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OR Spectrum

, Volume 29, Issue 3, pp 513–533 | Cite as

Two very large-scale neighborhoods for single machine scheduling

  • Tobias Brueggemann
  • Johann L. Hurink
Regular Article

Abstract

In this paper, the problem of minimizing the total completion time on a single machine with the presence of release dates is studied. We introduce two different approaches leading to very large-scale neighborhoods in which the best improving neighbor can be determined in polynomial time. Furthermore, computational results are presented to get insight in the performance of the developed neighborhoods.

Keywords

Very large-scale neighborhoods Local search Single machine 

MSC Classification

90B35 68M20 

Notes

Acknowledgements

The authors are grateful to the anonymous referees for their helpful comments on an earlier draft of the paper.

Tobias Brueggemann is supported by the Netherlands Organization for Scientific Research (NWO) grant 613.000.225 (Local Search with Exponential Neighborhoods). Johann L. Hurink is supported by BSIK grant 03018 (BRICKS: Basic Research in Informatics for Creating the Knowledge Society).

References

  1. Ahmadi RH, Bagchi U (1990) Lower bounds for single-machine scheduling problems. Nav Res Logist 37(6):967–979Google Scholar
  2. Ahuja RK, Özlem E, Orlin JB, Punnen AP (2002) A survey of very large-scale neighborhood search techniques. Discrete Appl Math 123:75–102CrossRefGoogle Scholar
  3. Baker KR (1974) Introduction to sequencing and scheduling. Wiley, New YorkGoogle Scholar
  4. Chu C (1992) A branch-and-bound algorithm to minimize total flow time with unequal release dates. Nav Res Logist 39:859–875Google Scholar
  5. Congram RK, Potts CN, van de Velde SL (2002) An iterated dynasearch algorithm for the single-machine total weighted tardiness scheduling problem. INFORMS J Comput 14(1):52–67CrossRefGoogle Scholar
  6. Graham RL, Lawler EL, Lenstra JK, Rinnooy Kan AHG (1979) Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann Discrete Math 5:287–326CrossRefGoogle Scholar
  7. Hurink J (1999) An exponential neighborhood for a one machine batching problem. OR Spectrum 21:461–476CrossRefGoogle Scholar
  8. Lenstra JK, Rinnooy Kan AHG, Brucker P (1977) Complexity of machine scheduling problems. Ann Discrete Math 1:343–362Google Scholar
  9. Potts CN, van de Velde SL (1995) Dynasearch-iterative local improvement by dynamic programming. Part 1. The traveling salesman problem. Technical Report, University of Twente, The NetherlandsGoogle Scholar
  10. Rinnooy Kan AHG (1976) Machine scheduling problems: classification, complexity and computations. Martinus Nijhoff, The Hague, pp 79–88Google Scholar
  11. Smith WE (1956) Various optimizers for single-stage production. Nav Res Logist Q 3:59–66CrossRefGoogle Scholar
  12. Yanai S, Fujie T (2004) On a dominance test for the single machine scheduling problem with release dates to minimize total flow time. J Oper Res Soc Jpn 47(2):96–111Google Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Department of Applied MathematicsUniversity of TwenteAE EnschedeThe Netherlands

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