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On the exact bounds of SPT for scheduling on parallel machines with availability constraints

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  • Tan, Zhiyi
  • Chen, Yong
  • Zhang, An

Abstract

This paper considers the scheduling problems with the objective of minimizing the total completion time on two parallel identical machines with given unavailable periods. The jobs are assumed to be nonresumable. If there is one unavailable period on one of the two machines, we prove that SPT has a tight worst-case ratio of 3/2. If there is one unavailable period on each machine, and the unavailable periods on two machines do not overlap, we prove that SPT has a worst-case ratio of 2, which is the smallest possible worst-case ratio that an polynomial time algorithm can have unless P=NP.

Suggested Citation

  • Tan, Zhiyi & Chen, Yong & Zhang, An, 2013. "On the exact bounds of SPT for scheduling on parallel machines with availability constraints," International Journal of Production Economics, Elsevier, vol. 146(1), pages 293-299.
    • Handle: RePEc:eee:proeco:v:146:y:2013:i:1:p:293-299
    DOI: 10.1016/j.ijpe.2013.07.013
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    References listed on IDEAS

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    1. Tan, Zhiyi & Chen, Yong & Zhang, An, 2011. "Parallel machines scheduling with machine maintenance for minsum criteria," European Journal of Operational Research, Elsevier, vol. 212(2), pages 287-292, July.
    2. Cheng, T.C.E. & Yang, Suh-Jenq & Yang, Dar-Li, 2012. "Common due-window assignment and scheduling of linear time-dependent deteriorating jobs and a deteriorating maintenance activity," International Journal of Production Economics, Elsevier, vol. 135(1), pages 154-161.
    3. Mor, Baruch & Mosheiov, Gur, 2012. "Scheduling a maintenance activity and due-window assignment based on common flow allowance," International Journal of Production Economics, Elsevier, vol. 135(1), pages 222-230.
    4. Sun, Kaibiao & Li, Hongxing, 2010. "Scheduling problems with multiple maintenance activities and non-preemptive jobs on two identical parallel machines," International Journal of Production Economics, Elsevier, vol. 124(1), pages 151-158, March.
    5. Sadfi, Cherif & Penz, Bernard & Rapine, Christophe & Blazewicz, Jacek & Formanowicz, Piotr, 2005. "An improved approximation algorithm for the single machine total completion time scheduling problem with availability constraints," European Journal of Operational Research, Elsevier, vol. 161(1), pages 3-10, February.
    6. Lee, Chung-Yee, 1999. "Two-machine flowshop scheduling with availability constraints," European Journal of Operational Research, Elsevier, vol. 114(2), pages 420-429, April.
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