IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v48y2000i6p894-914.html
   My bibliography  Save this article

Performance Analysis and Best Implementations of Old and New Algorithms for the Open-Pit Mining Problem

Author

Listed:
  • Dorit S. Hochbaum

    (Department of IE&OR and Haas School of Business, University of California, Berkeley, California 94720)

  • Anna Chen

    (Department of IE&OR, University of California, Berkeley, California 94720)

Abstract

The open-pit mining problem is to determine the contours of a mine, based on economic data and engineering feasibility requirements, to yield maximum possible net income. This practical problem needs to be solved for very large data sets. In practice, moreover, it is necessary to test multiple scenarios, taking into account a variety of realizations of geological predictions and forecasts of ore value.The industry is experiencing computational difficulties in solving the problem. Yet, the problem is known to be equivalent to the minimum cut or maximum flow problem. For the maximum flow problem there are a number of very efficient algorithms that have been developed over the last decade. On the other hand, the algorithm that is most commonly used by the mining industry has been devised by Lerchs and Grossmann (LG). This algorithm is used in most commercial software packages for open-pit mining.This paper describes a detailed study of the LG algorithm as compared to the maximum flow “push-relabel” algorithm. We propose here an efficient implementation of the push-relabel algorithm adapted to the features of the open-pit mining problem. We study issues such as the properties of the mine and ore distribution and how they affect the running time of the algorithm. We also study some features that improve the performance of the LG algorithm. The proposed implementations offer significant improvements compared to existing algorithms and make the related sensitivity analysis problem practically solvable.

Suggested Citation

  • Dorit S. Hochbaum & Anna Chen, 2000. "Performance Analysis and Best Implementations of Old and New Algorithms for the Open-Pit Mining Problem," Operations Research, INFORMS, vol. 48(6), pages 894-914, December.
    • Handle: RePEc:inm:oropre:v:48:y:2000:i:6:p:894-914
    DOI: 10.1287/opre.48.6.894.12392
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.48.6.894.12392
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.48.6.894.12392?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
    ---><---

    References listed on IDEAS

    as
    1. R. K. Ahuja & James B. Orlin, 1989. "A Fast and Simple Algorithm for the Maximum Flow Problem," Operations Research, INFORMS, vol. 37(5), pages 748-759, October.
    2. J. M. W. Rhys, 1970. "A Selection Problem of Shared Fixed Costs and Network Flows," Management Science, INFORMS, vol. 17(3), pages 200-207, November.
    3. Jean-Claude Picard, 1976. "Maximal Closure of a Graph and Applications to Combinatorial Problems," Management Science, INFORMS, vol. 22(11), pages 1268-1272, July.
    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. Gary Kochenberger & Jin-Kao Hao & Fred Glover & Mark Lewis & Zhipeng Lü & Haibo Wang & Yang Wang, 2014. "The unconstrained binary quadratic programming problem: a survey," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 58-81, July.
    2. José R. Correa & Andreas S. Schulz, 2005. "Single-Machine Scheduling with Precedence Constraints," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 1005-1021, November.
    3. Dorit S. Hochbaum, 2004. "50th Anniversary Article: Selection, Provisioning, Shared Fixed Costs, Maximum Closure, and Implications on Algorithmic Methods Today," Management Science, INFORMS, vol. 50(6), pages 709-723, June.
    4. Queyranne, M. & Wolsey, L.A., 2015. "Modeling poset convex subsets," LIDAM Discussion Papers CORE 2015049, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Gary R. Waissi, 1993. "A new polynomial algorithm for maximum value flow with an efficient parallel implementation," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(3), pages 393-414, April.
    6. 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.
    7. Rolf H. Möhring & Andreas S. Schulz & Frederik Stork & Marc Uetz, 2003. "Solving Project Scheduling Problems by Minimum Cut Computations," Management Science, INFORMS, vol. 49(3), pages 330-350, March.
    8. Chatterjee, Snehamoy & Sethi, Manas Ranjan & Asad, Mohammad Waqar Ali, 2016. "Production phase and ultimate pit limit design under commodity price uncertainty," European Journal of Operational Research, Elsevier, vol. 248(2), pages 658-667.
    9. Biswas, Pritam & Sinha, Rabindra Kumar & Sen, Phalguni, 2023. "A review of state-of-the-art techniques for the determination of the optimum cut-off grade of a metalliferous deposit with a bibliometric mapping in a surface mine planning context," Resources Policy, Elsevier, vol. 83(C).
    10. Arbib, Claudio & Servilio, Mara & Archetti, Claudia & Speranza, M. Grazia, 2014. "The directed profitable location Rural Postman Problem," European Journal of Operational Research, Elsevier, vol. 236(3), pages 811-819.
    11. Hezhi Luo & Xiaodi Bai & Jiming Peng, 2019. "Enhancing Semidefinite Relaxation for Quadratically Constrained Quadratic Programming via Penalty Methods," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 964-992, March.
    12. Chunli Liu & Jianjun Gao, 2015. "A polynomial case of convex integer quadratic programming problems with box integer constraints," Journal of Global Optimization, Springer, vol. 62(4), pages 661-674, August.
    13. Csapó, Gergely & Müller, Rudolf, 2013. "Optimal mechanism design for the private supply of a public good," Games and Economic Behavior, Elsevier, vol. 80(C), pages 229-242.
    14. Jesus Cunha & Luidi Simonetti & Abilio Lucena, 2016. "Lagrangian heuristics for the Quadratic Knapsack Problem," Computational Optimization and Applications, Springer, vol. 63(1), pages 97-120, January.
    15. Domenico Moramarco & Umutcan Salman, 2023. "Equal opportunities in many-to-one matching markets," Working Papers 649, ECINEQ, Society for the Study of Economic Inequality.
    16. Dorit S. Hochbaum, 2003. "Efficient Algorithms for the Inverse Spanning-Tree Problem," Operations Research, INFORMS, vol. 51(5), pages 785-797, October.
    17. Esmaeili, Ahmadreza & Hamidi, Jafar Khademi & Mousavi, Amin, 2023. "Determination of sublevel stoping layout using a network flow algorithm and the MRMR classification system," Resources Policy, Elsevier, vol. 80(C).
    18. 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.
    19. 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.
    20. Pavlos Eirinakis & Dimitrios Magos & Ioannis Mourtos & Panayiotis Miliotis, 2012. "Finding All Stable Pairs and Solutions to the Many-to-Many Stable Matching Problem," INFORMS Journal on Computing, INFORMS, vol. 24(2), pages 245-259, May.

    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:inm:oropre:v:48:y:2000:i:6:p:894-914. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.