Solving a Scheduling Problem with Controllable Processing Times by using PTAS algorithm

In this paper, we consider single machine scheduling problem in which job processing times are controllable variables with linear costs. 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. we improve a linear complexity bound of the best known polynomial bound obtained by Hall and Shmoys for the special case without controllable processing times and by mastrolilli for the special case with controllable processing times by using a new approximation algorithm for knapsack problems.

Keywords:

scheduling , approximation algorithms , PTAS , controllable processing times , knapsack problem