A computational study of the permutation flow shop problem based on a tight lower bound

Authors:
Talel Ladhari;Mohamed Haouari
Affiliations:
Laboratory of Mathematical Engineering, Ecole Polytechnique de Tunisie, BP 743, La Marsa 2078, Tunisia and Ecole Supérieure des Sciences Economiques et Commerciales, Tunis 1089, Tunisia;Laboratory of Mathematical Engineering, Ecole Polytechnique de Tunisie, BP 743, La Marsa 2078, Tunisia
Venue:
Computers and Operations Research
Year:
2005

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Abstract

We consider the classical permutation flow shop problem which requires scheduling n jobs through m machines which are placed in series so as to minimize the makespan. This problem is known to be NP-hard. We describe a branch-and-bound algorithm with a lower bounding procedure based on the so-called two-machine flow shop problem with time lags, ready times, and delivery times. We present extensive computational results on both random instances, with up to 8000 operations, and well-known benchmarks, with up to 2000 operations, which show that the proposed algorithm solves large-scale instances in moderate CPU time. In particular, we report proven optimal solutions for benchmark problems which have been open for some time.