A study of the Bienstock-Zuckerberg algorithm, Applications in Mining and Resource Constrained Project Scheduling
Gonzalo Mu\~noz, Daniel Espinoza, Marcos Goycoolea, Eduardo Moreno,, Maurice Queyranne, Orlando Rivera

TL;DR
This paper explores the Bienstock-Zuckerberg algorithm's broader applicability to various scheduling problems, providing new proofs, computational techniques, and empirical evidence of its superior performance over traditional methods.
Contribution
It extends the BZ algorithm's application to a wider class of scheduling problems, offers a new proof of correctness, and demonstrates its computational advantages through experiments.
Findings
BZ algorithm outperforms Dantzig-Wolfe in tested problems
Speed-up techniques significantly reduce solution times
Computational experiments validate the algorithm's effectiveness
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 (DW) algorithm. We discuss practical computational techniques for speeding up the performance of the BZ and DW algorithms on project scheduling problems. Finally, we…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
