A framework for adaptive open-pit mining planning under geological uncertainty
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A framework for adaptive open‑pit mining planning under geological uncertainty Tomás Lagos1 · Margaret Armstrong2,3 · Tito Homem‑de‑Mello2 · Guido Lagos4 · Denis Sauré1 Received: 6 March 2020 / Revised: 12 July 2020 / Accepted: 26 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
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 decisiondependent 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. Keywords Mine planning · Geostatistics · Stochastic optimization · Adaptive algorithms · Iterative learning algorithm
* Tito Homem‑de‑Mello [email protected] Extended author information available on the last page of the article
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1 Introduction Motivation. Open-pit mining planning optimization aims at maximizing the profit obtained from extracting valuable ore when a mineral deposit is mined from the surface. A mining project typically starts with a prospecting stage, during which mineral deposits are discovered, followed by an exploration phase, where drilling campaigns are carried out to sample and collect information on the ore content. This information is then used to create a geological model of the mineral content, using techniques such as kriging, see Krige (1951). Once a geological model of the deposit is in place, a mine is designed, together with an exploitation plan, both of which are evalua
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