Computational Optimization and Applications

, Volume 69, Issue 2, pp 501–534 | Cite as

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

  • Gonzalo Muñoz
  • Daniel Espinoza
  • Marcos GoycooleaEmail author
  • Eduardo Moreno
  • Maurice Queyranne
  • Orlando Rivera Letelier


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.


Column generation Dantzig–Wolfe Optimization RCPSP 


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Industrial Engineering and Operations ResearchColumbia UniversityNew YorkUSA
  2. 2.Gurobi OptimizationHoustonUSA
  3. 3.School of BusinessUniversidad Adolfo IbañezSantiagoChile
  4. 4.Faculty of EngineeringUniversidad Adolfo IbañezSantiagoChile
  5. 5.School of BusinessUniversity of British ColumbiaVancouverCanada
  6. 6.School of Business and Faculty of EngineeringUniversidad Adolfo IbañezSantiagoChile

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