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Combined column generation and constructive heuristic for a proportionate flexible flow shop scheduling

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Abstract

In a proportionate flow shop problem, jobs have to be processed through a fixed sequence of machines, and processing time for each job is equal on all machines. Such a problem has seldom been tackled. Proportionate flexible flow shop (PFFS) scheduling problems combine the properties of proportionate flow shop scheduling problems and parallel machine scheduling problems. This study presents a combined approach based on column generation (CG) for a PFFS problem with the criterion to minimize the objective of the total weighted completion time (TWCT). Minimizing TWCT in a PFFS problem significantly differs from the parallel-identical-machine scheduling problem, an optimal schedule in which jobs on each machine are in the weighted shortest processing time (WSPT) order. This combined approach adopts a CG approach to effectively handle job assignments to machines, and a constructive heuristic to obtain an optimal sequence for a single machine. Experimental results show the effectiveness of the combined approach in obtaining excellent quality solutions in a reasonable time, especially for large-scale problems.

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Authors and Affiliations

  1. Department of Engineering Science, National Cheng-Kung University, Tainan, 701, Taiwan, Republic of China

    Yueh-Min Huang & Der-Fang Shiau

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  1. Yueh-Min Huang
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  2. Der-Fang Shiau
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Correspondence to Yueh-Min Huang.

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Huang, YM., Shiau, DF. Combined column generation and constructive heuristic for a proportionate flexible flow shop scheduling. Int J Adv Manuf Technol 38, 691–704 (2008). https://doi.org/10.1007/s00170-007-1130-9

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  • DOI: https://doi.org/10.1007/s00170-007-1130-9

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