Journal of Scheduling

, Volume 16, Issue 5, pp 539-547

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Lower bounds for online makespan minimization on a small number of related machines

  • Łukasz JeżAffiliated withInstitute of Computer Science, University of WrocławInstitute of Mathematics, Academy of Sciences of the Czech Republic Email author 
  • , Jarett SchwartzAffiliated withDepartment of Applied Mathematics, Faculty of Mathematics and Physics, Charles University
  • , Jiří SgallAffiliated withFaculty of Mathematics and Physics, Computer Science Inst. of Charles University
  • , József BékésiAffiliated withDepartment of Applied Informatics, Gyula Juhász Faculty of Education, University of Szeged


In online makespan minimization, the jobs characterized by their processing time arrive one-by-one and each has to be assigned to one of the m uniformly related machines. The goal is to minimize the length of the schedule. We prove new combinatorial lower bounds for m=4 and m=5, and computer-assisted lower bounds for m≤11.


Online algorithms Scheduling Makespan Related machines