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Maximizing the weighted number of just-in-time jobs in several two-machine scheduling systems

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Abstract

The problem of maximizing the weighted number of just-in-time jobs in a two-machine flow shop scheduling system is known to be \(\mathcal {NP}\)-hard (Choi and Yoon in J. Shed. 10:237–243, 2007). However, the question of whether this problem is strongly or ordinarily \(\mathcal{NP}\)-hard remains an open question. We provide a pseudo-polynomial time algorithm to solve this problem, proving that it is \(\mathcal{NP}\)-hard in the ordinary sense. Moreover, we show how the pseudo-polynomial algorithm can be converted to a fully polynomial time approximation scheme (FPTAS). In addition, we prove that the same problem is strongly \(\mathcal{NP}\)-hard for both a two-machine job shop scheduling system and a two-machine open shop scheduling system.

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Authors and Affiliations

  1. Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Beer Sheva, Israel

    Dvir Shabtay & Yaron Bensoussan

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  1. Dvir Shabtay
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  2. Yaron Bensoussan
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Corresponding author

Correspondence to Dvir Shabtay.

Additional information

This research was supported by THE ISRAEL SCIENCE FOUNDATION (grant No. 633/08). Partial support by the Paul Ivanier Center for Robotics and Production Management, Ben-Gurion University of the Negev is also gratefully acknowledged.

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Shabtay, D., Bensoussan, Y. Maximizing the weighted number of just-in-time jobs in several two-machine scheduling systems. J Sched 15, 39–47 (2012). https://doi.org/10.1007/s10951-010-0204-y

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  • DOI: https://doi.org/10.1007/s10951-010-0204-y

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