Journal of the Operational Research Society

, Volume 58, Issue 10, pp 1375–1388 | Cite as

Heuristics for a coupled-operation scheduling problem

Theoretical Paper

Abstract

In this paper, we study a strongly NP-hard single machine scheduling problem in which each job consists of two operations that are separated by a time delay which lies within a specified range. The objective is to minimize the makespan. Determining the feasibility and, if applicable, makespan of any proposed permutation of the operations is non-trivial, requiring a longest path algorithm with O(n2) complexity for each permutation. Several heuristic algorithms are proposed: a deterministic and randomized construction algorithm, three descent algorithms and two reactive tabu search algorithms. The local search algorithms use a first improvement neighbourhood and mainly visit only feasible solutions within the search space. Results of extensive computational tests are reported, showing that the heavy computational burden of testing potential solutions renders the local search algorithms uncompetitive in comparison to the construction algorithms. The iterated descent algorithm performs least well.

Keywords

scheduling/sequencing bounded delay heuristics local search combinatorial optimization 

Notes

Acknowledgements

This research was partially funded under INTAS Grant number 96-2183. We thank the anonymous referees for their useful comments and suggestions.

References

  1. Ahuja RK, Magnanti TL and Orlin JB (1993). Network Flows: Theory, Algorithms and Applications. Prentice Hall: Englewood Cliffs, NJ.Google Scholar
  2. Balas E, Lenstra JK and Vazacopoulos A (1995). The one machine problem with delayed precedence constraints and its use in job shop scheduling. Mngt Sci 41: 94–109.CrossRefGoogle Scholar
  3. Battiti R and Tecchiolli G (1994). The reactive tabu search. ORSA J Comput 6: 126–140.CrossRefGoogle Scholar
  4. Brucker P, Hilbig T and Hurink J (1999). A branch and bound algorithm for a single-machine scheduling problem with positive and negative time-lags. Discrete Appl Math 94: 77–99.CrossRefGoogle Scholar
  5. Brucker P and Knust S (1999). Complexity results for single-machine problems with positive finish-start time-lags. Computing 63: 299–316.CrossRefGoogle Scholar
  6. Bruno J, Jones JW and So K (1980). Deterministic scheduling with pipelined processors. IEEE Trans Comput 29: 308–316.CrossRefGoogle Scholar
  7. Gallo G and Pallottino S (1988). Shortest path algorithms. Ann Opns Res 13: 703–709.CrossRefGoogle Scholar
  8. Gupta JND (1996). Comparative evaluation of heuristic algorithms for the single machine scheduling problem with two operations per job and time-lags. J Glob Opt 9: 239–250.CrossRefGoogle Scholar
  9. Hurink J and Keuchel J (2001). Local search algorithms for a single machine scheduling problem with positive and negative time lags. Discrete Appl Math 112: 179–197.CrossRefGoogle Scholar
  10. Lin CKY and Haley KB (1993). Scheduling two-phase jobs with arbitrary time lags in a single-server system. IMA J Math Appl Bus Ind 5: 143–161.Google Scholar
  11. Lin CKY, Haley KB and Sparks C (1995). A comparative study of both standard and adaptive versions of threshold accepting and simulated annealing algorithms in three scheduling problems. Eur J Opl Res 83: 330–346.CrossRefGoogle Scholar
  12. Munier A and Sourd F (2003). Scheduling chains on a single machine with non-negative time lags. Math Meth Opns Res 57: 111–123.CrossRefGoogle Scholar
  13. Orman AJ and Potts CN (1997). On the complexity of coupled-task scheduling. Discrete Appl Math 72: 141–154.CrossRefGoogle Scholar
  14. Orman AJ, Potts CN, Shahani AK and Moore AR (1996). Scheduling for a multifunction phased array radar system. Eur J Opl Res 90: 13–25.CrossRefGoogle Scholar
  15. Wikum ED, Llewellyn DC and Nemhauser GL (1994). One-machine generalized precedence constrained scheduling problems. Opns Res Let 16: 87–99.CrossRefGoogle Scholar
  16. Yu Wenci (1996). The two machine flow shop problem with delays and the one machine total tardiness problem. PhD thesis, Eindhoven University of Technology.Google Scholar

Copyright information

© Palgrave Macmillan Ltd 2006

Authors and Affiliations

  1. 1.University of SouthamptonSouthamptonUK

Personalised recommendations