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Approximation algorithms to minimize a special weighted flow-time criterion on a single machine with a fixed job and release dates

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2 Author(s)
Kacem, I. ; Univ. of Paul Verlaine, Metz, France ; Kellerer, H.

Motivated by an interesting algorithmic application, 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 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 for the considered problem. The complexity of our algorithm is strongly polynomial.

Published in:

Computers & Industrial Engineering, 2009. CIE 2009. International Conference on

Date of Conference:

6-9 July 2009