Tight upper bounds for semi-online scheduling on two uniform machines with known optimum

György Dósa, Armin Fügenschuh, Zhiyi Tan, Zsolt Tuza, Krzysztof Węsek

Research output: Contribution to journalArticle

3 Citations (Scopus)


We consider a semi-online version of the problem of scheduling a sequence of jobs of different lengths on two uniform machines with given speeds 1 and s. Jobs are revealed one by one (the assignment of a job has to be done before the next job is revealed), and the objective is to minimize the makespan. In the considered variant the optimal offline makespan is known in advance. The most studied question for this online-type problem is to determine the optimal competitive ratio, that is, the worst-case ratio of the solution given by an algorithm in comparison to the optimal offline solution. In this paper, we make a further step towards completing the answer to this question by determining the optimal competitive ratio for s between 5+24112≈1.7103 and 3≈1.7321, one of the intervals that were still open. Namely, we present and analyze a compound algorithm achieving the previously known lower bounds.

Original languageEnglish
Pages (from-to)161-180
Number of pages20
JournalCentral European Journal of Operations Research
Issue number1
Publication statusPublished - Mar 1 2018


  • Makespan minimization
  • Mixed-integer linear programming
  • Scheduling
  • Semi-online algorithm

ASJC Scopus subject areas

  • Management Science and Operations Research

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