Flow shop scheduling with deteriorating jobs under dominating machines to minimize makespan

Original Article


In this paper, we consider an n-job, m-machine flow shop scheduling problem with deteriorating jobs. By deteriorating jobs, we mean jobs whose processing times are an increasing function of their execution starting time. A simple linear deterioration function is assumed. When some dominant relationships between m − 1 machines can be satisfied, we show that the makespan minimization problem can be solved in polynomial time.


Scheduling Flow shop Simple linear deterioration Makespan Dominating machines 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alidaee B, Womer NK (1999) Scheduling with time dependent processing times: review and extensions. J Oper Res Soc 50:711–720MATHGoogle Scholar
  2. 2.
    Cheng TCE, Ding Q, Lin BMT (2004) A concise survey of scheduling with time-dependent processing times. Eur J Oper Res 152:1–13MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Wu C-C, Lee W-C, Shiau Y-R (2007) Minimizing the total weighted completion time on a single machine under linear deterioration. Int J Adv Manuf Technol 33:1237–1243CrossRefGoogle Scholar
  4. 4.
    Toksar MD, Guner E (2007) Minimizing the earliness/tardiness costs on parallel machine with learning effects and deteriorating jobs: a mixed nonlinear integer programming approach. Int J Adv Manuf Technol. doi:10.1007/s00170-007-1128-3 Google Scholar
  5. 5.
    Lee W-C, Wu C-C, Liu H-C (2008) A note on single-machine makespan problem with general deteriorating function. Int J Adv Manuf Technol. doi:10.1007/s00170-008-1421-9 Google Scholar
  6. 6.
    Kononov A, Gawiejnowicz S (2001) NP-hard cases in scheduling deteriorating jobs on dedicated machines. J Oper Res Soc 52:708–717MATHCrossRefGoogle Scholar
  7. 7.
    Mosheiov G (2002) Complexity analysis of job-shop scheduling with deteriorating jobs. Discrete Appl Math 117:195–209MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Wang J-B, Xia Z-Q (2006) Flow shop scheduling with deteriorating jobs under dominating machines. Omega 34:327–336CrossRefMathSciNetGoogle Scholar
  9. 9.
    Wang J-B, Ng CT, Cheng TCE, Liu L-L (2006) Minimizing total completion time in a two-machine flow shop with deteriorating jobs. Appl Math Comput 180:185–193MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Wu C-C, Lee W-C (2006) Two-machine flowshop scheduling to minimize mean flow time under linear deterioration. Int J Prod Econ 103:572–584CrossRefGoogle Scholar
  11. 11.
    Lee W-C, Wu C-C, Wen C-C, Chung Y-H (2008) A two-machine flowshop makespan scheduling problem with deteriorating jobs. Comput Ind Eng 54(4):737–749CrossRefGoogle Scholar
  12. 12.
    Lee W-C, Wu C-C (2008) Multi-machine scheduling with deteriorating jobs and scheduled maintenance. Appl Math Model 32(3):362–373MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Lee W-C, Wu C-C, Chung Y-H, Liu H-C (2008) Minimizing the total completion time in permutation flow shop with machine-dependent job deterioration rates. Comput Oper Res. doi:10.1016/j.cor.2008.07.008 Google Scholar
  14. 14.
    He C-C, Wu C-C, Lee W-C (2008) Branch-and-bound and weight-combination search algorithms for the total completion time problem with step-deteriorating jobs. J Oper Res Soc. doi:10.1057/jors.2008.123 Google Scholar
  15. 15.
    Wang J-B, 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 41:1221–1226CrossRefGoogle Scholar
  16. 16.
    Wang L-Y, Wang J-B, Wang D, Yin N, Huang X, Feng E-M (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 Google Scholar
  17. 17.
    Wang L-Y, Wang J-B, Gao W-J, Huang X, Feng E-M (2009) Two single-machine scheduling problems with the effects of deterioration and learning. Int J Adv Manuf Technol. doi:10.1007/s00170-009-2145-1 Google Scholar
  18. 18.
    Huang X, Wang J-B, Wang X-R (2009) A generalization for single-machine scheduling with deteriorating jobs to minimize earliness penalties. Int J Adv Manuf Technol. doi:10.1007/s00170-009-2242-1 Google Scholar
  19. 19.
    Mosheiov G (1994) Scheduling jobs under simple linear deterioration. Comput Oper Res 21:653–659MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2009

Authors and Affiliations

  1. 1.School of ScienceShenyang Institute of Aeronautical EngineeringShenyangPeople’s Republic of China

Personalised recommendations