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Optimal pits and optimal transportation

Author

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  • EKELAND, Iver

    (Université Paris-Dauphine)

  • QUEYRANNE, Maurice

    (Université catholique de Louvain, CORE, Belgium)

Abstract

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 +8. We show that this transportation problem is a strong dual to the optimum pit problem, and also yields optimality (complementarity slackness) conditions.

Suggested Citation

  • EKELAND, Iver & QUEYRANNE, Maurice, 2014. "Optimal pits and optimal transportation," LIDAM Discussion Papers CORE 2014052, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2014052
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    References listed on IDEAS

    as
    1. Ivar Ekeland, 2010. "Existence, uniqueness and efficiency of equilibrium in hedonic markets with multidimensional types," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(2), pages 275-315, February.
    2. Felipe Alvarez & Jorge Amaya & Andreas Griewank & Nikolai Strogies, 2011. "A continuous framework for open pit mine planning," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 73(1), pages 29-54, February.
    3. repec:dau:papers:123456789/6443 is not listed on IDEAS
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