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2017 Improved Combinatorial Benders Decomposition for a Scheduling Problem with Unrelated Parallel Machines
Francisco Regis Abreu Gomes, Geraldo Robson Mateus
J. Appl. Math. 2017: 1-10 (2017). DOI: 10.1155/2017/9452762

Abstract

This paper addresses the unrelated parallel machines scheduling problem with sequence and machine dependent setup times. Its goal is to minimize the makespan. The problem is solved by a combinatorial Benders decomposition. This method can be slow to converge. Therefore, three procedures are introduced to accelerate its convergence. The first procedure is a new method that consists of terminating the execution of the master problem when a repeated optimal solution is found. The second procedure is based on the multicut technique. The third procedure is based on the warm-start. The improved Benders decomposition scheme is compared to a mathematical formulation and a standard implementation of Benders decomposition algorithm. In the experiments, two test sets from the literature are used, with 240 and 600 instances with up to 60 jobs and 5 machines. For the first set the proposed method performs 21.85% on average faster than the standard implementation of the Benders algorithm. For the second set the proposed method failed to find an optimal solution in only 31 in 600 instances, obtained an average gap of 0.07%, and took an average computational time of 377.86 s, while the best results of the other methods were 57, 0.17%, and 573.89 s, respectively.

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Francisco Regis Abreu Gomes. Geraldo Robson Mateus. "Improved Combinatorial Benders Decomposition for a Scheduling Problem with Unrelated Parallel Machines." J. Appl. Math. 2017 1 - 10, 2017. https://doi.org/10.1155/2017/9452762

Information

Received: 27 March 2017; Accepted: 29 May 2017; Published: 2017
First available in Project Euclid: 15 August 2017

zbMATH: 1437.90077
MathSciNet: MR3805987
Digital Object Identifier: 10.1155/2017/9452762

Rights: Copyright © 2017 Hindawi

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