @ alexi.delcanto @ Serial 1506
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Author (up) Barrera, J.; Lagos, G.
Title Limit distributions of the upper order statistics for the Levy-frailty Marshall-Olkin distribution Type
Year 2020 Publication Extremes Abbreviated Journal Extremes
Volume 23 Issue Pages 603-628
Keywords Marshall-Olkin distribution; Dependent random variables; Upper order statistics; Extreme-value theory; Reliability
Abstract The Marshall-Olkin (MO) distribution is considered a key model in reliability theory and in risk analysis, where it is used to model the lifetimes of dependent components or entities of a system and dependency is induced by “shocks” that hit one or more components at a time. Of particular interest is the Levy-frailty subfamily of the Marshall-Olkin (LFMO) distribution, since it has few parameters and because the nontrivial dependency structure is driven by an underlying Levy subordinator process. The main contribution of this work is that we derive the precise asymptotic behavior of the upper order statistics of the LFMO distribution. More specifically, we consider a sequence ofnunivariate random variables jointly distributed as a multivariate LFMO distribution and analyze the order statistics of the sequence asngrows. Our main result states that if the underlying Levy subordinator is in the normal domain of attraction of a stable distribution with index of stability alpha then, after certain logarithmic centering and scaling, the upper order statistics converge in distribution to a stable distribution if alpha> 1 or a simple transformation of it if alpha <= 1. Our result can also give easily computable confidence intervals for the last failure times, provided that a proper convergence analysis is carried out first.
Address [Barrera, Javiera; Lagos, Guido] Univ Adolfo Ibanez, Fac Engn & Sci, Av Diagonal Las Torres 2640, Santiago, Chile, Email: javiera.barrera@uai.cl;
Corporate Author Thesis
Publisher Springer Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1386-1999 ISBN Medium
Area Expedition Conference
Notes WOS:000557129100001 Approved
Call Number UAI @ eduardo.moreno @ Serial 1218
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Author (up) Lagos, G.; Espinoza, D.; Moreno, E.; Vielma, J.P.
Title Restricted risk measures and robust optimization Type
Year 2015 Publication European Journal Of Operational Research Abbreviated Journal Eur. J. Oper. Res.
Volume 241 Issue 3 Pages 771-782
Keywords Risk management; Stochastic programming; Uncertainty modeling
Abstract In this paper we consider characterizations of the robust uncertainty sets associated with coherent and distortion risk measures. In this context we show that if we are willing to enforce the coherent or distortion axioms only on random variables that are affine or linear functions of the vector of random parameters, we may consider some new variants of the uncertainty sets determined by the classical characterizations. We also show that in the finite probability case these variants are simple transformations of the classical sets. Finally we present results of computational experiments that suggest that the risk measures associated with these new uncertainty sets can help mitigate estimation errors of the Conditional Value-at-Risk. (C) 2014 Elsevier B.V. All rights reserved.
Address [Lagos, Guido] Georgia Inst Technol, H Milton Stewart Sch Ind & Syst Engn, Atlanta, GA 30332 USA, Email: glagos@gatech.edu;
Corporate Author Thesis
Publisher Elsevier Science Bv Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0377-2217 ISBN Medium
Area Expedition Conference
Notes WOS:000347605100018 Approved
Call Number UAI @ eduardo.moreno @ Serial 438
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Author (up) 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
Year 2021 Publication Optimization And Engineering Abbreviated Journal Optim. Eng.
Volume 72 Issue 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
Corporate Author Thesis
Publisher Springer Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1389-4420 ISBN Medium
Area Expedition Conference
Notes WOS:000569001700001 Approved
Call Number UAI @ alexi.delcanto @ Serial 1244
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