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A single-machine learning effect scheduling problem with release times


  • Lee, Wen-Chiung
  • Wu, Chin-Chia
  • Hsu, Peng-Hsiang


In this paper, we investigate a single-machine problem with the learning effect and release times where the objective is to minimize the makespan. A branch-and-bound algorithm incorporating with several dominance properties and lower bounds is developed to derive the optimal solution. A heuristic algorithm is proposed to obtain a near-optimal solution. The computational experiments show that the branch-and-bound algorithm can solve instances up to 36 jobs, and the average error percentage of the proposed heuristic is less than 0.11%.

Suggested Citation

  • Lee, Wen-Chiung & Wu, Chin-Chia & Hsu, Peng-Hsiang, 2010. "A single-machine learning effect scheduling problem with release times," Omega, Elsevier, vol. 38(1-2), pages 3-11, February.
  • Handle: RePEc:eee:jomega:v:38:y:2010:i:1-2:p:3-11

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    References listed on IDEAS

    1. Lee, Wen-Chiung & Wu, Chin-Chia, 2004. "Minimizing total completion time in a two-machine flowshop with a learning effect," International Journal of Production Economics, Elsevier, vol. 88(1), pages 85-93, March.
    2. Wang, F. -K. & Lee, W., 2001. "Learning curve analysis in total productive maintenance," Omega, Elsevier, vol. 29(6), pages 491-499, December.
    3. Koulamas, Christos & Kyparisis, George J., 2007. "Single-machine and two-machine flowshop scheduling with general learning functions," European Journal of Operational Research, Elsevier, vol. 178(2), pages 402-407, April.
    4. Biskup, Dirk, 2008. "A state-of-the-art review on scheduling with learning effects," European Journal of Operational Research, Elsevier, vol. 188(2), pages 315-329, July.
    5. Wu, Chin-Chia & Lee, Wen-Chiung, 2009. "A note on the total completion time problem in a permutation flowshop with a learning effect," European Journal of Operational Research, Elsevier, vol. 192(1), pages 343-347, January.
    6. Reddy Dondeti, V. & Mohanty, Bidhu B., 1998. "Impact of learning and fatigue factors on single machine scheduling with penalties for tardy jobs," European Journal of Operational Research, Elsevier, vol. 105(3), pages 509-524, March.
    7. Biskup, Dirk, 1999. "Single-machine scheduling with learning considerations," European Journal of Operational Research, Elsevier, vol. 115(1), pages 173-178, May.
    8. Mosheiov, Gur, 2001. "Scheduling problems with a learning effect," European Journal of Operational Research, Elsevier, vol. 132(3), pages 687-693, August.
    9. Wang, Ji-Bo, 2007. "Single-machine scheduling problems with the effects of learning and deterioration," Omega, Elsevier, vol. 35(4), pages 397-402, August.
    10. Nawaz, Muhammad & Enscore Jr, E Emory & Ham, Inyong, 1983. "A heuristic algorithm for the m-machine, n-job flow-shop sequencing problem," Omega, Elsevier, vol. 11(1), pages 91-95.
    11. T.C. Cheng & Guoqing Wang, 2000. "Single Machine Scheduling with Learning Effect Considerations," Annals of Operations Research, Springer, vol. 98(1), pages 273-290, December.
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    Cited by:

    1. Cheng, T.C.E. & Wu, Chin-Chia & Chen, Juei-Chao & Wu, Wen-Hsiang & Cheng, Shuenn-Ren, 2013. "Two-machine flowshop scheduling with a truncated learning function to minimize the makespan," International Journal of Production Economics, Elsevier, vol. 141(1), pages 79-86.
    2. Yang, Suh-Jenq & Yang, Dar-Li, 2010. "Minimizing the makespan on single-machine scheduling with aging effect and variable maintenance activities," Omega, Elsevier, vol. 38(6), pages 528-533, December.
    3. Chen, Xi & Thomas, Barrett W. & Hewitt, Mike, 2016. "The technician routing problem with experience-based service times," Omega, Elsevier, vol. 61(C), pages 49-61.
    4. Janiak, Adam & Rudek, RadosLaw, 2010. "A note on a makespan minimization problem with a multi-ability learning effect," Omega, Elsevier, vol. 38(3-4), pages 213-217, June.
    5. Lee, Wen-Chiung & Chung, Yu-Hsiang, 2013. "Permutation flowshop scheduling to minimize the total tardiness with learning effects," International Journal of Production Economics, Elsevier, vol. 141(1), pages 327-334.
    6. Lai, Peng-Jen & Lee, Wen-Chiung, 2011. "Single-machine scheduling with general sum-of-processing-time-based and position-based learning effects," Omega, Elsevier, vol. 39(5), pages 467-471, October.
    7. Sterna, Malgorzata, 2011. "A survey of scheduling problems with late work criteria," Omega, Elsevier, vol. 39(2), pages 120-129, April.
    8. repec:spr:annopr:v:238:y:2016:i:1:d:10.1007_s10479-015-2054-7 is not listed on IDEAS
    9. Turabieh, Hamza & Abdullah, Salwani, 2011. "An integrated hybrid approach to the examination timetabling problem," Omega, Elsevier, vol. 39(6), pages 598-607, December.


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