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: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

2 Citations (Scopus)
58 Downloads (Pure)


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 (SODA 2019). 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
Title of host publicationInteger Programming and Combinatorial Optimization - 22nd International Conference, IPCO 2021, Proceedings
EditorsMohit Singh, David P. Williamson
Number of pages14
ISBN (Electronic)978-3-030-73879-2
ISBN (Print)978-3-030-73878-5
Publication statusPublished - 5 May 2021
Event22nd International Conference on Integer Programming and Combinatorial Optimization, IPCO 2021 - Virtual, Online
Duration: 19 May 202121 May 2021
Conference number: 22

Publication series

NameLecture Notes in Computer Science
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference22nd International Conference on Integer Programming and Combinatorial Optimization, IPCO 2021
Abbreviated titleIPCO 2021
CityVirtual, Online


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