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Single machine scheduling problems with subcontracting options

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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.

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Acknowledgements

This work has been financed by Shanghai Leading Academic Discipline Project (S30104).

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, China

    Weiya Zhong & Zhiming Huo

Authors
  1. Weiya Zhong
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  2. Zhiming Huo
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Correspondence to Weiya Zhong.

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Zhong, W., Huo, Z. Single machine scheduling problems with subcontracting options. J Comb Optim 26, 489–498 (2013). https://doi.org/10.1007/s10878-011-9442-y

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  • DOI: https://doi.org/10.1007/s10878-011-9442-y

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