##
**Machine scheduling problems with a general learning effect.**
*(English)*
Zbl 1190.90076

Summary: Recently, learning effects in scheduling problems have received growing attention. The position-based learning model seems to be a realistic assumption for the case where the actual processing of the job is mainly machine driven. In this paper, we consider the sum-of-processing-time-based learning model. We propose a learning model which considers both the machine and human learning effects, simultaneously. We first show that the position-based learning and the sum-of-processing-time-based learning models in the literature are special cases of the proposed model. Moreover, we present the solution procedures for some single-machine and some flowshop problems. Editorial remark: A counterexample for the main theorems was given in [ibid. 51, No. 5-6, 847–849 (2010; Zbl 1190.90069)].

### MSC:

90B35 | Deterministic scheduling theory in operations research |

68T05 | Learning and adaptive systems in artificial intelligence |

### Keywords:

scheduling; position-based learning; sum-of-processing-time-based learning; single machine; flowshop### Citations:

Zbl 1190.90069
PDF
BibTeX
XML
Cite

\textit{X. Zhang} and \textit{G. Yan}, Math. Comput. Modelling 51, No. 1--2, 84--90 (2010; Zbl 1190.90076)

Full Text:
DOI

### References:

[1] | Pinedo, M., Scheduling: theory, and systems, (2001), Prentice-Hall Upper Saddle River, NJ |

[2] | Biskup, D., Single-machines scheduling with learning considerations, European of journal operation research, 115, 173-178, (1999) · Zbl 0946.90025 |

[3] | Wright, T.P., Factors affecting the cost of airplanes, Journal of aeronautical science, 3, 122-128, (1936) |

[4] | Biskup, D., A state-of-the-art review on scheduling with learning effect, European journal of operational research, 188, 315-329, (2008) · Zbl 1129.90022 |

[5] | Mosheiov, G., Scheduling problems with a learning effect, European of journal operation research, 132, 687-693, (2001) · Zbl 1017.90051 |

[6] | Mosheiov, G., Parallel machine scheduling with a learning effect, Journal of operation research society, 52, 1165-1169, (2001) · Zbl 1178.90159 |

[7] | Mosheiov, G.; Sidney, J.B., Scheduling with general job-dependent learning curves, European journal of operation research, 147, 665-670, (2003) · Zbl 1037.90529 |

[8] | Mosheiov, G.; Sidney, J.B., Note on scheduling with general learning curves to minimize the number of tardy jobs, Journal of operation research society, 56, 110-112, (2005) · Zbl 1122.90356 |

[9] | Cheng, M.B.; Sun, S.J.; Yu, Y., A note on flow shop scheduling problems with a learning effect on non-idle dominant machines, Applied mathematics and computation, 184, 945-949, (2007) · Zbl 1143.90011 |

[10] | Wu, C.C.; Lee, W.C., A note on the total completion time problem in a permutation flowshop with a learning effect, European journal of operational research, 192, 343-347, (2009) · Zbl 1180.90144 |

[11] | Cheng, T.C.E.; Wang, G., Single machine scheduling with learning effect consideration, Annals of operation research, 98, 273-290, (2000) · Zbl 0967.68019 |

[12] | Bachman, A.; Janiak, A., Scheduling jobs with position-dependent processing times, Journal of the operational research society, 55, 257-264, (2004) · Zbl 1095.90033 |

[13] | Wang, J.B., A note on scheduling problems with learning effects and deteriorating jobs, International journal of systems science, 37, 827-833, (2006) · Zbl 1126.90347 |

[14] | Wang, J.B., Single-machine scheduling problems with the effects of learning and deterioration, Omega, 35, 397-402, (2007) |

[15] | Cheng, T.C.E.; Wu, C.C.; Lee, W.C., Some scheduling problems with sum-of-processing-times-based and job-position-based learning effects, Information sciences, 178, 2476-2487, (2008) · Zbl 1172.90397 |

[16] | Yin, Y.Q.; Xu, D.H.; Sun, K.B.; Li, H.X., Some scheduling problems with general position-dependent and time-dependent learning effects, Information sciences, 179, 2416-2425, (2009) · Zbl 1166.90342 |

[17] | Wu, C.C.; Lee, W.C., Single-machine scheduling problems with a learning effect, Applied mathematical modelling, 32, 1191-1197, (2008) · Zbl 1172.90415 |

[18] | Lee, W.C.; Wu, C.C., Some single-machine and \(m\)-machine flowshop scheduling problems with learning considerations, Information sciences, 179, 3885-3892, (2009) · Zbl 1179.90141 |

[19] | Wang, J.B.; Wang, D.; Wang, L.Y.; Lin, L.; Yin, N.; Wang, W.W., Single machine scheduling with exponential time-dependent learning effect and past sequence-dependent setup times, Computers and mathematics with applications, 57, 9-16, (2009) · Zbl 1165.90471 |

[20] | Cheng, T.C.E.; Lai, P.J.; Wu, C.C.; Lee, W.C., Single-machine scheduling with sum-of-logarithm-processing-times-based learning considerations, Information sciences, 179, 3127-3135, (2009) · Zbl 1170.90387 |

[21] | Kuo, W.H.; Yang, D.L., Minimizing the total completion time in a single-machine scheduling problem with a time-dependent learning effect, European journal of operational research, 174, 1184-1190, (2006) · Zbl 1103.90341 |

[22] | Koulamas, C.; Kyparisis, G.J., Single-machine and two-machine flowshop scheduling with general learning function, European journal of operational research, 178, 402-407, (2007) · Zbl 1107.90018 |

[23] | Wu, C.C.; Lee, W.C., Single-machine and flowshop scheduling with a general learning effect model, Computers & industrial engineering, 56, 1553-1558, (2009) |

[24] | Graham, R.L.; Lawler, E.L.; Lenstra, J.K.; Rinnooy Kan, A.H.G., Optimization and approximation in deterministic sequencing and scheduling: A survey, 5, 287-326, (1979) · Zbl 0411.90044 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.