Skip to main content
SpringerLink
Log in

Rescheduling on a single machine with part-type dependent setup times and deadlines

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

We consider the problem of rescheduling a facility modeled as a single machine in the face of newly arrived jobs with part-type dependent setup times. The facility contains a number of jobs that have been assigned due dates and scheduled so as to meet them. We wish to insert the new jobs into the existing schedule in a manner that will minimize the disruption of the jobs in the system and minimize the total weighted completion time or the maximum completion time of the new jobs. We provide a polynomial-time algorithm for the maximum completion time problem, prove that the total weighted completion time problem is NP-hard in the strong sense and study several of its special cases. In particular, we show that the case with reverse-agreeable weights (of which the unit weight problem is a special case) can be solved in polynomial time when the number of part types is fixed. We also present two heuristics for the problem with arbitrary weights and develop data-dependent worst-case error bounds. Extensive computational experiments show that the heuristics consistently obtain near-optimal solutions in very reasonable CPU times.

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. G.R. Bitran and S.M. Gilbert, Sequencing production on parallel machines with two magnitudes of sequence-dependent setup cost, Journal of Manufacturing and Operations Management 3(1989) 24–52.

    Google Scholar 

  2. J. Bruno and P. Downey, Complexity of task sequencing with deadlines, setup times and changeover costs, SIAM Journal on Computing 7(1978)393–404.

    Article  Google Scholar 

  3. L.K. Church and R. Uzsoy, Analysis of periodic and event-driven rescheduling policies in dynamic shops, International Journal of Computer-Integrated Manufacturing 5(1992)153–163.

    Google Scholar 

  4. B.L. Dietrich, Scheduling on parallel unrelated machines with setups. Research Report, IBM Thomas J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY 10598, 1988.

    Google Scholar 

  5. S. French, Sequencing and Scheduling, Ellis Horwood, Chichester, England, 1982.

    Google Scholar 

  6. M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, W.H. Freeman, 1979.

  7. J.N.D. Gupta, Optimal schedules for single facility with two job classes, Computers and Operations Research 11(1984)409–413.

    Article  Google Scholar 

  8. J.N.D. Gupta, Single facility scheduling with multiple job classes, European Journal of Operational Research 8(1988)42–45.

    Article  Google Scholar 

  9. E.L. Lawler, Combinatorial Optimization: Networks and Matroids, Holt, Rinehart and Winston, 1976.

  10. E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan and D.B. Shmoys, Sequencing and scheduling: Algorithms and complexity, in: Handbooks in Operations Research and Management Science, Vol. 4: Logistics of Production and Inventory, S.C. Graves and P. Zipkin, eds., Elsevier Science Publishers, 1993.

  11. A.J. Mason and E.J. Anderson, Minimizing flow time on a single machine with job classes and setup times, Naval Research Logistics 38(1991)333–350.

    Google Scholar 

  12. C.L. Monma and C.N. Potts, On the complexity of scheduling with batch setup times, Operations Research 37(1989)798–804.

    Article  Google Scholar 

  13. I.M. Ovacik and R. Uzsoy, Worst-case error bounds for parallel machine scheduling problems with bounded sequence-dependent setup times, Operations Research Letters 14(1993)251–256.

    Article  Google Scholar 

  14. I.M. Ovacik and R. Uzsoy, Rolling horizon algorithms for a single-machine dynamic scheduling problem with sequence-dependent setup times, International Journal of Production Research 32(1994)1243–1263.

    Google Scholar 

  15. C.N. Potts, Scheduling two job classes on a single machine, Computers and Operations Research 18(1991)411–415.

    Article  Google Scholar 

  16. N. Raman, F.B. Talbot and R.V. Rachamadugu, Due date based scheduling in a general flexible manufacturing system, Journal of Operations Management 8(1989)115–132.

    Article  Google Scholar 

  17. C.S. Tang, Scheduling batches on parallel machines with major and minor setups, European Journal of Operational Research 46(1990)28–37.

    Article  Google Scholar 

  18. A.T. Unal and A.S. Kiran, Batch sequencing, IIE Transactions on Scheduling and Logistics 24 (1992)73–83.

    Google Scholar 

  19. R. Uzsoy, C.Y. Lee and L.A. Martin-Vega, Scheduling semiconductor test operations: Minimizing maximum lateness and number of tardy jobs on a single machine, Naval Research Logistics 39 (1992) 369–388.

    Google Scholar 

  20. R. Uzsoy, L.A. Martin-Vega, C.Y. Lee and P.A. Leonard, Production scheduling algorithms for a semiconductor test facility, IEEE Transactions on Semiconductor Manufacturing 4(1991)270–280.

    Article  Google Scholar 

  21. R.J. Wittrock, Scheduling parallel machines with setups, Research Report, IBM Thomas J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY 10598, 1986.

    Google Scholar 

  22. D.L. Woodruff and M.L. Spearman, Scheduling and batching for two classes of jobs with deadlines and setup times, Production and Operations Management 1(1992)87–102.

    Article  Google Scholar 

  23. S.D. Wu, R.H. Storer and P.C. Chang, A rescheduling procedure for manufacturing systems under random disruptions, in: New Directions for Operations Research in Manufacturing, G. Fandel, T. Gulledge and A. Jones, eds., Springer, 1992, pp. 292–308.

  24. S.D. Wu, R.H. Storer and P.C. Chang, One-machine rescheduling with efficiency and stability as criteria, Computers and Operations Research 20(1993)1–14.

    Article  Google Scholar 

Download references

Authors
  1. Ali Tamer Unal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Reha Uzsoy
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ali S. Kiran
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tamer Unal, A., Uzsoy, R. & Kiran, A.S. Rescheduling on a single machine with part-type dependent setup times and deadlines. Annals of Operations Research 70, 93–113 (1997). https://doi.org/10.1023/A:1018955111939

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1018955111939

Keywords

Search

Navigation