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Minimizing mean absolute deviation of completion time about a common due window subject to maximum tardiness for a single machine


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  • Su, Ling-Huey
  • Tien, Yi-Yu
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    This study deals with the problem of scheduling jobs on a single machine to minimize the mean absolute deviation of the job completion time about a large common due window subject to the maximum tardiness constraint. Using the well-known three-field notation, the problem is identified as MAD/large DueWindow/Tmax. The common due window is set to be large enough to allow idle time prior to the beginning of a schedule to investigate the effect of the Tmax constraint. Penalties arise if a job is completed outside the due window. A branch and bound algorithm and a heuristic are proposed. Many properties of the solutions and precedence relationships are identified. Our computational results reveal that the branch and bound algorithm is capable of solving problems of up to 50 jobs and the heuristic algorithm yields approximate solutions that are very close to the exact solution.

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    Bibliographic Info

    Article provided by Elsevier in its journal International Journal of Production Economics.

    Volume (Year): 134 (2011)
    Issue (Month): 1 (November)
    Pages: 196-203

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    Handle: RePEc:eee:proeco:v:134:y:2011:i:1:p:196-203

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    Keywords: Scheduling Single machine Common due window Mean absolute deviation Maximum tardiness;


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    1. Seo, Jong Hwa & Kim, Chae-Bogk & Lee, Dong Hoon, 2001. "Minimizing mean squared deviation of completion times with maximum tardiness constraint," European Journal of Operational Research, Elsevier, vol. 129(1), pages 95-104, February.
    2. Biskup, Dirk & Feldmann, Martin, 2005. "On scheduling around large restrictive common due windows," European Journal of Operational Research, Elsevier, vol. 162(3), pages 740-761, May.
    3. Li, Shisheng & Ng, C.T. & Yuan, Jinjiang, 2011. "Group scheduling and due date assignment on a single machine," International Journal of Production Economics, Elsevier, vol. 130(2), pages 230-235, April.
    4. Liman, Surya D. & Panwalkar, Shrikant S. & Thongmee, Sansern, 1996. "Determination of common due window location in a single machine scheduling problem," European Journal of Operational Research, Elsevier, vol. 93(1), pages 68-74, August.
    5. Shabtay, Dvir, 2010. "Scheduling and due date assignment to minimize earliness, tardiness, holding, due date assignment and batch delivery costs," International Journal of Production Economics, Elsevier, vol. 123(1), pages 235-242, January.
    6. Li, Lei & Fonseca, Daniel J. & Chen, Der-San, 2006. "Earliness-tardiness production planning for just-in-time manufacturing: A unifying approach by goal programming," European Journal of Operational Research, Elsevier, vol. 175(1), pages 508-515, November.
    7. Li, Shisheng & Ng, C.T. & Yuan, Jinjiang, 2011. "Scheduling deteriorating jobs with CON/SLK due date assignment on a single machine," International Journal of Production Economics, Elsevier, vol. 131(2), pages 747-751, June.
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    Cited by:
    1. Yang, Dar-Li & Lai, Chien-Jung & Yang, Suh-Jenq, 2014. "Scheduling problems with multiple due windows assignment and controllable processing times on a single machine," International Journal of Production Economics, Elsevier, vol. 150(C), pages 96-103.


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