Approximation algorithms for the makespan minimization with positive tails on a single machine with a fixed non-availability interval

In this article, we consider the non-resumable case of the single machine scheduling problem with a fixed non-availability interval. We aim to minimize the makespan when every job has a positive tail. We propose a polynomial approximation algorithm with a worst-case performance ratio of 3/2 for this...

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Bibliographic Details
Published in:Journal of combinatorial optimization Vol. 17; no. 2; pp. 117 - 133
Main Author: Kacem, Imed
Format: Journal Article
Language:English
Published: Boston Springer US 01.02.2009
Springer
Springer Verlag
Subjects:
Applied sciences
Combinatorics
Computer Science
Convex and Discrete Geometry
Exact sciences and technology
Flows in networks. Combinatorial problems
Inventory control, production control. Distribution
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Operational research and scientific management
Operational research. Management science
Operations Research/Decision Theory
Optimization
Scheduling, sequencing
Theory of Computation
Scheduling
Makespan
Approximation
Non-availability constraint
Availability
Polynomial approximation
Worst case method
Minimization
Polynomial method
Approximation algorithm
Combinatorial optimization
Polynomial time
Scheduling . Non-availability constraint . Approximation
Dynamic programming
Single machine
ISSN:1382-6905, 1573-2886
Online Access:Get full text
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Summary:In this article, we consider the non-resumable case of the single machine scheduling problem with a fixed non-availability interval. We aim to minimize the makespan when every job has a positive tail. We propose a polynomial approximation algorithm with a worst-case performance ratio of 3/2 for this problem. We show that this bound is tight. We present a dynamic programming algorithm and we show that the problem has an FPTAS (Fully Polynomial Time Approximation Algorithm) by exploiting the well-known approach of Ibarra and Kim (J. ACM 22:463–468, 1975 ). Such an FPTAS is strongly polynomial. The obtained results outperform the previous polynomial approximation algorithms for this problem.
ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-007-9102-4