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2012•Journal of SchedulingOpen access

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

Łukasz Jeż, Jarett Schwartz, Jiřı́ Sgall, József Békési

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Abstract

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.

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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.

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Available abstract

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.

Key concepts: Job shop scheduling, Minification, Schedule, Computer science, Mathematical optimization, Upper and lower bounds, Scheduling (production processes), Combinatorics

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