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Optimality conditions for the continuous model of the final open pit problem

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Abstract

In this work we address the Final Open Pit problem in a continuous framework, that is, the problem of finding the optimal profile for an open pit that satisfies an additional slope and maximum capacity conditions on extraction. Using optimal control theory and calculus of variations tools, we provide optimality conditions for that problem. In particular, we prove that the distribution of gain along the lower border of the optimal pit must be zero, when the slope and capacity constraints are not active.

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Acknowledgements

J. Amaya was supported by CONICYT-PIA Basal Program CMM-AFB170001 and CONICYT-FONDECYT under Grant 1130816. E. Molina was supported by CONICYT-PFCHA/Doctorado Nacional/2018-21180348 and CONICYT-FONDECYT under Grant 1130816. C. Hermosilla was supported by CONICYT-FONDECYT under Grant 11190456.

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Authors and Affiliations

  1. Departamento de Ingeniería Matemática, Centro de Modelamiento Matemático (CNRS UMI 2807), Universidad de Chile, Santiago, Chile

    Jorge Amaya & Emilio Molina

  2. Departamento de Matemática, Universidad Técnica Federico Santa María, Valparaíso, Chile

    Cristopher Hermosilla

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  1. Jorge Amaya
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  2. Cristopher Hermosilla
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  3. Emilio Molina
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Correspondence to Jorge Amaya.

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Amaya, J., Hermosilla, C. & Molina, E. Optimality conditions for the continuous model of the final open pit problem. Optim Lett 15, 991–1007 (2021). https://doi.org/10.1007/s11590-019-01516-8

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