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

Gonzalo Muñoz, Daniel Espinoza, Marcos Goycoolea, Eduardo Moreno, Maurice Queyranne, Orlando Rivera Letelier

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

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.

Original languageEnglish
Pages (from-to)501-534
Number of pages34
JournalComputational Optimization and Applications
Volume69
Issue number2
DOIs
StatePublished - 1 Mar 2018

Keywords

  • Column generation
  • Dantzig–Wolfe
  • Optimization
  • RCPSP

Fingerprint

Dive into the research topics of 'A study of the Bienstock–Zuckerberg algorithm: applications in mining and resource constrained project scheduling'. Together they form a unique fingerprint.

Cite this