Alternative algorithms for identical machines scheduling to maximize total early work with a common due date

We study a scheduling problem with a given number of identical parallel machines, a common job due date and the total early work criterion, i.e., Pm|dj=d|max{X}, which is known to be NP-hard. A new dynamic programming algorithm is proposed, which is more efficient than the existing exact approach fo...

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Bibliographic Details
Published in:Computers & industrial engineering Vol. 171; p. 108386
Main Authors: Chen, Xin, Shen, Xuefeng, Kovalyov, Mikhail Y., Sterna, Malgorzata, Blazewicz, Jacek
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.09.2022
Subjects:
Common due date
Dynamic programming
Early work maximization
Fully polynomial time approximation scheme
Identical machines scheduling
Fully polynomial time approximation scheme
Early work maximization
Common due date
Dynamic programming
Identical machines scheduling
ISSN:0360-8352, 1879-0550
Online Access:Get full text
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Summary:We study a scheduling problem with a given number of identical parallel machines, a common job due date and the total early work criterion, i.e., Pm|dj=d|max{X}, which is known to be NP-hard. A new dynamic programming algorithm is proposed, which is more efficient than the existing exact approach for this problem. Based on the proposed dynamic programming, we further design two new fully polynomial time approximation schemes. The effectiveness and efficiency of the new exact and approximation approaches are validated in the computational experiments. •New dynamic programming algorithm with lower complexity is proposed for Pm|dj=d|max{X}.•Two new FPTASes are designed based on this algorithm.•Practical efficiency of the methods is validated in computational experiments.
ISSN:0360-8352
1879-0550
DOI:10.1016/j.cie.2022.108386