Preemptive Multi-Machine Scheduling of Equal-Length Jobs to Minimize the Average Flow Time

We study the problem of preemptive scheduling of n equal-length jobs with given release times on m identical parallel machines. The objective is to minimize the average flow time. Recently, Brucker and Kravchenko proved that the optimal schedule can be computed in polynomial time by solving a linear...

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Bibliographic Details
Published in:arXiv.org 2004-12
Main Authors: Baptiste, Philippe, Chrobak, Marek, Durr, Christoph, Sourd, Francis
Format: Article
Language:English
Subjects:
Job shops
Linear programming
Polynomials
Post-processing
Preempting
Production scheduling
Schedules
Scheduling
Online Access:Get full text
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Summary:We study the problem of preemptive scheduling of n equal-length jobs with given release times on m identical parallel machines. The objective is to minimize the average flow time. Recently, Brucker and Kravchenko proved that the optimal schedule can be computed in polynomial time by solving a linear program with O(n^3) variables and constraints, followed by some substantial post-processing (where n is the number of jobs.) In this note we describe a simple linear program with only O(mn) variables and constraints. Our linear program produces directly the optimal schedule and does not require any post-processing.
ISSN:2331-8422