Abstract
This paper considers a single-machine scheduling model with past-sequence-dependent setup times and a general learning effect. It develops a general model with setup times and learning effect considerations where the actual processing time of a job is not only a function of the total actual processing time of the jobs already processed, but also a function of the job’s scheduled position. The paper shows that the single-machine scheduling problems to minimize the makespan and the sum of the kth power of completion times are polynomially solvable under the proposed model. It further shows that the problems to minimize the total weighted completion time and the maximum lateness are polynomially solvable under certain conditions.
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References
Allahverdi A, Gupta JND, Aldowaisan T (1999) A review of scheduling research involving setup considerations. Omega 27:219–239
Allahverdi A, Ng CT, Cheng TCE, Kovalyov MY (2008) A survey of scheduling problems with setup times or costs. Eur J Oper Res 187:985–1032
Koulamas C, Kyparisis GJ (2008) Single-machine scheduling problems with past-sequence-dependent setup times. Eur J Oper Res 187:68–72
Kuo W-H, Yang D-L (2007) Single-machine scheduling with pastsequence- dependent setup and learning effects. Inf Process Lett 102:22–26
Wang JB (2008) Single-machine scheduling with pastsequence- dependent setup times and time-dependent learning effect. Comput Ind Eng 55:584–591
Wang JB, Jiang Y, Wang G (2009) Single machine scheduling with past-sequence-dependent setup times and effects of deterioration and learning. Int J Adv Manuf Technol 41:1221–1226
Jaber YM, Bonney M (1999) The economic manufacture/order quantity (EMQ/EOQ) and the learning curve: past, present, and future. Int J Prod Econ 59:93–102
Biskup D (1999) Single-machine scheduling with learning considerations. Eur J Oper Res 115:173–178
Cheng TCE, Wang G (2000) Single machine scheduling with learning effect considerations. Ann Oper Res 98:273–290
Mosheiov G (2001) Scheduling problems with a learning effect. Eur J Oper Res 132:687–692
Mosheiov G, Sidney JB (2003) Scheduling with general job-dependent learning curves. Eur J Oper Res 147:665–670
Lin BMT (2007) Complexity results for single-machine scheduling with positional learning effects. J Oper Res Soc 58:1099–1102
Lee WC, Wu CC, Sung HJ (2004) A bi-criterion single-machine scheduling problem with learning considerations. Acta Informatica 40:303–315
Eren T, Güner E (2009) A bicriteria parallel machine scheduling with a learning effect. Int J Adv Manuf Technol 40:1202–1205
Wu CC, Lee WC (2007) A note on single-machine scheduling with learning effect and an availability constraint. Int J Adv Manuf Technol 33:540–544. doi:10.1007/s00170-006-0469-7
Wu CC, Lee WC, Wang WC (2007) A two-machine flowshop maximum tardiness scheduling problem with a learning effect. Int J Adv Manuf Technol 31:743–750
Toksar MD, Güner E (2009) Scheduling problems with the nonlinear effects of learning and deterioration. Int J Adv Manuf Technol. doi:10.1007/s00170-009-2016-9
Kuo WH, Yang DL (2006) Minimizing the total completion time in a single-machine scheduling problem with a time-dependent learning effect. Eur J Oper Res 174:1184–1190
Kuo WH, Yang DL (2006) Single-machine group scheduling with a time-dependent learning effect. Comput Oper Res 33:2099–2112
Koulamas C, Kyparisis GJ (2007) Single-machine and two-machine flowshop scheduling with general learning functions. Eur J Oper Res 178:402–407
Wang LY, Wang JB, Wang D, Yin N, Huang X, Feng EM (2009) Single-machine scheduling with a sum-of-processing-time based learning effect and deteriorating jobs. Int J Adv Manuf Technol. doi:10.1007/s00170-009-1950-x
Wu CC, Lee WC (2008) Single-machine scheduling problems with a learning effect. Appl Math Model 32:1191–1197
Cheng TCE, Wu CC, Lee WC (2008) Some scheduling problems with sum-of-processing-times-based and job-position-based learning effects. Inf Sci 178:2476–2487
Yin Y, Xu D, Sun K, Li H (2009) Some scheduling problems with general position-dependent and time-dependent learning effects. Inf Sci 179:2416–2425
Biskup D (2008) A state-of-the-art review on scheduling with learning effects. Eur J Oper Res 188:315–329
Yang DL, Kuo WH (2007) Single-machine scheduling with an actual time-dependent learning effect. J Oper Res Soc 58:1348–1353
Townsend W (1978) The single machine problem with quadratic penalty function of completion times: a branch-and-bound solution. Manage Sci 24:530–533
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Yin, Y., Xu, D. & Wang, J. Some single-machine scheduling problems with past-sequence-dependent setup times and a general learning effect. Int J Adv Manuf Technol 48, 1123–1132 (2010). https://doi.org/10.1007/s00170-009-2360-9
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DOI: https://doi.org/10.1007/s00170-009-2360-9