liu.seSök publikationer i DiVA
Ändra sökning
RefereraExporteraLänk till posten
Permanent länk

Direktlänk
Referera
Referensformat
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Annat format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annat språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf
Open-Pit Production Scheduling - Suggestions for Lagrangian Dual Heuristic and Time Aggregation Approaches
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.
Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.ORCID-id: 0000-0002-2081-2888
(Engelska)Manuskript (preprint) (Övrigt vetenskapligt)
Abstract [en]

Open-pit production scheduling deals with the problem of deciding what and when to mine from an open-pit, given potential profits of the different fractions of the mining volume, pit-slope restrictions, and mining capacity restrictions for successive time periods. We give suggestions for Lagrangian dual heuristic approaches for the open-pit production scheduling problem. First, the case with a single mining capacity restriction per time period is considered. For this case, linear programming relaxations are solved to find values of the multipliers for the capacity restrictions, to be used in a Lagrangian relaxation of the constraints. The solution to the relaxed problem will not in general satisfy the capacity restrictions, but can be made feasible by adjusting the multiplier values for one time period at a time. Further, a time aggregation approach is suggested as a way of reducing the computational burden of solving linear programming relaxations, especially for largescale real-life mine problems. For the case with multiple capacity restrictions per time period we apply newly developed conditions for optimality and nearoptimality in general discrete optimization problems to construct a procedure for heuristically constructing near-optimal intermediate pits.

Nyckelord [en]
Open-pit mining, mine scheduling, Lagrangian relaxation, maximum flow, time aggregation
Nationell ämneskategori
Matematik
Identifikatorer
URN: urn:nbn:se:liu:diva-70842OAI: oai:DiVA.org:liu-70842DiVA, id: diva2:442016
Tillgänglig från: 2011-09-20 Skapad: 2011-09-20 Senast uppdaterad: 2018-06-25Bibliografiskt 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

Open Access i DiVA

Fulltext saknas i DiVA

Personposter BETA

Amankwah, HenryLarsson, TorbjörnTextorius, BjörnRönnberg, Elina

Sök vidare i DiVA

Av författaren/redaktören
Amankwah, HenryLarsson, TorbjörnTextorius, BjörnRönnberg, Elina
Av organisationen
OptimeringsläraTekniska högskolanTillämpad matematik
Matematik

Sök vidare utanför DiVA

GoogleGoogle Scholar

urn-nbn

Altmetricpoäng

urn-nbn
Totalt: 492 träffar
RefereraExporteraLänk till posten
Permanent länk

Direktlänk
Referera
Referensformat
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Annat format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annat språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf