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A study of the Bienstock–Zuckerberg algorithm: applications in mining and resource constrained project scheduling

Author

Listed:
  • Gonzalo Muñoz

    (Columbia University)

  • Daniel Espinoza

    (Gurobi Optimization)

  • Marcos Goycoolea

    (Universidad Adolfo Ibañez)

  • Eduardo Moreno

    (Universidad Adolfo Ibañez)

  • Maurice Queyranne

    (University of British Columbia)

  • Orlando Rivera Letelier

    (Universidad Adolfo Ibañez)

Abstract

We study a Lagrangian decomposition algorithm recently proposed by Dan Bienstock and Mark Zuckerberg for solving the LP relaxation of a class of open pit mine project scheduling problems. In this study we show that the Bienstock–Zuckerberg (BZ) algorithm can be used to solve LP relaxations corresponding to a much broader class of scheduling problems, including the well-known Resource Constrained Project Scheduling Problem (RCPSP), and multi-modal variants of the RCPSP that consider batch processing of jobs. We present a new, intuitive proof of correctness for the BZ algorithm that works by casting the BZ algorithm as a column generation algorithm. This analysis allows us to draw parallels with the well-known Dantzig–Wolfe decomposition (DW) algorithm. We discuss practical computational techniques for speeding up the performance of the BZ and DW algorithms on project scheduling problems. Finally, we present computational experiments independently testing the effectiveness of the BZ and DW algorithms on different sets of publicly available test instances. Our computational experiments confirm that the BZ algorithm significantly outperforms the DW algorithm for the problems considered. Our computational experiments also show that the proposed speed-up techniques can have a significant impact on the solve time. We provide some insights on what might be explaining this significant difference in performance.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:coopap:v:69:y:2018:i:2:d:10.1007_s10589-017-9946-1
    DOI: 10.1007/s10589-017-9946-1
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    References listed on IDEAS

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    Cited by:

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    2. Yan, Ran & Wang, Shuaian & Cao, Jiannong & Sun, Defeng, 2021. "Shipping Domain Knowledge Informed Prediction and Optimization in Port State Control," Transportation Research Part B: Methodological, Elsevier, vol. 149(C), pages 52-78.
    3. Armstrong, Margaret & Lagos, Tomas & Emery, Xavier & Homem-de-Mello, Tito & Lagos, Guido & Sauré, Denis, 2021. "Adaptive open-pit mining planning under geological uncertainty," Resources Policy, Elsevier, vol. 72(C).
    4. Renaud Chicoisne, 2023. "Computational aspects of column generation for nonlinear and conic optimization: classical and linearized schemes," Computational Optimization and Applications, Springer, vol. 84(3), pages 789-831, April.
    5. Nesbitt, Peter & Blake, Lewis R. & Lamas, Patricio & Goycoolea, Marcos & Pagnoncelli, Bernardo K. & Newman, Alexandra & Brickey, Andrea, 2021. "Underground mine scheduling under uncertainty," European Journal of Operational Research, Elsevier, vol. 294(1), pages 340-352.
    6. Steven Lamontagne & Margarida Carvalho & Emma Frejinger & Bernard Gendron & Miguel F. Anjos & Ribal Atallah, 2023. "Optimising Electric Vehicle Charging Station Placement Using Advanced Discrete Choice Models," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1195-1213, September.

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