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doi:10.1016/0305-0548(87)90066-9 
Copyright © 1987 Published by Elsevier Science Ltd.
Scheduling on machines with variable service rates*1
Available online 16 May 2003.
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Abstract
This paper deals with scheduling on single and parallel machines where the service rate of a machine remains constant while a job is being processed and is changed upon its completion. Associated with machine Ml there is a vector of service factors αl = (α1l, α2l,…,); it is described as cyclic of order k iff α1(k) = (α1l,…, αkl, α1l,…,). Processing job Ji in the jth position on Ml consumes αjlti time units. We present an 0(n log n) algorithm for l/vsr/Cmax and an 0(nm log n) algorithm for Pm/vsr/∑ Ci, m 
1. It is proved that l/vsr/Lmax is NP-hard even for a monotone non-decreasing or a cyclic series of service factors, thus l/vsr/δ, δε {∑ Ui, ∑ Ti} are NP-hard as well. Finally, efficiently solvable special cases of l/vsr/δ, δε{Lmax, ∑ Ui, ∑ Ti} are studied.
