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

Philippe Baptiste·Marek Chrobak·Christoph Durr·Francis Sourd
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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.

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Philippe Baptiste, Marek Chrobak, Christoph Durr, Francis Sourd. 2004-12-20. Preemptive Multi-Machine Scheduling of Equal-Length Jobs to Minimize the Average Flow Time. https://arxiv.org/abs/cs/0412094

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