scholarly journals Corrigendum to “Improved Combinatorial Benders Decomposition for a Scheduling Problem with Unrelated Parallel Machines”

2017 ◽  
Vol 2017 ◽  
pp. 1-2
Author(s):  
Francisco Regis Abreu Gomes ◽  
Geraldo Robson Mateus
Keyword(s):  
Parallel Machines ◽  
Benders Decomposition ◽  
Scheduling Problem ◽  
Unrelated Parallel Machines

scholarly journals Improved Combinatorial Benders Decomposition for a Scheduling Problem with Unrelated Parallel Machines

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Francisco Regis Abreu Gomes ◽  
Geraldo Robson Mateus
Keyword(s):  
Parallel Machines ◽  
Benders Decomposition ◽  
Mathematical Formulation ◽  
Optimal Solution ◽  
Master Problem ◽  
Computational Time ◽  
Scheduling Problem ◽  
Unrelated Parallel Machines ◽  
Warm Start ◽  
Dependent Setup Times

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.

Exact algorithms for a scheduling problem with unrelated parallel machines and sequence and machine-dependent setup times

2008 ◽  
Vol 35 (4) ◽  
pp. 1250-1264 ◽  
Author(s):  
Pedro Leite Rocha ◽  
Martín Gómez Ravetti ◽  
Geraldo Robson Mateus ◽  
Panos M. Pardalos
Keyword(s):  
Parallel Machines ◽  
Exact Algorithms ◽  
Setup Times ◽  
Scheduling Problem ◽  
Unrelated Parallel Machines ◽  
Dependent Setup Times
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