Brucker et al. (Math Methods Oper Res 56: 407–412, 2003) have given an O(n 2 )-time algorithm for the problems $$P \mid p_{j}=1, r_{j}$$ , outtree $$\mid \sum C_{j}$$ and $$P \mid pmtn, p_{j}=1, r_{j}$$ , outtree $$\mid \sum C_{j}$$ . In this note, we show that their algorithm admits an O(n...

This paper studies preemptive bi-criteria scheduling on m parallel machines with machine unavailable intervals. The goal is to minimize the total completion time subject to the constraint that the makespan is at most a constant T. We study the unavailability model such that the number of...

Brucker et al. (Math Methods Oper Res 56: 407–412, 2003) have given an O(n <Superscript>2</Superscript>)-time algorithm for the problems <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$P \mid p_{j}=1, r_{j}$$</EquationSource> </InlineEquation>, outtree <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$\mid \sum C_{j}$$</EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$P \mid pmtn, p_{j}=1, r_{j}$$</EquationSource> </InlineEquation>, outtree <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$\mid \sum C_{j}$$</EquationSource> </InlineEquation>. In this note, we show that their algorithm admits an...</equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></superscript>

We consider the m-machine ordered flow shop scheduling problem with machines subject to maintenance and with the makespan as objective. It is assumed that the maintenances are scheduled in advance and that the jobs are resumable. We consider permutation schedules and show that the problem is...