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Gradient-constrained discounted Steiner trees II: optimally locating a discounted Steiner point

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

Abstract

A gradient-constrained discounted Steiner tree is a network interconnecting given set of nodes in Euclidean space where the gradients of the edges are all no more than an upper bound which defines the maximum gradient. In such a tree, the costs are associated with its edges and values are associated with nodes and are discounted over time. In this paper, we study the problem of optimally locating a single Steiner point in the presence of the gradient constraint in a tree so as to maximize the sum of all the discounted cash flows, known as the net present value (NPV). An edge in the tree is labelled as a b edge, or a m edge, or an f edge if the gradient between its endpoints is greater than, or equal to, or less than the maximum gradient respectively. The set of edge labels at a discounted Steiner point is called its labelling. The optimal location of the discounted Steiner point is obtained for the labellings that can occur in a gradient-constrained discounted Steiner tree. In this paper, we propose the gradient-constrained discounted Steiner point algorithm to optimally locate the discounted Steiner point in the presence of a gradient constraint in a network. This algorithm is applied to a case study. This problem occurs in underground mining, where we focus on the optimization of underground mine access to obtain maximum NPV in the presence of a gradient constraint. The gradient constraint defines the navigability conditions for trucks along the underground tunnels. Copyright Springer Science+Business Media New York 2016

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:64:y:2016:i:3:p:515-532
    DOI: 10.1007/s10898-015-0325-0
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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. 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.
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    Cited by:

    1. Akshay Chowdu & Peter Nesbitt & Andrea Brickey & Alexandra M. Newman, 2022. "Operations Research in Underground Mine Planning: A Review," Interfaces, INFORMS, vol. 52(2), pages 109-132, March.

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