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 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...

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 several two-agent scheduling problems with controllable job processing times, where agents A and B have to share either a single machine or two identical machines in parallel while processing their jobs. The processing times of the jobs of agent A are compressible at additional cost....