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Author Munoz, G.; Espinoza, D.; Goycoolea, M.; Moreno, E.; Queyranne, M.; Rivera Letelier, O.
Title A study of the Bienstock-Zuckerberg algorithm: applications in mining and resource constrained project scheduling Type
Year 2018 Publication Computational Optimization And Applications Abbreviated Journal Comput. Optim. Appl.
Volume 69 Issue 2 Pages 501-534
Keywords Column generation; Dantzig-Wolfe; Optimization; RCPSP
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.
Address [Munoz, Gonzalo] Columbia Univ, Ind Engn & Operat Res, New York, NY USA, Email: marcos.goycoolea@uai.cl
Corporate Author Thesis
Publisher Springer Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0926-6003 ISBN Medium
Area Expedition Conference
Notes WOS:000426295000009 Approved
Call Number UAI @ eduardo.moreno @ Serial 835
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Author Rivera Letelier, O.; Espinoza, D.; Goycoolea, M.; Moreno, E.; Munoz, G.
Title Production scheduling for strategic open pit mine planning: A mixed integer programming approach Type
Year 2020 Publication Operations Research Abbreviated Journal Oper. Res.
Volume 68 Issue 5 Pages 1425-1444
Keywords
Abstract Given a discretized representation of an ore body known as a block model, the open pit mining production scheduling problem that we consider consists of defining which blocks to extract, when to extract them, and how or whether to process them, in such a way as to comply with operational constraints and maximize net present value. Although it has been established that this problem can be modeled with mixed-integer programming, the number of blocks used to represent real-world mines (millions) has made solving large instances nearly impossible in practice. In this article, we introduce a new methodology for tackling this problem and conduct computational tests using real problem sets ranging in size from 20,000 to 5,000,000 blocks and spanning 20 to 50 time periods. We consider both direct block scheduling and bench-phase scheduling problems, with capacity, blending, and minimum production constraints. Using new preprocessing and cutting planes techniques, we are able to reduce the linear programming relaxation value by up to 33\%, depending on the instance. Then, using new heuristics, we are able to compute feasible solutions with an average gap of 1.52% relative to the previously computed bound. Moreover, after four hours of running a customized branch-and-bound algorithm on the problems with larger gaps, we are able to further reduce the average from 1.52% to 0.71%
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0030-364X ISBN Medium
Area Expedition Conference
Notes Approved
Call Number UAI @ eduardo.moreno @ Serial 1052
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