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A Multi-Parametric Maximum Flow Characterization of the Open-Pit Scheduling Problem
Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.ORCID iD: 0000-0003-2094-7376
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We consider the problem of finding an optimal mining schedule for an openpit during a number of time periods, subject to a mining capacity restriction for each time period. By applying Lagrangian relaxation to the capacities, a multi-parametric formulation is obtained. We show that this formulation can be restated as a maximum flow problem in a time-expanded network. This result extends a well-known result of Picard from 1976 for the open-pit design problem, that is, the single-period case, to the case of multiple time periods.

Keyword [en]
Open-pit mining, scheduling, maximum flow, minimum cut, Lagrangian relaxation
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-70841OAI: oai:DiVA.org:liu-70841DiVA: diva2:442013
Available from: 2011-09-20 Created: 2011-09-20 Last updated: 2013-08-30Bibliographically approved
In thesis
1. Mathematical Optimization Models and Methods for Open-Pit Mining
Open this publication in new window or tab >>Mathematical Optimization Models and Methods for Open-Pit Mining
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
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.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2011. 38 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1396
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-70844 (URN)978-91-7393-073-4 (ISBN)
Public defence
2011-10-18, Alan Turing, hus E, Campus Valla, Linköpings universitet, Linköping, 13:15 (English)
Opponent
Supervisors
Available from: 2011-09-20 Created: 2011-09-20 Last updated: 2013-08-30Bibliographically approved

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