Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-10T13:29:02.169Z Has data issue: false hasContentIssue false
  • English
  • Français

OPTIMAL LOCATION OF AN UNDERGROUND CONNECTOR USING DISCOUNTED STEINER TREE THEORY

Part of: Operations research and management science

Published online by Cambridge University Press:  18 January 2021

K. G. SIRINANDA Open the ORCID record for K. G. SIRINANDA [Opens in a new window] ,
M. BRAZIL Open the ORCID record for M. BRAZIL [Opens in a new window] ,
P. A. GROSSMAN Open the ORCID record for P. A. GROSSMAN [Opens in a new window] ,
J. H. RUBINSTEIN Open the ORCID record for J. H. RUBINSTEIN [Opens in a new window]  and
D. A. THOMAS Open the ORCID record for D. A. THOMAS [Opens in a new window]
K. G. SIRINANDA
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, VIC3010, Australia; e-mail: kashyapa.sirinanda@gmail.com, peterag@unimelb.edu.au, doreen.thomas@unimelb.edu.au.
M. BRAZIL*
Affiliation:
Department of Electrical and Electronic Engineering, The University of Melbourne, VIC3010, Australia; e-mail: brazil@unimelb.edu.au.
P. A. GROSSMAN
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, VIC3010, Australia; e-mail: kashyapa.sirinanda@gmail.com, peterag@unimelb.edu.au, doreen.thomas@unimelb.edu.au.
J. H. RUBINSTEIN
Affiliation:
Department of Mathematics and Statistics, The University of Melbourne, VIC3010, Australia; e-mail: hyam.rubinstein@gmail.com.
D. A. THOMAS
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, VIC3010, Australia; e-mail: kashyapa.sirinanda@gmail.com, peterag@unimelb.edu.au, doreen.thomas@unimelb.edu.au.
*
e-mail: brazil@unimelb.edu.au
Get access Rights & Permissions [Opens in a new window]

Abstract

The objective of this paper is to demonstrate that the gradient-constrained discounted Steiner point algorithm (GCDSPA) described in an earlier paper by the authors is applicable to a class of real mine planning problems, by using the algorithm to design a part of the underground access in the Rubicon gold mine near Kalgoorlie in Western Australia. The algorithm is used to design a decline connecting two ore bodies so as to maximize the net present value (NPV) associated with the connector. The connector is to break out from the access infrastructure of one ore body and extend to the other ore body. There is a junction on the connector where it splits in two near the second ore body. The GCDSPA is used to obtain the optimal location of the junction and the corresponding NPV. The result demonstrates that the GCDSPA can be used to solve certain problems in mine planning for which currently available methods cannot provide optimal solutions.

Keywords

network optimizationmine planningunderground miningSteiner treesnet present value

MSC classification

Primary: 90B80: Discrete location and assignment
Type
Research Article
Information
The ANZIAM Journal , Volume 62 , Issue 3 , July 2020 , pp. 334 - 351
Check for updates
Copyright
© Australian Mathematical Society 2021

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ben-Awuah, E., Richter, O., Elkington, T. and Pourrahimian, Y., “Strategic mining options optimization: open pit mining, underground mining or both”, Int. J. Min. Sci. Technol. 26 (2016) 1065–1071; doi:10.1016/j.ijmst.2016.09.015.CrossRefGoogle Scholar
Brazil, M., Grossman, P. A., Lee, D. H., Rubinstein, J. H., Thomas, D. A. and Wormald, N. C., “Decline design in underground mines using constrained path optimization”, Min. Technol. 117 (2008) 93–99; doi:10.1179/174328608X362668.CrossRefGoogle Scholar
Brazil, M., Rubinstein, J. H., Thomas, D. A., Weng, J. F. and Wormald, N. C., “Gradient-constrained minimum networks (I). Fundamentals”, J. Glob. Optim. 21 (2001) 139–155; doi:10.1023/A:1011903210297.CrossRefGoogle Scholar
Brazil, M. and Thomas, D. A., “Network optimisation for the design of underground mines”, Networks 49 (2007) 40–50; doi:10.1002/net.20140.CrossRefGoogle Scholar
Brazil, M., Thomas, D. A. and Weng, J. F., “Gradient-constrained minimum networks (II). Labelled or locally minimal Steiner points”, J. Glob. Optim. 42(2008)23–37; doi:10.1007/s10898-007-9201-x.CrossRefGoogle Scholar
Brazil, M. and Zachariasen, M., Optimal interconnection trees in the plane, Volume 29 of Algorithms Comb. Ser. (Springer International Publishing, Cham, 2015); doi:10.1007/978-3-319-13915-9. CrossRefGoogle Scholar
Dagdelen, K., “Open pit optimization – Strategies for improving economics of mining projects through mine planning”, 17th Int. Min. Congr. Exhib. of Turkey (Chamber of Mining Engineers of Turkey, Ankara, Turkey, 2001) 117–121.Google Scholar
Grossman, P. A., Brazil, M., Rubinstein, J. H. and Thomas, D. A., “Scheduling the construction of value and discount weighted trees for maximum net present value”, Comput. Oper. Res. 115 (2020) 104578; doi:10.1016/j.cor.2018.10.018.CrossRefGoogle Scholar
Hou, J., Xu, C., Dowd, P. A. and Li, G., “Integrated optimisation of stope boundary and access layout for underground mining operations”, Min. Technol. 128 (2019) 193–205; doi:25726668.2019.1603920.CrossRefGoogle Scholar
Johnson, T. B. and Sharp, R. W., “A three dimensional dynamic programming method for optimal ultimate pit design”, US Department of the Interior, Bureau of Mines, Report of Investigation 7553, Washington, 1971, available at https://books.google.com.au/books?id=XXu36F7yAasC&pg=PP1#v=onepage&q&f=false.Google Scholar
King, B. and Newman, A., “Optimizing the cutoff grade for an operational underground mine”, Interfaces 48 (2018) 291–397; doi:10.1287/inte.2017.0934.Google Scholar
Lerchs, H. and Grossmann, I. F., “Optimum design of open pit mines”, Can. Inst. Min. Bull. 58 (1965) 17–24.Google Scholar
Little, J., Topal, E. and Knights, P., “Simultaneous optimisation of stope layouts and long term production schedules”, Min. Technol. 120 (2011) 129–136; doi:10.1179/1743286311Y.0000000011.CrossRefGoogle Scholar
Meyer, M., “Applying linear programming to the design of ultimate pit limits”, Manag. Sci. 16 (1969) B121–B135, available at https://www.jstor.org/stable/2628495.CrossRefGoogle Scholar
Newman, A. M. and Kuchta, M., “Using aggregation to optimize long-term production planning at an underground mine”, Eur. J. Oper. Res. 176 (2007) 1205–1218; doi:10.1016/j.ejor.2005.09.008.CrossRefGoogle Scholar
Newman, A. M., Rubio, E., Caro, R., Weintraub, A. and Eurek, K., “A review of operations research in mine planning”, Interfaces 40 (2010) 222–245; doi:10.1287/inte.1090.0492.CrossRefGoogle Scholar
Northern Star Ltd (2015), Official website and factsheets, available at http://www.nsrltd.com/.Google Scholar
Sirinanda, K. G., Brazil, M., Grossman, P. A., Rubinstein, J. H. and Thomas, D. A., “Optimally locating a junction point for an underground mine to maximise the net present value”, ANZIAM J. 55 (2014) C315–C328; doi:10.21914/anziamj.v55i0.7791.CrossRefGoogle Scholar
Sirinanda, K. G., Brazil, M., Grossman, P. A., Rubinstein, J. H., and Thomas, D. A., “Maximizing the net present value of a Steiner tree”, J. Glob. Optim. 62 (2015) 391–407; doi:10.1007/s10898-014-0246-3.CrossRefGoogle Scholar
Sirinanda, K. G., Brazil, M., Grossman, P. A., Rubinstein, J. H. and Thomas, D. A., “Time delayed discounted Steiner trees to locate two or more discounted Steiner points”, ANZIAM J. 57 (2016) C253–C267; doi:10.21914/anziamj.v57i0.10400.CrossRefGoogle Scholar
Sirinanda, K. G., Brazil, M., Grossman, P. A., Rubinstein, J. H. and Thomas, D. A., “Gradient-constrained discounted Steiner trees I – Optimal tree configurations”, J. Glob. Optim. 64 (2016) 497–513; doi:10.1007/s10898-015-0326-z.CrossRefGoogle Scholar
Sirinanda, K. G., Brazil, M., Grossman, P. A., Rubinstein, J. H. and Thomas, D. A., “Gradient-constrained discounted Steiner trees II – Optimally locating a discounted Steiner point”, J. Glob. Optim. 64 (2016) 515–532; doi:10.1007/s10898-015-0325-0.CrossRefGoogle Scholar
Sirinanda, K. G., Brazil, M., Grossman, P. A., Rubinstein, J. H. and Thomas, D. A., “Strategic underground mine access design to maximise the net present value”, in: Advances in Applied Strategic Mine Planning, (Springer, Cham, 2018) 607–624; doi:10.1007/978-3-319-69320-0.CrossRefGoogle Scholar
Trout, L. P., “Underground mine production scheduling using mixed integer programming”, 25th Int. APCOM Symp., Melbourne, Australia, (1995) 395–400, available at https://ausimm.com/product/underground-mine-production-scheduling-using-mixed-integer-programming/.Google Scholar
Zhao, Y. and Kim, Y. C., “A new graph theory algorithm for optimal ultimate design”, Proc. 23rd Int. APCOM Symp., (1992) 423–434, available at https://www.onemine.org/document/abstract.cfm?docid=173106&title=A-New-Graph-Theory-Algorithm-For-Optimal-Ultimate-Pit-Design.Google Scholar