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Open-Pit Mining with Uncertainty - A Conditional Value-at-Risk Approach
Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.ORCID-id: 0000-0003-2094-7376
Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
(Engelska)Manuskript (preprint) (Övrigt vetenskapligt)
Abstract [en]

The selection of a mine design is based on estimating net present values of all possible, technically feasible mine plans so as to select the one with the maximum value. It is a hard task to know with certainty the quantity and quality of ore in the ground. This geological uncertainty, and also the future market behaviour of metal prices and foreign exchange rates, which are impossible to be known with certainty, make mining a high risk business.

Value-at-Risk (VaR) is a measure that is used in financial decisions to minimize the loss caused by inadequate monitoring of risk. This measure does however have certain drawbacks such as lack of consistency, nonconvexity, and nondifferentiability. Rockafellar and Uryasev (2000) introduce the Conditional Value-at-Risk (CVaR) measure as an alternative to the VaR measure. The CVaR measure gives rise to a convex problem.

An optimization model that maximizes expected return while minimizing risk is important for the mining sector as this will help make better decisions on the blocks of ore to mine at a particular point in time. We present a CVaR approach to the uncertainty involved in open-pit mining. We formulate investment and design models for the open-pit mine and also give a nested pit scheduling model based on CVaR. Several numerical results based on our models are presented by using scenarios from simulated geological and price uncertainties.

Nyckelord [en]
Conditional value-at-risk (CVaR), open-pit mining, geological uncertainty, price uncertainty
Nationell ämneskategori
Matematik
Identifikatorer
URN: urn:nbn:se:liu:diva-70843OAI: oai:DiVA.org:liu-70843DiVA, id: diva2:442017
Tillgänglig från: 2011-09-20 Skapad: 2011-09-20 Senast uppdaterad: 2013-08-30Bibliografiskt granskad
Ingår i avhandling
1. Mathematical Optimization Models and Methods for Open-Pit Mining
Öppna denna publikation i ny flik eller fönster >>Mathematical Optimization Models and Methods for Open-Pit Mining
2011 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
Abstract [en]

Open-pit mining is an operation in which blocks from the ground are dug to extract the ore contained in them, and in this process a deeper and deeper pit is formed until the mining operation ends. Mining is often a highly complex industrial operation, with respect to both technological and planning aspects. The latter may involve decisions about which ore to mine and in which order. Furthermore, mining operations are typically capital intensive and long-term, and subject to uncertainties regarding ore grades, future mining costs, and the market prices of the precious metals contained in the ore. Today, most of the high-grade or low-cost ore deposits have already been depleted, and to obtain sufficient profitability in mining operations it is therefore today often a necessity to achieve operational efficiency with respect to both technological and planning issues.

In this thesis, we study the open-pit design problem, the open-pit mining scheduling problem, and the open-pit design problem with geological and price uncertainty. These problems give rise to (mixed) discrete optimization models that in real-life settings are large scale and computationally challenging.

The open-pit design problem is to find an optimal ultimate contour of the pit, given estimates of ore grades, that are typically obtained from samples in drill holes, estimates of costs for mining and processing ore, and physical constraints on mining precedence and maximal pit slope. As is well known, this problem can be solved as a maximum flow problem in a special network. In a first paper, we show that two well known parametric procedures for finding a sequence of intermediate contours leading to an ultimate one, can be interpreted as Lagrangian dual approaches to certain side-constrained design models. In a second paper, we give an alternative derivation of the maximum flow problem of the design problem.

We also study the combined open-pit design and mining scheduling problem, which is the problem of simultaneously finding an ultimate pit contour and the sequence in which the parts of the orebody shall be removed, subject to mining capacity restrictions. The goal is to maximize the discounted net profit during the life-time of the mine. We show in a third paper that the combined problem can also be formulated as a maximum flow problem, if the mining capacity restrictions are relaxed; in this case the network however needs to be time-expanded.

In a fourth paper, we provide some suggestions for Lagrangian dual heuristic and time aggregation approaches for the open-pit scheduling problem. Finally, we study the open-pit design problem under uncertainty, which is taken into account by using the concept of conditional value-atrisk. This concept enables us to incorporate a variety of possible uncertainties, especially regarding grades, costs and prices, in the planning process. In real-life situations, the resulting models would however become very computationally challenging.

Ort, förlag, år, upplaga, sidor
Linköping: Linköping University Electronic Press, 2011. s. 38
Serie
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1396
Nationell ämneskategori
Matematik
Identifikatorer
urn:nbn:se:liu:diva-70844 (URN)978-91-7393-073-4 (ISBN)
Disputation
2011-10-18, Alan Turing, hus E, Campus Valla, Linköpings universitet, Linköping, 13:15 (Engelska)
Opponent
Handledare
Tillgänglig från: 2011-09-20 Skapad: 2011-09-20 Senast uppdaterad: 2013-08-30Bibliografiskt granskad

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