Optimally locating a junction point for an underground mine to maximise the net present value

Kashyapa Sirinanda; Marcus Brazil; Peter Grossman; Hyam Rubinstein; Doreen Thomas

doi:10.21914/anziamj.v55i0.7791

Authors

Kashyapa Sirinanda Department of Mechanical Engineering, The University of Melbourne.
Marcus Brazil Department of Electrical and Electronic Engineering, The University of Melbourne
Peter Grossman Department of Mechanical Engineering, The University of Melbourne
Hyam Rubinstein Department of Mathematics and Statistics, The University of Melbourne
Doreen Thomas Department of Mechanical Engineering, The University of Melbourne

DOI:

https://doi.org/10.21914/anziamj.v55i0.7791

Keywords:

Network optimisation, Underground mine design, NPV, Steiner points

Abstract

A review of the relevant literature identified an opportunity to develop algorithms for designing the access and construction schedule for an underground mine to maximise the net present value (NPV). The methods currently available perform the optimisation separately. However, this article focuses on optimising the access design and construction schedule simultaneously to yield a higher NPV. Underground mine access design was previously studied with the objective of minimising the haulage and development costs. However, when scheduling is included, time value of money has a crucial effect on locating the junction points (Steiner points) in the access network for maximum value. This article proposes an efficient algorithm to optimally locate a single junction, given a surface portal and two ore bodies, for maximum NPV where NPV includes the value of the ore bodies and the construction costs. We describe the variation in the location of the junction for a range of discount rates. References

K. F. Lane, The economic definition of ore---cutoff grade in theory and practice. Mining Journal Books Limited, London 1988.
F. K. Hwang, D. S. Richards and P. Winter, The Steiner tree problem. Elsevier, 1992. http://www.elsevier.com/books/the-steiner-tree-problem/hwang/978-0-444-89098-6
M. Brazil and D. A. Thomas, Network optimisation for the design of underground mines. Networks 49:40–50, 2007. doi:10.1002/net.20140
M. Brazil, J. H. Rubinstein, D. A. Thomas, J. F. Weng and N. C. Wormald, Gradient-constrained minimum networks (I). Fundamentals. J. Global Optim. 21:139–155, 2001. doi:10.1023/A:1011903210297

Author Biographies

Kashyapa Sirinanda, Department of Mechanical Engineering, The University of Melbourne.

2nd year PhD student.

Marcus Brazil, Department of Electrical and Electronic Engineering, The University of Melbourne

Associate Professor and Reader, Department of Electrical and Electronic Engineering

Peter Grossman, Department of Mechanical Engineering, The University of Melbourne

Senior Research Fellow, Department of Mechanical Engineering, The University of Melbourne

Hyam Rubinstein, Department of Mathematics and Statistics, The University of Melbourne

Professor, Department of Mathematics and Statistics, The University of Melbourne

Doreen Thomas, Department of Mechanical Engineering, The University of Melbourne

Professor and Head of the Department, Department of Mechanical Engineering, The University of Melbourne