Fast approximation algorithms to minimize a special weighted flow-time criterion on a single machine with a non-availability interval and release dates

This paper is the first attempt to successfully design efficient approximation algorithms for the single-machine weighted flow-time minimization problem when jobs have different release dates and weights equal to their processing times under the assumption that one job is fixed (i.e., the machine is...

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Bibliographic Details
Published in:Journal of scheduling Vol. 14; no. 3; pp. 257 - 265
Main Authors: Kacem, Imed, Kellerer, Hans
Format: Journal Article
Language:English
Published: Boston Springer US 01.06.2011
Springer Science + Business Media
Springer Nature B.V
Springer Verlag
Subjects:
Algorithms
Approximation
Artificial Intelligence
Business and Management
Calculus of Variations and Optimal Control; Optimization
Computer Science
Design engineering
Employment
Flow control
Inequalities
Intervals
Linear programming
Mathematical analysis
Operations Research/Decision Theory
Optimization
Production scheduling
Release dates
Running
Schedules
Studies
Supply Chain Management
Single-machine
Approximation
Non-availability constraint
Flow-time
ISSN:1094-6136, 1099-1425
Online Access:Get full text
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Summary:This paper is the first attempt to successfully design efficient approximation algorithms for the single-machine weighted flow-time minimization problem when jobs have different release dates and weights equal to their processing times under the assumption that one job is fixed (i.e., the machine is unavailable during a fixed interval corresponding to the fixed job). Our work is motivated by an interesting algorithmic application to the generation of valid inequalities in a branch-and-cut method. Our analysis shows that the trivial FIFO sequence can lead to an arbitrary large worst-case performance bound. Hence, we modify this sequence so that a new 2-approximation solution can be obtained for every instance and we prove the tightness of this bound. Then, we propose a fully polynomial-time approximation algorithm with efficient running time for the considered problem. Especially, the complexity of our algorithm is strongly polynomial.
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ISSN:1094-6136
1099-1425
DOI:10.1007/s10951-009-0146-4