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Maximizing the net present value of a Steiner tree

Author

Listed:
  • K. Sirinanda
  • M. Brazil
  • P. Grossman
  • J. Rubinstein
  • D. Thomas

Abstract

The theory of Steiner trees has been extensively applied in physical network design problems to locate a Steiner point that minimizes the total length of a tree. However, maximizing the total generated cash flows of a tree has not been investigated. Such a tree has costs associated with its edges and values associated with nodes. In order to reach the nodes in the tree, the edges need to be constructed. The edges are constructed in a particular order and the costs of constructing the edges and the values at the nodes are discounted over time. These discounted costs and values generate cash flows. In this paper, we study the problem of optimally locating a single Steiner point so as to maximize the sum of all the discounted cash flows, known as the net present value (NPV). An application of this problem occurs in underground mining where, we want to optimally locate a junction point in the underground access network to maximize the NPV. We propose an efficient iterative algorithm to optimally locate a single degree-3 Steiner point. We show this algorithm converges quickly and the Steiner point is unique subject to realistic design parameters. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • K. Sirinanda & M. Brazil & P. Grossman & J. Rubinstein & D. Thomas, 2015. "Maximizing the net present value of a Steiner tree," Journal of Global Optimization, Springer, vol. 62(2), pages 391-407, June.
    • Handle: RePEc:spr:jglopt:v:62:y:2015:i:2:p:391-407
    DOI: 10.1007/s10898-014-0246-3
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    References listed on IDEAS

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    1. Alexandra M. Newman & Enrique Rubio & Rodrigo Caro & Andrés Weintraub & Kelly Eurek, 2010. "A Review of Operations Research in Mine Planning," Interfaces, INFORMS, vol. 40(3), pages 222-245, June.
    2. Newman, Alexandra M. & Kuchta, Mark, 2007. "Using aggregation to optimize long-term production planning at an underground mine," European Journal of Operational Research, Elsevier, vol. 176(2), pages 1205-1218, January.
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    1. K. Sirinanda & M. Brazil & P. Grossman & J. Rubinstein & D. Thomas, 2016. "Gradient-constrained discounted Steiner trees II: optimally locating a discounted Steiner point," Journal of Global Optimization, Springer, vol. 64(3), pages 515-532, March.
    2. K. Sirinanda & M. Brazil & P. Grossman & J. Rubinstein & D. Thomas, 2016. "Gradient-constrained discounted Steiner trees I: optimal tree configurations," Journal of Global Optimization, Springer, vol. 64(3), pages 497-513, March.

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