Online scheduling with reassignment

Tan, Zhiyi; Yu, Shuai

doi:10.1016/j.orl.2007.06.004

Cited by 30 publications

(19 citation statements)

References 9 publications

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“…Since the online environment has not been taken into account in the context of late work minimization so far, the scope for future research is overwhelming. For the parallel machines case with a common due date, one can take into accountfor example-semi-online problems, allowing some jobs rearrangements (cf., e.g., Tan and Yu 2008;Chen et al 2011) or assuming existence of buffers (cf., e.g., Englert et al 2008;Lan et al 2012).…”

Section: Discussionmentioning

confidence: 99%

Scheduling on parallel identical machines with late work criterion: Offline and online cases

Chen

Sterna

Han

et al. 2015

J Sched

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In the paper, we consider the problem of scheduling jobs on parallel identical machines with the late work criterion and a common due date, both offline and online cases. Since the late work criterion has not been studied in the online mode so far, the analysis of the online problem is preceded by the analysis of the offline problem, whose complexity status has not been formally stated in the literature yet. Namely, for the offline mode, we prove that the twomachine problem is binary NP-hard, and the general case is unary NP-hard. In the online mode we assume that jobs arrive in the system one by one, i.e., we consider the online over list model. We give an algorithm with a competitive ratio being a function of the number of machines, and we prove the optimality of this approach for two identical machines.

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Section: Discussionmentioning

confidence: 99%

Scheduling on parallel identical machines with late work criterion: Offline and online cases

Chen

Sterna

Han

et al. 2015

J Sched

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“…In order to minimize the makespan, we need to reassign some jobs to gain a better effect. Three problems of online scheduling with reassignment have been proposed in [8]. In the first problem P L , we can reassign the last k jobs of the sequence.…”

Section: Introductionmentioning

confidence: 99%

Online scheduling on two uniform machines to minimize the makespan

Liu

Chen

et al. 2009

Theoretical Computer Science

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a b s t r a c tWe consider two problems of online scheduling on two uniform machines: online scheduling under a grade of service (GoS) and online scheduling with reassignment. These problems are online in the sense that when a job presents, we have to irrevocably assign it to one of the machines before the next job is seen. The objective is to minimize the makespan.In the first problem, GoS means that some jobs have to be processed by some machine so that they can be guaranteed a higher quality. Assume that the speed of the higher GoS machine is normalized to 1, while the speed of the other one is s. We show that a lower bound of competitive ratio is 1 + 2s s+2 in the case 0 < s ≤ 1 and 1 + s+1 s(2s+1) in the case s > 1. Then we propose and analyze two online algorithms: HSF algorithm and EX-ONLINE algorithm. HSF is optimal in the case where s > 1 and Σ 1 ≥ Σ 2 s , where Σ 1 and Σ 2 denote the total processing time of jobs which request higher GoS machine and the total processing time of jobs which request the normal one, respectively. EX-ONLINE is optimal in the case 2(In the second problem, we study two subproblems P L and P A proposed in [Z. Tan, S. Yu, Online scheduling with reassignment, Operations Research Letters 36 (2008) 250-254].Assume that the speeds of 2 uniform machines are 1 and s ≥ 1, respectively. For P L where we can reassign the last k jobs of the sequence, we show a lower bound of competitive ratio 1 + 1 1+s . For P A where we can reassign arbitrary k jobs, we show a lower bound of competitive ratio (s+1) 2 s 2 +s+1 . We propose a s+1 s -competitive algorithm HSF-1 for both P L and P A . For P A , we propose a (s+1) 2 s+2 -competitive algorithm EX-RA, which is superior to HSF-1 when 1 ≤ s ≤ √ 2.

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“…We prove that √ 2 is a lower bound of this problem and present an optimal Algorithm RO with a matching competitive ratio. It means that the same competitive ratio can be given but the condition has been reduced from the problem of P E in Tan and Yu [1].…”

Section: Optimal Algorithm For P Romentioning

confidence: 99%

“…First based on the problem P E introduced by Tan and Yu [1] that the last job on each machine can be reassigned after all jobs have been assigned, we show that the optimal algorithm with same competitive ratio √ 2 can be obtained by only reassigning the last job of one machine. Furthermore, we investigate the combination of the total size of all jobs is known in advance and one can reassign the last job of one machine.…”

Section: Introductionmentioning

confidence: 96%