Fully polynomial time approximation scheme to maximize early work on parallel machines with common due date

•Fully polynomial time approximation scheme for early work maximization is proposed.•The new FPTAS dominates PTAS for the two-machine case known from the literature.•Complexity of parallel machine scheduling problems with common due date is studied.•Theoretical studies are completed with computation...

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Bibliographic Details
Published in:European journal of operational research Vol. 284; no. 1; pp. 67 - 74
Main Authors: Chen, Xin, Liang, Yage, Sterna, Małgorzata, Wang, Wen, Błażewicz, Jacek
Format: Journal Article
Language:English
Published: Elsevier B.V 01.07.2020
Subjects:
Early work
Fully polynomial time approximation scheme
Late work
Parallel identical machines
Scheduling
Fully polynomial time approximation scheme
Late work
Scheduling
Early work
Parallel identical machines
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary:•Fully polynomial time approximation scheme for early work maximization is proposed.•The new FPTAS dominates PTAS for the two-machine case known from the literature.•Complexity of parallel machine scheduling problems with common due date is studied.•Theoretical studies are completed with computational experiments. We study the scheduling problem on parallel identical machines in order to maximize the total early work, i.e. the parts of non-preemptive jobs executed before a common due date, and investigate mainly the model with a fixed number of machines, for which a dynamic programming approach and a fully polynomial time approximation scheme (FPTAS) are proposed. The proposal of these methods allowed us to establish the complexity and approximability status of this problem more exactly. Moreover, since our FPTAS can be also applied for the two-machine case, we improve considerably the result known in the literature for this model, in which a polynomial time approximation scheme (PTAS) was given. The new FPTAS has not only the best computational complexity, but also the much better approximation ratio than the PTAS. Finally, the theoretical studies are completed with computational experiments, performed for dynamic programming, PTAS and FPTAS, showing the high efficiencies of FPTAS both in terms of time consumption and solution quality.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2019.12.003