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Due‐window assignment with unit processing‐time jobs

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  • Gur Mosheiov
  • Daniel Oron

Abstract

In due‐window assignment problems, jobs completed within a designated time interval are regarded as being on time, whereas early and tardy jobs are penalized. The objective is to determine the location and size of the due‐window, as well as the job schedule. We address a common due‐window assignment problem on parallel identical machines with unit processing time jobs. We show that the number of candidate values for the optimal due‐window starting time and for the optimal due‐window completion time are bounded by 2. We also prove that the starting time of the first job on each of the machines is either 0 or 1, thus introducing a fairly simple, constant‐time solution for the problem. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004

Suggested Citation

  • Gur Mosheiov & Daniel Oron, 2004. "Due‐window assignment with unit processing‐time jobs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(7), pages 1005-1017, October.
    • Handle: RePEc:wly:navres:v:51:y:2004:i:7:p:1005-1017
    DOI: 10.1002/nav.20039
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    References listed on IDEAS

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    1. Hoogeveen, J. A. & van de Velde, S. L., 1991. "Scheduling around a small common due date," European Journal of Operational Research, Elsevier, vol. 55(2), pages 237-242, November.
    2. Gordon, Valery & Proth, Jean-Marie & Chu, Chengbin, 2002. "A survey of the state-of-the-art of common due date assignment and scheduling research," European Journal of Operational Research, Elsevier, vol. 139(1), pages 1-25, May.
    3. S. S. Panwalkar & M. L. Smith & A. Seidmann, 1982. "Common Due Date Assignment to Minimize Total Penalty for the One Machine Scheduling Problem," Operations Research, INFORMS, vol. 30(2), pages 391-399, April.
    4. Nicholas G. Hall & Marc E. Posner, 1991. "Earliness-Tardiness Scheduling Problems, I: Weighted Deviation of Completion Times About a Common Due Date," Operations Research, INFORMS, vol. 39(5), pages 836-846, October.
    5. Michael X. Weng & Jose A. Ventura, 1994. "Scheduling about a large common due date with tolerance to minimize mean absolute deviation of completion times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(6), pages 843-851, October.
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    Cited by:

    1. G Mosheiov & A Sarig, 2011. "A note: a due-window assignment problem on parallel identical machines," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(1), pages 238-241, January.

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