A Binary Linear Programming Model for Optimizing Underground Sublevel Stope Layout

Abstract

Engineers face significant challenges when determining what geometry provides the most profitable and safe stope for extraction. Several techniques and optimization algorithms have been developed in recent years, but most fail to find optimal solutions because they are heuristic or LP-Based without efficient geometric constraints. This paper presents a two-dimensional binary linear programming (BLP) model for determining the optimal combination of blocks in a stope that maximizes the economic value of the layout of stopes for a sublevel deposit. the work draws from Queyranne and Wolsey's (2017 & 2018) formulations of tight constraints for bounded up/down times in production planning problems to formulate novel and efficient geometric constraints along with geotechnical and grade constraints for the BLP stope layout optimization problem. Results from the model indicate that it is possible to formulate efficient shape constraints in LP-Based approaches. the model used for the numerical example contained 144 valuable blocks out of 774 blocks, which translates into an economic value of $53.21M. the BLP model selected 60 valuable blocks and 13 waste blocks that met all constraints translating into a maximum economic value of $34.4M in 1.83 hours within a gap tolerance of 0.00%.

Department(s)

Mining Engineering

International Standard Book Number (ISBN)

978-087335521-6

Document Type

Article - Conference proceedings

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2025 Curran Associates Inc., All rights reserved.

Publication Date

01 Jan 2023

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