Improved Approximation Schemes for Early Work Scheduling on Identical Parallel Machines with a Common Due Date

We study the early work scheduling problem on identical parallel machines in order to maximize the total early work, i.e., the parts of non-preemptive jobs that are executed before a common due date. By preprocessing and constructing an auxiliary instance which has several good properties, for any d...

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Bibliographic Details
Published in:Journal of the Operations Research Society of China (Internet) Vol. 12; no. 2; pp. 341 - 350
Main Author: Li, Wei-Dong
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2024
Springer Nature B.V
Subjects:
Accuracy
Algorithms
Approximation
Employment
Management Science
Mathematics
Mathematics and Statistics
Operations Research
Polynomials
Preempting
Schedules
Scheduling
Workloads
China
90B35
Fully polynomial time approximation scheme
Polynomial time approximation scheme
Scheduling
68M20
Early work
Efficient polynomial time approximation scheme
ISSN:2194-668X, 2194-6698
Online Access:Get full text
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Summary:We study the early work scheduling problem on identical parallel machines in order to maximize the total early work, i.e., the parts of non-preemptive jobs that are executed before a common due date. By preprocessing and constructing an auxiliary instance which has several good properties, for any desired accuracy ε , we propose an efficient polynomial time approximation scheme with running time O f ( 1 / ε n ) , where n is the number of jobs and f ( 1 / ε ) is exponential in 1 / ε , and a fully polynomial time approximation scheme with running time O 1 ε 2 m + 1 + n when the number of machines is fixed.
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ISSN:2194-668X
2194-6698
DOI:10.1007/s40305-022-00402-y