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 and Orlando Rivera Letelier
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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

Computational Optimization and Applications, 2018, vol. 69, issue 2, No 9, 534 pages

Abstract: 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.

Keywords: Column generation; Dantzig–Wolfe; Optimization; RCPSP (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10589-017-9946-1

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