Implementing a parametric maximum flow algorithm for optimal open pit mine design under uncertain supply and demand

Abstract

Conventional open pit mine optimization models for designing mining phases and ultimate pit limit do not consider expected variations and uncertainty in metal content available in a mineral deposit (supply) and commodity prices (market demand). Unlike the conventional approach, a stochastic framework relies on multiple realizations of the input data so as to account for uncertainty in metal content and financial parameters, reflecting potential supply and demand. This paper presents a new method that jointly considers uncertainty in metal content and commodity prices, and incorporates time-dependent discounted values of mining blocks when designing optimal production phases and ultimate pit limit, while honouring production capacity constraints. The structure of a graph representing the stochastic framework is proposed, and it is solved with a parametric maximum flow algorithm. Lagragnian relaxation and the subgradient method are integrated in the proposed approach to facilitate producing practical designs. An application at a copper deposit in Canada demonstrates the practical aspects of the approach and quality of solutions over conventional methods, as well as the effectiveness of the proposed stochastic approach in solving mine planning and design problems.

Keywords:

• open pit mine optimization
• maximum flow algorithm
• Lagrangian relaxation
• subgradient method

Acknowledgements

The work in this paper was funded from NSERC CDR Grant 335696 and BHP Billiton, NSERC Discovery grant 239019, and the members of the COSMO Stochastic Mine Planning Laboratory: AngloGold Ashanti, Barrick, BHP Billiton, De Beers, Newmont, and Vale. Thanks are in order to Brian Baird, Peter Stone, Darren Dyck, and Gavin Yates of BHP Billiton for their support, collaboration, and technical comments.