Skip to main content

Advertisement

SpringerLink
Log in

Robust and stable scheduling of a single machine with random machine breakdowns

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

For single-machine scheduling with random machine breakdowns, a new method considering both robustness and stability is proposed in this paper. The stability of the predictive schedule is measured by the sum of the absolute deviations between the planned job completion times and the realized ones. A surrogate measure is developed to evaluate the stability, assuming that there is only one breakdown. Generating a robust and stable schedule becomes a bi-objective optimization problem. A two-stage multi-population genetic algorithm is proposed to solve the bi-objective optimization problem. The method is applied to minimizing the total weighted tardiness of all jobs. The computational results show that the schedule generated by the proposed method is insensitive to disturbances, along with providing better robustness and stability.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Pinedo M (1995) Scheduling: theory, algorithms, and systems. Prentice-Hall, Englewood Cliffs, New Jersey

    MATH  Google Scholar 

  2. Herrmann JW, Lee C-Y, Snowdon JL (1993) A classification of static scheduling problems. In: Pardalos PM (ed) Complexity in numerical optimization. World Scientific, Singapore, pp 203–253

    Google Scholar 

  3. Uzsoy R, Lee C-Y, Martin-Vega LA (1992) A review of production planning and scheduling models in the semiconductor industry. Part I: system characteristics, performance evaluation and production planning. IIE Trans 24:47–60

    Google Scholar 

  4. Uzsoy R, Lee C-Y, Martin-Vega LA (1994) A review of production planning and scheduling models in the semiconductor industry. Part II: shop-floor control. IIE Trans 26:44–55

    Google Scholar 

  5. Leon VJ, Wu SD, Storer RH (1994) Robustness measures and robust scheduling for job shops. IIE Trans 26:32–43

    Google Scholar 

  6. Mehta SV, Uzsoy R (1998) Predictable scheduling of a job shop subject to breakdowns. IEEE Trans Robot Autom 14:365–378

    Article  Google Scholar 

  7. Mehta SV, Uzsoy R (1999) Predictable scheduling of a single machine subject to breakdowns. Int J Comput Integr Manuf 12:15–38

    Article  Google Scholar 

  8. O’Donovan R, Uzsoy R, McKay KN (1999) Predictable scheduling of a single machine with breakdowns and sensitive jobs. Int J Prod Res 37:4217–4233

    Article  MATH  Google Scholar 

  9. Wu SD, Storer RH, Chang PC (1993) One-machine rescheduling heuristics with efficiency and stability as criteria. Comput Oper Res 20:1–14

    Article  MATH  Google Scholar 

  10. Daniels RL, Kouvelis P (1995) Robust scheduling to hedge against processing time uncertainty in single-stage production. Manage Sci 41:363–376

    Article  MATH  Google Scholar 

  11. Kouvelis P, Daniels RL, Vairaktarakis G (2000) Robust scheduling of a two-machine flow shop with uncertain processing times. IIE Trans 32:421–432

    Article  Google Scholar 

  12. Abumaizar RJ, Svestka JA (1997) Rescheduling job shops under random disruptions. Int J Prod Res 35:2065–2082

    Article  MATH  Google Scholar 

  13. Jain AK, Elmaraghy HA (1997) Production scheduling/rescheduling in flexible manufacturing. Int J Prod Res 35:281–309

    Article  MATH  Google Scholar 

  14. Sabuncuoglu I, Karabuk S (1999) Rescheduling frequency in an FMS with uncertain processing times and unreliable machines. J Manuf Syst 18:268–283

    Article  Google Scholar 

  15. McKay KN, Safayeni FR, Buzacott JA (1989) The scheduler’s knowledge of uncertainty: the missing link. In: Browne J (ed) Knowledge-based production management systems. Elsevier, Amsterdam, The Netherlands

    Google Scholar 

  16. Alcaide D, Rodriguez-Gonzalez A, Sicilia J (2002) An approach to solve the minimum expected makespan flow-shop problem subject to breakdowns. Eur J Oper Res 140:384–398

    Article  MathSciNet  MATH  Google Scholar 

  17. Zadeh L (1963) Optimality and non-scalar-valued performance criteria. IEEE Trans Automat Contr 8:59–60

    Article  Google Scholar 

  18. Murata T, Ishibuchi H, Tanaka H (1996) Multi-objective genetic algorithm and its application to flowshop scheduling. Comput Ind Eng 30:957–968

    Article  Google Scholar 

  19. Cochran JK, Horng S-M, Fowler JW (2003) A multi-population genetic algorithm to solve multi-objective scheduling problems for parallel machines. Comput Oper Res 30:1087–1102

    Article  MathSciNet  MATH  Google Scholar 

  20. Pasupathy T, Rajendran C, Suresh RK (2005) A multi-objective genetic algorithm for scheduling in flow shops to minimize the makespan and total flow time of jobs. Int J Adv Manuf Technol. DOI 10.1007/s00170-004-2249-6

  21. Ponnambalam SG, Jagannathan H, Kataria M, Gadicherlaet A (2004) A TSP-GA multi-objective algorithm for flow-shop scheduling. Int J Adv Manuf Technol 23:909–915

    Article  Google Scholar 

  22. Khoo LP, Lee SG, Yin XF (2000) A prototype genetic algorithm enhanced multi-objective scheduler for manufacturing systems. Int J Adv Manuf Technol 16:131–138

    Article  Google Scholar 

  23. Fonseca CM, Fleming PJ (1995) An overview of evolutionary algorithms in multiobjective optimization. Evol Comput 3:1–16

    Google Scholar 

  24. Tamaki H, Kita H, Kobayashi S (1996) Multiobjective optimization by genetic algorithms: a review. In: Proceedings of the 1996 IEEE International Conference on Evolutionary Computation (ICEC’96), Nagoya, Japan, May 1996, pp 517–522

  25. Horn J (1997) Multicriterion decision making. In: Back T, Fogel DB, Michalewicz (eds) Handbook of evolutionary computation. Oxford University Press, New York, pp F1.9:1–15

    Google Scholar 

  26. Holland JH (1992) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence, 2nd edn. MIT Press, Cambridge, Massachusetts

    Google Scholar 

  27. Miller DM, Chen H-C, Matson J, Liu Q (1999) A hybrid genetic algorithm for the single machine scheduling problem. J Heuristics 5:437–454

    Article  MATH  Google Scholar 

  28. Rachamadugu RMV, Morton TE (1981) Myopic heuristics for the single machine weighted tardiness problem. Working paper 28-81-82, Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, Pennsylvania

  29. Michalewicz Z (1994) Genetic algorithm + data structure = evolution programs, 2nd edn. Springer, Berlin Heidelberg New York

    Google Scholar 

  30. Falkenauer E, Bouffoix S (1991) A genetic algorithm for job shop. In: Proceedings of the 1991 IEEE International Conference on Robotics and Automation, Sacramento, California, April 1991, pp 824–829

  31. Cheng R, Gen M, Tsujimura Y (1999) A tutorial survey of job-shop scheduling problems using genetic algorithms. Part II: hybrid genetic search strategies. Comput Ind Eng 36:343–364

    Article  CAS  Google Scholar 

  32. Gen M, Cheng R (1997) Genetic algorithms and engineering design. Wiley, New York

    Google Scholar 

  33. Bäck T (1994) Selective pressure in evolutionary algorithms: a characterization of selection mechanisms. In: Proceedings of the 1st IEEE Conference on Evolutionary Computation (ICEC’94), Orlando, Florida, June 1994, vol 1, pp 57–62

Download references

Author information

Authors and Affiliations

  1. Department of Automation, Shanghai Jiaotong University, 200030, Shanghai, China

    Lin Liu, Han-yu Gu & Yu-geng Xi

  2. Department of Automation, Shanghai Jiaotong University, No.800 Dongchuan Road, 200240, Shanghai, China

    Lin Liu

Authors
  1. Lin Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Han-yu Gu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yu-geng Xi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lin Liu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, L., Gu, Hy. & Xi, Yg. Robust and stable scheduling of a single machine with random machine breakdowns. Int J Adv Manuf Technol 31, 645–654 (2007). https://doi.org/10.1007/s00170-005-0237-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-005-0237-0

Keywords

Search

Navigation