Speed-robust scheduling: sand, bricks, and rocks

Franziska Eberle, Ruben Hoeksma, Nicole Megow, Lukas Nölke, Kevin Schewior*, Bertrand Simon

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


The speed-robust scheduling problem is a two-stage problem where, given m machines, jobs must be grouped into at most m bags while the processing speeds of the machines are unknown. After the speeds are revealed, the grouped jobs must be assigned to the machines without being separated. To evaluate the performance of algorithms, we determine upper bounds on the worst-case ratio of the algorithm’s makespan and the optimal makespan given full information. We refer to this ratio as the robustness factor. We give an algorithm with a robustness factor 2-1m for the most general setting and improve this to 1.8 for equal-size jobs. For the special case of infinitesimal jobs, we give an algorithm with an optimal robustness factor equal to ee-1≈1.58. The particular machine environment in which all machines have either speed 0 or 1 was studied before by Stein and Zhong (ACM Trans Algorithms 16(1):1-20, 2020. https://doi.org/10.1145/3340320). For this setting, we provide an algorithm for scheduling infinitesimal jobs with an optimal robustness factor of 1+22≈1.207. It lays the foundation for an algorithm matching the lower bound of 43 for equal-size jobs.

Original languageEnglish
JournalMathematical Programming
Issue number2
Pages (from-to)1009-1048
Publication statusPublished - Feb 2023


  • Makespan
  • Resource allocation
  • Robust
  • Scheduling
  • Unknown processing speed


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