The risk-averse ultimate pit problem

Gianpiero Canessa, Eduardo Moreno, Bernardo K. Pagnoncelli

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


In this work, we consider a risk-averse ultimate pit problem where the grade of the mineral is uncertain. We derive conditions under which we can generate a set of nested pits by varying the risk level instead of using revenue factors. We propose two properties that we believe are desirable for the problem: risk nestedness, which means the pits generated for different risk aversion levels should be contained in one another, and additive consistency, which states that preferences in terms of order of extraction should not change if independent sectors of the mine are added as precedences. We show that only an entropic risk measure satisfies these properties and propose a two-stage stochastic programming formulation of the problem, including an efficient approximation scheme to solve it. We illustrate our approach in a small self-constructed example, and apply our approximation scheme to a real-world section of the Andina mine, in Chile.

Original languageEnglish
Pages (from-to)2655-2678
Number of pages24
JournalOptimization and Engineering
Issue number4
StatePublished - Dec 2021


  • Integer programming
  • Mining
  • Risk-averse optimization
  • Ultimate pit


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