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Two approximation schemes for scheduling on parallel machines under a grade of service provision. (English) Zbl 1251.90166

Summary: We consider the offline scheduling problem to minimize the makespan on m parallel and identical machines with certain features. Each job and machine are labeled with the grade of service (GoS) levels, and each job can only be executed on the machine whose GoS level is no more than that of the job. In this paper, we present an efficient polynomial-time approximation scheme (EPTAS) with running time \(O(n \log n)\) for the special case where the GoS level is either 1 or 2. This partially solves an open problem posed by J. Ou et al. [Nav. Res. Logist. 55, No. 4, 328–338 (2008; Zbl 1153.90432)]. We also present a simpler full polynomial-time approximation scheme (FPTAS) with running time \(O(n)\) for the case where the number of machines is fixed.

MSC:

90B35 Deterministic scheduling theory in operations research

Keywords:

makespan; EPTAS; FPTAS

Citations:

Zbl 1153.90432
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References:

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