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Optimal pits and optimal transportation

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Date
2015
Dewey
Analyse
Sujet
Transport theory
Journal issue
ESAIM: Mathematical Modelling and Numerical Analysis
Volume
49
Number
6
Publication date
2015
Article pages
1659-1670
DOI
http://dx.doi.org/10.1051/m2an/2015026
URI
https://basepub.dauphine.fr/handle/123456789/13811
Collections
  • CEREMADE : Publications
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Author
Ekeland, Ivar
Queyranne, Maurice
Type
Article accepté pour publication ou publié
Abstract (EN)
In open pit mining, one must dig a pit, that is, excavate the upperlayers of ground before reaching the ore. The walls of the pit must satisfysome mechanical constraints, in order not to collapse. The question thenarises how to mine the ore optimally, that is, how to Önd the optimalpit. We set up the problem in a continuous (as opposed to discrete)framework, and we show, under weak assumptions, the existence of anoptimum pit. For this, we formulate an optimal transportation problem,where the criterion is lower semi-continuous and is allowed to take thevalue+1. We show that this transportation problem is a strong dualto the optimum pit problem, and also yields optimality (complementarityslackness) conditions.

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