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is the worst-case performance bound of a procedure used in the proposed algorithm for solving the pure sequencing problem. The best approximation procedure known has 
doi:10.1016/j.jalgor.2005.01.004 
Copyright © 2005 Elsevier Inc. All rights reserved.
A linear time approximation scheme for the single machine scheduling problem with controllable processing times
Monaldo Mastrolillia, 
Received 4 July 2003.
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Abstract
In a scheduling problem with controllable processing times the job processing time can be compressed through incurring an additional cost. We consider the problem of scheduling n jobs on a single machine with controllable processing times. Each job has a release date when it becomes available for processing, and, after completing its processing, requires an additional delivery time. Feasible schedules are further restricted by job precedence constraints. We develop a polynomial time approximation scheme whose running time depends only linearly on the input size. This improves and generalizes the previous (3/2+
)-approximation algorithm by Zdrzalka. Moreover, this linear complexity bound gives a substantial improvement of the best previously known polynomial bound obtained by Hall and Shmoys for the special case without controllable processing times.
Keywords: Scheduling; Approximation algorithms
