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Optimal pits and optimal transportation

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Ekeland, Ivar [CEREMADE, Université Paris-Dauphine] Queyranne, Maurice [UCL]

In open pit mining, one must dig a pit, that is, excavate the upper layers of ground before reaching the ore. The walls of the pit must satisfy some geomechanical constraints, in order not to collapse. The question then arises how to mine the ore optimally, that is, how to find the optimal pit. We set up the problem in a continuous (as opposed to discrete) framework, and we show, under weak assumptions, the existence of an optimum pit. For this, we formulate an optimal transportation problem, where the criterion is lower semi-continuous and is allowed to take the value + ∞. We show that this transportation problem is a strong dual to the optimum pit problem, and also yields optimality (complementarity slackness) conditions.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès libre
Publication date 2015
Language Anglais
Journal information "Modelisation Mathematique et Analyse Numerique" - Vol. 49, no.6, p. 1659-1670 (2015)
Peer reviewed yes
Publisher E D P Sciences (Les Ulis)
issn 0764-583X
e-issn 1290-3841
Publication status Publié
Affiliation UCL - SSH/LIDAM/CORE - Center for operations research and econometrics
Keywords Optimal transportation ; optimal pit mine design ; Kantorovich duality
Links
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See also
[boreal:152565] Optimal pits and optimal transportation
Bibliographic reference Ekeland, Ivar ; Queyranne, Maurice. Optimal pits and optimal transportation. In: Modelisation Mathematique et Analyse Numerique, Vol. 49, no.6, p. 1659-1670 (2015)
Permanent URL http://hdl.handle.net/2078.1/172498