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Scheduling chains on a single machine with non-negative time lags

Author

Listed:
  • Alix Munier
  • Francis Sourd

Abstract

Chains of operations have to be scheduled on a single machine such that a minimum delay is set between any two operations linked by a precedence relation. Three sub-problems are shown to be solved in polynomial time. First, we consider the problem of minimizing the makespan when all the operations have the same duration p and all the delays are equal to a constant l. Next, we consider that the length of any delay is less than the shortest processing time and we present an algorithm to minimize the makespan and another one to minimize the flow time when all the processing times are equal. Copyright Springer-Verlag Berlin Heidelberg 2003

Suggested Citation

  • Alix Munier & Francis Sourd, 2003. "Scheduling chains on a single machine with non-negative time lags," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 57(1), pages 111-123, April.
    • Handle: RePEc:spr:mathme:v:57:y:2003:i:1:p:111-123
    DOI: 10.1007/s001860200242
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    Citations

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    Cited by:

    1. C N Potts & J D Whitehead, 2007. "Heuristics for a coupled-operation scheduling problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(10), pages 1375-1388, October.
    2. J-B Wang & J-J Wang & P Ji, 2011. "Scheduling jobs with chain precedence constraints and deteriorating jobs," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(9), pages 1765-1770, September.
    3. Courtad, Brenda & Baker, Kenneth & Magazine, Michael & Polak, George, 2017. "Minimizing flowtime for paired tasks," European Journal of Operational Research, Elsevier, vol. 259(3), pages 818-828.
    4. Peter Brucker & Sigrid Knust & Ceyda Oğuz, 2006. "Scheduling chains with identical jobs and constant delays on a single machine," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(1), pages 63-75, February.
    5. N. Brauner & Y. Crama & A. Grigoriev & J. Klundert, 2005. "A Framework for the Complexity of High-Multiplicity Scheduling Problems," Journal of Combinatorial Optimization, Springer, vol. 9(3), pages 313-323, May.
    6. Novak, Antonin & Sucha, Premysl & Hanzalek, Zdenek, 2019. "Scheduling with uncertain processing times in mixed-criticality systems," European Journal of Operational Research, Elsevier, vol. 279(3), pages 687-703.

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