A Best Possible Online Algorithm for the Parallel-Machine Scheduling to Minimize the Maximum Weighted Completion Time

Li, Wenjie

doi:10.1142/s021759591550030x

Cited by 12 publications

(1 citation statement)

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“…Fang et al [6] presented a best possible online algorithm with a competitive ratio of 1 + φ for a set of processing time scheduling problems, where φ = √ 5−1 2 . For minimizing a maximum weighted completion time problem, Li et al [7] established a best possible online algorithm with a competitive ratio of √ 5+1…”

Section: Introductionmentioning

confidence: 99%

Online Bi-Criteria Scheduling on Batch Machines with Machine Costs

Zhai

Chai

2019

Mathematics

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We consider online scheduling with bi-criteria on parallel batch machines, where the batch capacity is unbounded. In this paper, online means that jobs’ arrival is over time. The objective is to minimize the maximum machine cost subject to the makespan being at its minimum. In unbounded parallel batch scheduling, a machine can process several jobs simultaneously as a batch. The processing time of a job and a batch is equal to 1. When job J j is processed on machine M i , it results cost c i j . We only consider two types of cost functions: c i j = a + c j and c i j = a · c j , where a is the fixed cost of machines and c j is the cost of job J j . The number of jobs is n and the number of machines is m. For this problem, we provide two online algorithms, which are showed to be the best possible with a competitive ratio of ( 1 + β m , ⌈ n m ⌉ ) , where β m is the positive root of the equation ( 1 + β m ) m + 1 = β m + 2 .

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Section: Introductionmentioning

confidence: 99%