Masters Theses

Keywords and Phrases

Binary integer linear programming; heuristics; integer linear programming; mathematical programming; stope layout optimization; underground mine planning


"Underground mine planning 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 thesis work proposes a two-dimensional binary linear programming (BILP) 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 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. The BILP 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%. A series of experiments show that the model is sensitive to cutoff grade, stope frame size, pillar size, the number of stopes, and the optimization problem size. Depending on the input values for these key parameters selected, they impact the objective function value, the solution time and the final layout of stopes generated by the algorithm. The main limitation of the proposed model is that pillar constraints are implemented in the Z – X or Z – Y directions but not implemented diagonally"-- Abstract, p. iii


Awuah-Offei, Kwame, 1975-

Committee Member(s)

Ben-Awuah, Eugene
Frimpong, Samuel


Mining Engineering

Degree Name

M.S. in Mining Engineering


Missouri University of Science and Technology

Publication Date

Spring 2024


xiv, 147 pages

Note about bibliography

Includes_bibliographical_references_(pages 131-146)


© 2023 Theophilus Mensah, All rights reserved

Document Type

Thesis - Open Access

File Type




Thesis Number

T 12339

Electronic OCLC #