Parallel machine scheduling with a convex resource consumption function

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Abstract

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(n2) 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.

Original languageEnglish
Pages (from-to)92-107
Number of pages16
JournalEuropean Journal of Operational Research
Volume173
Issue number1
DOIs
StatePublished - 16 Aug 2006

Keywords

  • Computational complexity
  • Equivalent load method
  • Parallel machine scheduling
  • Resource allocation
  • Scheduling

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