Geodesic
Optimal pits and optimal transportation
Ekeland, Ivar1  ; Queyranne, Maurice2, 3 
1 CEREMADE, Université Paris-Dauphine, Place du Maréchal De Lattre De Tassigny, 75775 Paris, France.
2 CORE, Université Catholique de Louvain, Voie du Roman Pays 34, 1348 Louvain-la-Neuve, cedex 16, Belgium, France.
3 Sauder School of Business, University of British Columbia, 2053 Main Mall, Vancouver, BC V6T 1Z2, Canada.
ESAIM: Mathematical Modelling and Numerical Analysis , Optimal Transport, Tome 49 (2015) no. 6, pp. 1659-1670

Voir la notice de l'article provenant de la source Numdam

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.

Reçu le :
DOI : 10.1051/m2an/2015026
Classification : 37A05, 49J20, 49J45, 90C26, 90C35, 90C48
Keywords: Optimal transportation, optimal pit mine design, Kantorovich duality

Ekeland, Ivar 1 ; Queyranne, Maurice 2, 3

1 CEREMADE, Université Paris-Dauphine, Place du Maréchal De Lattre De Tassigny, 75775 Paris, France.
2 CORE, Université Catholique de Louvain, Voie du Roman Pays 34, 1348 Louvain-la-Neuve, cedex 16, Belgium, France.
3 Sauder School of Business, University of British Columbia, 2053 Main Mall, Vancouver, BC V6T 1Z2, Canada. 
@article{M2AN_2015__49_6_1659_0,
     author = {Ekeland, Ivar and Queyranne, Maurice},
     title = {Optimal pits and optimal transportation},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1659--1670},
     publisher = {EDP-Sciences},
     volume = {49},
     number = {6},
     year = {2015},
     doi = {10.1051/m2an/2015026},
     zbl = {1357.37091},
     mrnumber = {3423270},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2015026/}
}
TY  - JOUR
AU  - Ekeland, Ivar
AU  - Queyranne, Maurice
TI  - Optimal pits and optimal transportation
JO  - ESAIM: Mathematical Modelling and Numerical Analysis 
PY  - 2015
SP  - 1659
EP  - 1670
VL  - 49
IS  - 6
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2015026/
DO  - 10.1051/m2an/2015026
LA  - en
ID  - M2AN_2015__49_6_1659_0
ER  - 
%0 Journal Article
%A Ekeland, Ivar
%A Queyranne, Maurice
%T Optimal pits and optimal transportation
%J ESAIM: Mathematical Modelling and Numerical Analysis 
%D 2015
%P 1659-1670
%V 49
%N 6
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2015026/
%R 10.1051/m2an/2015026
%G en
%F M2AN_2015__49_6_1659_0
Ekeland, Ivar; Queyranne, Maurice. Optimal pits and optimal transportation. ESAIM: Mathematical Modelling and Numerical Analysis , Optimal Transport, Tome 49 (2015) no. 6, pp. 1659-1670. doi: 10.1051/m2an/2015026

Cité par Sources :