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Near-Optimal Heuristics for Just-In-Time Jobs Maximization in Flow Shop Scheduling

Faculty of Sciences and Technology (FCT), Federal University of Goias (UFG), 74968-755 Aparecida de Goiânia, Brazil
School of Engineering and Information Technology (SEIT), University of New South Wales (UNSW), Canberra ACT 2610, Australia
Instituto de Biociências, Letras e Ciências Exatas (IBILCE), Universidade Estadual Paulista (UNESP), 19014-020 São Paulo Brazil
Author to whom correspondence should be addressed.
Algorithms 2018, 11(4), 43;
Received: 28 February 2018 / Revised: 2 April 2018 / Accepted: 4 April 2018 / Published: 6 April 2018
(This article belongs to the Special Issue Algorithms for Scheduling Problems)
PDF [908 KB, uploaded 3 May 2018]


The number of just-in-time jobs maximization in a permutation flow shop scheduling problem is considered. A mixed integer linear programming model to represent the problem as well as solution approaches based on enumeration and constructive heuristics were proposed and computationally implemented. Instances with up to 10 jobs and five machines are solved by the mathematical model in an acceptable running time (3.3 min on average) while the enumeration method consumes, on average, 1.5 s. The 10 constructive heuristics proposed show they are practical especially for large-scale instances (up to 100 jobs and 20 machines), with very good-quality results and efficient running times. The best two heuristics obtain near-optimal solutions, with only 0.6% and 0.8% average relative deviations. They prove to be better than adaptations of the NEH heuristic (well-known for providing very good solutions for makespan minimization in flow shop) for the considered problem. View Full-Text
Keywords: just-in-time scheduling; flow shop; heuristics just-in-time scheduling; flow shop; heuristics

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Fuchigami, H.Y.; Sarker, R.; Rangel, S. Near-Optimal Heuristics for Just-In-Time Jobs Maximization in Flow Shop Scheduling. Algorithms 2018, 11, 43.

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