Abstract
We consider the classic online scheduling problem on m uniform machines in the online setting where jobs arrive over time. Preemption is not allowed. The objective is to minimize total weighted completion time. An online algorithm based on the directly waiting strategy is proposed. Its competitive performance is proved to be max2smax1−1/2∑si,2smax/1+smax2.5−1/2m by the idea of instance reduction, where sm is the fastest machine speed after being normalized by the slowest machine speed.
Highlights
Scheduling is a commonly used term in several different contexts including production management, service operations, and computer systems
Inspired by the same idea of the directly waiting strategy mentioned above in the subsection of related work, we construct an online algorithm for Qm | rj, online | wjCj
We design an online algorithm for Qm|rj, online| wjCj and prove that it is max2sm(1 − (1/2 si)), (2sm/(1 + sm))(2.5 − (1/2m))-competitive. e result is a generalization from the identicalmachine scheduling considered in [24]
Summary
Scheduling is a commonly used term in several different contexts including production management, service operations, and computer systems. E effectiveness and efficiency of the proposed approach are often judged by its performance on randomly generated or benchmark instances or some case data Along this line, a rich variety of scheduling problems have been investigated, motivated by different applications from real-world situations. E theoretically guaranteed performance often refers to the worst-case performance Along this line, most of the work is focused on some classical and simplified scheduling models that are abstracted from similar applications, which can be often denoted by the widely used three-field classification scheme [16]. Interested readers can further refer to a review by Potts and Strusevich [22] Following this line of theoretical research, we consider a classical online scheduling problem in this work.
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