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Title: Parallel machine scheduling to minimize the sum of quadratic completion times
Authors: Cheng, T. C. Edwin
Liu, Zhaohui
Subjects: Parallel machine scheduling
Quadratic completion time
Probabilistic analysis
Issue Date: Jan-2004
Publisher: Taylor & Francis
Source: IIE transactions, Jan. 2004, v. 36, no. 1, p. 11-17.
Abstract: We consider the parallel machine scheduling problem of minimizing the sum of quadratic job completion times. We first prove that the problem is strongly NP-hard. We then demonstrate by probabilistic analysis that the shortest processing time rule solves the problem asymptotically. The relative error of the rule converges in probability to zero under the assumption that the job processing times are independent random variables uniformly distributed in (0, 1). We finally provide some computational results, which show that the rule is effective in solving the problem in practice.
Rights: Copyright © “IIE”.
This is an electronic version of an article published in T.C.E. Cheng and Z. Liu (2004), IIE Transactions, 36(1), 11–17. IIE Transactions is available online at:, the open URL of the article:
Type: Journal/Magazine Article
DOI: 10.1080/07408170490257844
ISSN: 0740-817X
Appears in Collections:LMS Journal/Magazine Articles

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