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Mathematical Model and Evaluation Function for Conflict-Free Warranted Makespan Minimization of Mixed Blocking Constraint Job-Shop Problems

1
Université de Lorraine, LGIPM, F-57000 Metz, France
2
ICN Business School, LGIPM, F-57000 Metz, France
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(1), 121; https://doi.org/10.3390/math8010121
Received: 6 November 2019 / Revised: 17 December 2019 / Accepted: 18 December 2019 / Published: 13 January 2020
In this paper, we consider a job-shop scheduling problem with mixed blocking constraints. Contrary to most previous studies, where no blocking or only one type of blocking constraint was used among successive operations, we assume that, generally, we may address several different blocking constraints in the same scheduling problem depending on the intermediate storage among machines, the characteristics of the machines, the technical constraints, and even the jobs. Our objective was to schedule a set of jobs to minimize the makespan. Thus, we propose, for the first time, a mathematical model of the job-shop problem taking into account the general case of mixed blocking constraints, and the results were obtained using Mosel Xpress software. Then, after explaining why and how groups of jobs have to be processed, a blocking constraint conflict-free warranted evaluation function is proposed and tested with the particle swarm optimization and genetic algorithm methods. The results prove that we obtained a near-optimal solution to this problem in a very short time. View Full-Text
Keywords: job shop; scheduling; mixed blocking constraints; mathematical model; genetic algorithm; particle swarm optimization job shop; scheduling; mixed blocking constraints; mathematical model; genetic algorithm; particle swarm optimization
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Sauvey, C.; Trabelsi, W.; Sauer, N. Mathematical Model and Evaluation Function for Conflict-Free Warranted Makespan Minimization of Mixed Blocking Constraint Job-Shop Problems. Mathematics 2020, 8, 121.

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