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A Duality-Based Derivation of the Maximum Flow Formulation of the Open-Pit Design Problem
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]

Open-pit mining is a surface mining operation whereby ore, or waste, is excavated from the surface of the land. The open-pit design problem is deciding on which blocks of an ore deposit to mine in order to maximize the total profit, while obeying digging constraints concerning pit slope and block precedence. The open-pit design problem can be formulated as a maximum flow problem in a certain capacitated network, as first shown by Picard in 1976. His derivation is based on a restatement of the problem as a quadratic binary program. We give an alternative derivation of the maximum flow formulation, which uses only linear programming duality.

Nyckelord [en]
Open-pit mining, pit design, maximum flow, maximum profit, block model
Nationell ämneskategori
Matematik
Identifikatorer
URN: urn:nbn:se:liu:diva-70840OAI: oai:DiVA.org:liu-70840DiVA, id: diva2:442012
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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