A PTAS for single machine scheduling with controllable processing times

Authors:
Petra Schuurman;Gerhard J. Woeginger
Affiliations:
Department of Mathematics and Computing Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands;Institut für Mathematik B, TU Graz, Steyrergasse 30, A-8010 Graz, Austria, and Department of Mathematics, University of Twente, 7500 AE Enschede, The Netherlands
Venue:
Acta Cybernetica
Year:
2002

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Abstract

We deal with a single machine scheduling problem in which each job has a release date, a delivery time and a controllable processing time. The fact that the jobs have a controllable processing time means that it is allowed to compress (a part of) the processing time of the job, in return for compression cost. The objective is to find a schedule that minimizes the total cost, that is, the latest delivery time of any job plus the total compression cost. In this note we discuss how the techniques of Hall and Shmoys [3] and Hall [1] can directly be applied to design a polynomial time approximation scheme for this problem.