Single-machine scheduling with past-sequence-dependent setup times and learning effects: a parametric analysis |
| |
Authors: | V. Mani Shih-Hsin Chen |
| |
Affiliation: | 1. Department of Aerospace Engineering , Indian Institute of Science , Bangalore, India;2. Department of Electronic Commerce Management , Nanhua University , Chiayi 62248, Taiwan, R.O.C. |
| |
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, s psd /TADC in Kuo and Yang (2007 Kuo, WH and Yang, DL. 2007. Single Machine Scheduling with Past-sequence-dependent Setup Times and Learning Effects. Information Processing Letters, 102: 22–26. [Crossref], [Web of Science ®] , [Google Scholar]) (‘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, s psd /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. |
| |
Keywords: | scheduling setup times learning effect |
|
|