Approximation algorithms for problems in scheduling with set-ups

In this paper, we present new approximation results for the offline problem of single machine scheduling with sequenceindependent set-ups and item availability, where the jobs to be scheduled are independent (i.e., have no precedence constraints) and have a common release time. We present polynomial-time approximation algorithms for two versions of this problem. In the first version, the input includes a weight for each job, and the goal is to minimize the total weighted completion time. On any input, our algorithm produces a schedule whose total weighted completion time is within a factor 2 of optimal for that input. In the second version, the input includes a due date for each job, and the goal is to minimize the maximum lateness of any job. On any input, our algorithm produces a schedule with the following performance guarantee: the maximum lateness of a job is at most the maximum lateness of the optimal schedule on a machine that runs at half the speed of our machine. © 2007 Elsevier B.V. All rights reserved.