Preemptive Multi-Machine Scheduling of Equal-Length Jobs to Minimize the Average Flow Time
Data Structures and Algorithms
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.cs/0412094,
title = {Preemptive Multi-Machine Scheduling of Equal-Length Jobs to Minimize the Average Flow Time},
author = {Philippe Baptiste and Marek Chrobak and Christoph Durr and Francis Sourd},
journal= {arXiv preprint arXiv:cs/0412094},
year = {2007}
}