Journal of the Operational Research Society

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

Heuristics for a coupled-operation scheduling problem

Theoretical Paper


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.


scheduling/sequencing bounded delay heuristics local search combinatorial optimization 



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


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Copyright information

© Palgrave Macmillan Ltd 2006

Authors and Affiliations

  1. 1.University of SouthamptonSouthamptonUK

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