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Approximation Schemes for Machine Scheduling

In: Operations Research Proceedings 2021

Author

Listed:
  • Marten Maack

    (Paderborn University)

Abstract

Makespan minimization on identical parallel machines, or machine scheduling for short, is a fundamental problem in combinatorial optimization. In this problem, a set of jobs with processing times has to be assigned to a set of machines with the goal of minimizing the latest finishing time of the jobs, i.e., the makespan. While machine scheduling in NP-hard and therefore does not admit a polynomial time algorithm guaranteed to find an optimal solution (unless P=NP), there is a well-known polynomial time approximation scheme (PTAS) for this problem, i.e., a family of $$(1+\varepsilon )$$ ( 1 + ε ) -approximations for each $$\varepsilon >0$$ ε > 0 . The question of whether there is a PTAS for a given problem is considered fundamental in approximation theory. The author’s dissertation considers this question for several variants of machine scheduling, and the present work summarizes the dissertation.

Suggested Citation

  • Marten Maack, 2022. "Approximation Schemes for Machine Scheduling," Lecture Notes in Operations Research, in: Norbert Trautmann & Mario Gnägi (ed.), Operations Research Proceedings 2021, pages 21-26, Springer.
    • Handle: RePEc:spr:lnopch:978-3-031-08623-6_4
    DOI: 10.1007/978-3-031-08623-6_4
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