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A note on the complexity of the problem of two-agent scheduling on a single machine

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Abstract

We consider a two-agent scheduling problem on a single machine, where the objective is to minimize the total completion time of the first agent with the restriction that the number of tardy jobs of the second agent cannot exceed a given number. It is reported in the literature that the complexity of this problem is still open. We show in this paper that this problem is NP-hard under high multiplicity encoding and can be solved in pseudo-polynomial time under binary encoding. When the first agent's objective is to minimize the total weighted completion time, we show that the problem is strongly NP-hard even when the number of tardy jobs of the second agent is restricted to be zero.

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Authors and Affiliations

  1. Department of Logistics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, People”s Republic of China

    C. T. Ng & T. C. E. Cheng

  2. Department of Mathematics, Zhengzhou University, Zhengzhou, Henan, 450052, People”s Republic of China

    J. J. Yuan

Authors
  1. C. T. Ng
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  2. T. C. E. Cheng
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  3. J. J. Yuan
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Ng, C.T., Cheng, T.C.E. & Yuan, J.J. A note on the complexity of the problem of two-agent scheduling on a single machine. J Comb Optim 12, 387–394 (2006). https://doi.org/10.1007/s10878-006-9001-0

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  • DOI: https://doi.org/10.1007/s10878-006-9001-0

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