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

scholarly journals MIP Models and Hybrid Algorithms for Simultaneous Job Splitting and Scheduling on Unrelated Parallel Machines

2014 ◽  
Vol 2014 ◽  
pp. 1-19 ◽  
Author(s):  
Duygu Yilmaz Eroglu ◽  
H. Cenk Ozmutlu
Keyword(s):  
Genetic Algorithms ◽  
Local Search ◽  
Parallel Machines ◽  
Search Algorithm ◽  
Mixed Integer ◽  
Unrelated Parallel Machines ◽  
Job Splitting ◽  
Mip Models ◽  
Dependent Setup Times ◽  
Genetic Local Search

We developed mixed integer programming (MIP) models and hybrid genetic-local search algorithms for the scheduling problem of unrelated parallel machines with job sequence and machine-dependent setup times and with job splitting property. The first contribution of this paper is to introduce novel algorithms which make splitting and scheduling simultaneously with variable number of subjobs. We proposed simple chromosome structure which is constituted by random key numbers in hybrid genetic-local search algorithm (GAspLA). Random key numbers are used frequently in genetic algorithms, but it creates additional difficulty when hybrid factors in local search are implemented. We developed algorithms that satisfy the adaptation of results of local search into the genetic algorithms with minimum relocation operation of genes’ random key numbers. This is the second contribution of the paper. The third contribution of this paper is three developed new MIP models which are making splitting and scheduling simultaneously. The fourth contribution of this paper is implementation of the GAspLAMIP. This implementation let us verify the optimality of GAspLA for the studied combinations. The proposed methods are tested on a set of problems taken from the literature and the results validate the effectiveness of the proposed algorithms.

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