Single-machine scheduling with past-sequence-dependent setup times and learning effects: a parametric analysis

Mani, V and Chang, Pei-Chann and Chen, Shih-Hsin (2011) Single-machine scheduling with past-sequence-dependent setup times and learning effects: a parametric analysis. In: International Journal of Systems Science (IJSSS), 42 (12). pp. 2097-2102.

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Abstract

In this article, we consider the single-machine scheduling problem with past-sequence-dependent (p-s-d) setup times and a learning effect. The setup times are proportional to the length of jobs that are already scheduled; i.e. p-s-d setup times. The learning effect reduces the actual processing time of a job because the workers are involved in doing the same job or activity repeatedly. Hence, the processing time of a job depends on its position in the sequence. In this study, we consider the total absolute difference in completion times (TADC) as the objective function. This problem is denoted as 1/LE, (Spsd)/TADC in Kuo and Yang (2007) ('Single Machine Scheduling with Past-sequence-dependent Setup Times and Learning Effects', Information Processing Letters, 102, 22-26). There are two parameters a and b denoting constant learning index and normalising index, respectively. A parametric analysis of b on the 1/LE, (Spsd)/TADC problem for a given value of a is applied in this study. In addition, a computational algorithm is also developed to obtain the number of optimal sequences and the range of b in which each of the sequences is optimal, for a given value of a. We derive two bounds b* for the normalising constant b and a* for the learning index a. We also show that, when a < a* or b > b*, the optimal sequence is obtained by arranging the longest job in the first position and the rest of the jobs in short processing time order.

Item Type:	Journal Article
Publication:	International Journal of Systems Science (IJSSS)
Publisher:	Taylor and Francis Group
Additional Information:	Copyright of this article belongs to Taylor and Francis Group.
Keywords:	scheduling;setup times;learning effect
Department/Centre:	Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited:	09 Nov 2011 05:54
Last Modified:	09 Nov 2011 05:54
URI:	http://eprints.iisc.ac.in/id/eprint/41944

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