Time delayed discounted Steiner trees to locate two or more discounted Steiner points

Authors

  • Kashyapa Sirinanda The University of Melbourne Australia
  • 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.v57i0.10400

Keywords:

Network optimisation, Underground mine design, NPV, Steiner points

Abstract

A discounted Steiner tree is a weighted Steiner tree in which the costs of constructing the edges and values at the nodes are discounted over time. Discounted Steiner points can be located to maximise the sum of the discounted cash flows, known as the net present value, and an algorithm for doing this for a single Steiner point, known as the discounted Steiner point algorithm, was previously established. An application of this problem is underground mine planning. This article proposes an algorithm to optimally locate two junction points, given a surface portal and three ore resource points, for maximum net present value, which includes the value of the ore bodies and the construction costs. The discounted Steiner point algorithm is extended to locate two junction points where time delays may occur at a discounted Steiner point before constructing the adjacent edges. The optimal locations of the junction points are obtained for a range of discount rates. Numerical trials show that this algorithm works well. A generalisation of the algorithm to locate more discounted Steiner points is also discussed. References

Author Biographies

Kashyapa Sirinanda, The University of Melbourne Australia

Postdoctoral Research Fellow at the Mechanical Engineering, the University of Melbourne.

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

Published

2016-10-11

Issue

Section

Proceedings Engineering Mathematics and Applications Conference