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NP-hard cases in scheduling deteriorating jobs on dedicated machines
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NP-hard cases in scheduling deteriorating jobs on dedicated machines
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Journal Article
NP-hard cases in scheduling deteriorating jobs on dedicated machines
2001
Overview
In this paper problems of time-dependent scheduling on dedicated machines are considered. The processing time of each job is described by a function which is dependent on the starting time of the job. The objective is to minimise the maximum completion time (makespan). We prove that under linear deterioration the two-machine flow shop problem is strongly NP-hard and the two-machine open shop problem is ordinarily NP-hard. We show that for the three-machine flow shop and simple linear deterioration there does not exist a polynomial-time approximation algorithm with the worst case ratio bounded by a constant, unless P=NP. We also prove that the three-machine open shop problem with simple linear deterioration is ordinarily NP-hard, even if the jobs have got equal deterioration rates on the third machine.
Publisher
Taylor & Francis,Macmillan Press,Palgrave Macmillan UK,Taylor & Francis Ltd
Subject
