Parallel machine scheduling with a convex resource consumption function

We consider some problems of scheduling jobs on identical parallel machines where job-processing times are controllable through the allocation of a nonrenewable common limited resource. The objective is to assign the jobs to the machines, to sequence the jobs on each machine and to allocate the reso...

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Veröffentlicht in:European journal of operational research Jg. 173; H. 1; S. 92 - 107
Hauptverfasser: Shabtay, Dvir, Kaspi, Moshe
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier B.V 16.08.2006
Elsevier
Elsevier Sequoia S.A
Schriftenreihe:European Journal of Operational Research
Schlagworte:
Applied sciences
Computational complexity
Equivalent load method
Exact sciences and technology
Flows in networks. Combinatorial problems
Job shops
Operational research and scientific management
Operational research. Management science
Operations research
Optimization
Parallel machine scheduling
Production scheduling
Resource allocation
Scheduling
Scheduling, sequencing
Sequential scheduling
Studies
Scheduling
Parallel machine scheduling
Computational complexity
Equivalent load method
Resource allocation
Task scheduling
Parallel machines
Controllability
Makespan
Combinatorial optimization
Precedence constraint
Completion time
ISSN:0377-2217, 1872-6860
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Beschreibung
Zusammenfassung:We consider some problems of scheduling jobs on identical parallel machines where job-processing times are controllable through the allocation of a nonrenewable common limited resource. The objective is to assign the jobs to the machines, to sequence the jobs on each machine and to allocate the resource so that the makespan or the sum of completion times is minimized. The optimization is done for both preemptive and nonpreemptive jobs. For the makespan problem with nonpreemptive jobs we apply the equivalent load method in order to allocate the resources, and thereby reduce the problem to a combinatorial one. The reduced problem is shown to be NP-hard. If preemptive jobs are allowed, the makespan problem is shown to be solvable in O( n 2) time. Some special cases of this problem with precedence constraints are presented and the problem of minimizing the sum of completion times is shown to be solvable in O( n log n) time.
Bibliographie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2004.12.008