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Convex resource allocation for minimizing the makespan in a single machine with job release dates. (English) Zbl 1076.68018
Summary: We consider the problem of scheduling jobs on a single machine where job-processing times are controllable through the allocation of a common limited resource. The release dates are known and the job-processing time is described by a convex decreasing resource consumption function. Our objective is to simultaneously determine the optimal job permutation and the resource allocation,such that the maximal completion time is minimized. We provide an $O(n)$ time optimization algorithm for the case of identical job release dates, and an $O(n^2)$ time optimization algorithm for the case of non-identical job release dates.

68M20Performance evaluation of computer systems; queueing; scheduling
90B35Scheduling theory, deterministic
Full Text: DOI
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