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Single machine scheduling problems with subcontracting options

Author

Listed:
  • Weiya Zhong

    (Shanghai University)

  • Zhiming Huo

    (Shanghai University)

Abstract

In this paper, we study a scheduling model as follows: there are n jobs which can be processed in house on a single machine or subcontracted to a subcontractor. If a job is subcontracted, its processing cost is different from the in-house cost and its delivery lead time is a stepwise function of the total processing time of outsourced jobs. Two objective functions are studied (1) to minimize the weighted sum of the maximal completion time and the total processing cost and (2) to minimize the weighted sum of the number of tardy jobs and the total processing cost. For the first problem, we prove that it is NP-hard and get a pseudo-polynomial time algorithm. For the second problem, we prove that it is NP-hard and get a pseudo-polynomial time algorithm for a special case.

Suggested Citation

  • Weiya Zhong & Zhiming Huo, 2013. "Single machine scheduling problems with subcontracting options," Journal of Combinatorial Optimization, Springer, vol. 26(3), pages 489-498, October.
    • Handle: RePEc:spr:jcomop:v:26:y:2013:i:3:d:10.1007_s10878-011-9442-y
    DOI: 10.1007/s10878-011-9442-y
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    References listed on IDEAS

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    1. Lee, Ik Sun & Sung, C.S., 2008. "Single machine scheduling with outsourcing allowed," International Journal of Production Economics, Elsevier, vol. 111(2), pages 623-634, February.
    2. Wang, J.-B. & Ng, C.T. & Cheng, T.C.E. & Liu, L.L., 2008. "Single-machine scheduling with a time-dependent learning effect," International Journal of Production Economics, Elsevier, vol. 111(2), pages 802-811, February.
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    Cited by:

    1. Koulamas, Christos & Kyparisis, George J., 2023. "A classification of dynamic programming formulations for offline deterministic single-machine scheduling problems," European Journal of Operational Research, Elsevier, vol. 305(3), pages 999-1017.

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