Optimization and Engineering

, Volume 17, Issue 4, pp 813–832 | Cite as

Stope optimization with vertical convexity constraints

  • Gonzalo Nelis
  • Michel Gamache
  • Denis Marcotte
  • Xiaoyu Bai


A new algorithm for the optimal stope design problem is proposed. It is based on a previous methodology developed by Bai et al. (Comput Geosci 52:361–371, 2013a) where a cylindrical coordinate system is used to define geomechanical restrictions and to find the optimal stope around an initial raise. The new algorithm extends this work using an integer programming formulation and a new set of constraints, aimed to solve geomechanical issues present on the original methodology. The new formulation is tested on two synthetic and one real deposits. An economic, geomechanical and feasibility analysis is performed, comparing the new results with Bai’s methodology. This methodology achieves better stope designs in terms of geomechanical stability and wall regularity, generating feasible stopes for real use. It also allows further extensions to incorporate other geometrical constraints in order to obtain more regular stope designs.


OR in mining Stope optimization Underground mining Sublevel stoping 



The Government of Canada provided a Research Scholarship to the first author. The authors are grateful for the comments, corrections and insights made by the three anonymous reviewers.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Gonzalo Nelis
    • 1
  • Michel Gamache
    • 2
  • Denis Marcotte
    • 3
  • Xiaoyu Bai
    • 3
  1. 1.Department of Mining Engineering, Delphos Mine Planning Laboratory and Advanced Mining Technology CenterUniversity of ChileSantiagoChile
  2. 2.GERAD Research Center and Department of Mathematics and Industrial EngineeringÉcole PolytechniqueMontrealCanada
  3. 3.Department of Civil, Geological and Mining EngineeringÉcole PolytechniqueMontrealCanada

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