An optimal online algorithm for single machine scheduling to minimize total general completion time

Ming Liu (), Chengbin Chu, Yinfeng Xu and Jiazhen Huo
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Ming Liu: Tongji University
Chengbin Chu: Ecole Centrale Paris
Yinfeng Xu: Xi’an Jiaotong University
Jiazhen Huo: Tongji University

Journal of Combinatorial Optimization, 2012, vol. 23, issue 2, No 3, 189-195

Abstract: Abstract We study the online problem of single machine scheduling to minimize total general completion time. General completion time is defined as $C^{\alpha}_{j}=(C_{j})^{\alpha}$ , where C j denotes the completion time of job J j and α≥1 is a constant integer. Total general completion time characterizes the feather in service that when a customer is served later in time, his dissatisfaction increases in a manner of power function. The objective function ∑(C j ) α can also be viewed as a total weighted completion time, but the “weight” is no longer a constant number. Our purpose to minimize customers’ total dissatisfaction. The problem is online in the sense that all jobs arrive over time. Each job’s processing time becomes known at its arrival time. Preemption is not allowed. For this online problem, we show that a lower bound on competitive ratio is 2 α and prove that D-SPT (delayed shortest processing time) algorithm is optimal with a competitive ratio 2 α .

Keywords: Online scheduling; Total general completion time; Competitive analysis (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10878-010-9348-0

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