IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v64y2016i3p497-513.html
   My bibliography  Save this article

Gradient-constrained discounted Steiner trees I: optimal tree configurations

Author

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

Abstract

A gradient-constrained discounted Steiner tree T is a maximum Net Present Value (NPV) tree, spanning a given set N of nodes in space with edges whose gradients are all no more than an upper bound m which is the maximum gradient. The nodes in T but not in N are referred to as discounted Steiner points. Such a tree has costs associated with its edges and values associated with its 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. In this paper, we study the optimal tree configurations so as to maximize the sum of all the discounted cash flows, known as the 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 in the presence of the gradient constraint. This constraint defines the navigability conditions on mining vehicles along the underground tunnels. Labellings are essential for defining a tree configuration and indicate gradients on the edges of the network. An edge in a gradient-constrained discounted Steiner tree is labelled as an f edge, an m edge or a b edge, if the gradient is less, equal or greater than m respectively. Each tree configuration is identified by the labellings of its edges. In this paper the non-optimal sets of labellings of edges that are incident with the discounted Steiner point in a gradient-constrained discounted Steiner network are classified. This reduces the number of configurations that need to be considered when optimizing. In addition, the gradient-constrained discounted Steiner point algorithm is outlined. 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 I: optimal tree configurations," Journal of Global Optimization, Springer, vol. 64(3), pages 497-513, March.
    • Handle: RePEc:spr:jglopt:v:64:y:2016:i:3:p:497-513
    DOI: 10.1007/s10898-015-0326-z
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-015-0326-z
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10898-015-0326-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Rafael Epstein & Marcel Goic & Andrés Weintraub & Jaime Catalán & Pablo Santibáñez & Rodolfo Urrutia & Raúl Cancino & Sergio Gaete & Augusto Aguayo & Felipe Caro, 2012. "Optimizing Long-Term Production Plans in Underground and Open-Pit Copper Mines," Operations Research, INFORMS, vol. 60(1), pages 4-17, February.
    3. Amina Lamghari & Roussos Dimitrakopoulos & Jacques Ferland, 2015. "A hybrid method based on linear programming and variable neighborhood descent for scheduling production in open-pit mines," Journal of Global Optimization, Springer, vol. 63(3), pages 555-582, November.
    4. César Flores-Fonseca & Rodrigo Linfati & John Willmer Escobar, 2022. "Exact algorithms for production planning in mining considering the use of stockpiles and sequencing of power shovels in open-pit mines," Operational Research, Springer, vol. 22(3), pages 2529-2553, July.
    5. Christina N. Burt & Lou Caccetta, 2014. "Equipment Selection for Surface Mining: A Review," Interfaces, INFORMS, vol. 44(2), pages 143-162, April.
    6. W. Brian Lambert & Andrea Brickey & Alexandra M. Newman & Kelly Eurek, 2014. "Open-Pit Block-Sequencing Formulations: A Tutorial," Interfaces, INFORMS, vol. 44(2), pages 127-142, April.
    7. Renaud Chicoisne & Daniel Espinoza & Marcos Goycoolea & Eduardo Moreno & Enrique Rubio, 2012. "A New Algorithm for the Open-Pit Mine Production Scheduling Problem," Operations Research, INFORMS, vol. 60(3), pages 517-528, June.
    8. Martin L. Smith & Stewart J. Wicks, 2014. "Medium-Term Production Scheduling of the Lumwana Mining Complex," Interfaces, INFORMS, vol. 44(2), pages 176-194, April.
    9. Nancel-Penard, Pierre & Morales, Nelson & Cornillier, Fabien, 2022. "A recursive time aggregation-disaggregation heuristic for the multidimensional and multiperiod precedence-constrained knapsack problem: An application to the open-pit mine block sequencing problem," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1088-1099.
    10. Nakousi, C. & Pascual, R. & Anani, A. & Kristjanpoller, F. & Lillo, P., 2018. "An asset-management oriented methodology for mine haul-fleet usage scheduling," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 336-344.
    11. Jélvez, Enrique & Morales, Nelson & Nancel-Penard, Pierre & Peypouquet, Juan & Reyes, Patricio, 2016. "Aggregation heuristic for the open-pit block scheduling problem," European Journal of Operational Research, Elsevier, vol. 249(3), pages 1169-1177.
    12. Kwame Awuah-Offei & Sisi Que & Atta Ur Rehman, 2021. "Evaluating Mine Design Alternatives for Social Risks Using Discrete Choice Analysis," Sustainability, MDPI, vol. 13(16), pages 1-15, August.
    13. Tabesh, Mohammad & Moradi Afrapoli, Ali & Askari-Nasab, Hooman, 2023. "A two-stage simultaneous optimization of NPV and throughput in production planning of open pit mines," Resources Policy, Elsevier, vol. 80(C).
    14. Pérez, Juan & Maldonado, Sebastián & González-Ramírez, Rosa, 2018. "Decision support for fleet allocation and contract renegotiation in contracted open-pit mine blasting operations," International Journal of Production Economics, Elsevier, vol. 204(C), pages 59-69.
    15. Gonzalo Muñoz & Daniel Espinoza & Marcos Goycoolea & Eduardo Moreno & Maurice Queyranne & Orlando Rivera Letelier, 2018. "A study of the Bienstock–Zuckerberg algorithm: applications in mining and resource constrained project scheduling," Computational Optimization and Applications, Springer, vol. 69(2), pages 501-534, March.
    16. O’Sullivan, Dónal & Newman, Alexandra, 2015. "Optimization-based heuristics for underground mine scheduling," European Journal of Operational Research, Elsevier, vol. 241(1), pages 248-259.
    17. Michelle L. Blom & Christina N. Burt & Adrian R. Pearce & Peter J. Stuckey, 2014. "A Decomposition-Based Heuristic for Collaborative Scheduling in a Network of Open-Pit Mines," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 658-676, November.
    18. Noriega, Roberto & Pourrahimian, Yashar, 2022. "A systematic review of artificial intelligence and data-driven approaches in strategic open-pit mine planning," Resources Policy, Elsevier, vol. 77(C).
    19. W. Lambert & A. Newman, 2014. "Tailored Lagrangian Relaxation for the open pit block sequencing problem," Annals of Operations Research, Springer, vol. 222(1), pages 419-438, November.
    20. Castillo, Emilio, 2021. "The impacts of profit-based royalties on early-stage mineral exploration," Resources Policy, Elsevier, vol. 73(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jglopt:v:64:y:2016:i:3:p:497-513. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.