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Equitable scheduling on a single machine

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Abstract

We introduce a natural but seemingly yet unstudied variant of the problem of scheduling jobs on a single machine so as to minimize the number of tardy jobs. The novelty of our new variant lies in simultaneously considering several instances of the problem at once. In particular, we have n clients over a period of m days, where each client has a single job with its own processing time and deadline per day. Our goal is to provide a schedule for each of the m days, so that each client is guaranteed to have their job meet its deadline in at least \(k \le m\) days. This corresponds to an equitable schedule where each client is guaranteed a minimal level of service throughout the period of m days. We provide a thorough analysis of the computational complexity of three main variants of this problem, identifying both efficient algorithms and worst-case intractability results.

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Notes

  1. In 2018, ACM started its new conference series on “Fairness, Accountability, and Transparency (originally FAT, since 2021 FAccT).”

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Author notes

  1. Klaus Heeger, Danny Hermelin, George B. Mertzios, Hendrik Molter, Rolf Niedermeier and Dvir Shabtay contributed equally to this work.

Authors and Affiliations

  1. Algorithmics and Computational Complexity, Faculty IV, TU Berlin, Berlin, Germany

    Klaus Heeger & Rolf Niedermeier

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

    Danny Hermelin, Hendrik Molter & Dvir Shabtay

  3. Department of Computer Science, Durham University, Durham, UK

    George B. Mertzios

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  1. Klaus Heeger
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Correspondence to Hendrik Molter.

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An extended abstract of this paper appeared in the proceedings of the 35th AAAI Conference on Artificial Intelligence (AAAI’21) (Heeger et al., 2021). This version contains full proof details and additional hardness results.

Klaus Heeger was supported by DFG Research Training Group 2434 “Facets of Complexity.” George B. Mertzios was supported by the EPSRC grant EP/P020372/1 and by DFG RTG 2434 while visiting TU Berlin. Hendrik Molter was supported by the German Research Foundation (DFG), project MATE (NI 369/17) and by the Israeli Science Foundation (ISF), grant No. 1070/20. Main work was done while Hendrik Molter was affiliated with TU Berlin.

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Heeger, K., Hermelin, D., Mertzios, G.B. et al. Equitable scheduling on a single machine. J Sched 26, 209–225 (2023). https://doi.org/10.1007/s10951-022-00754-6

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