Improved approximation algorithms for parallel machine scheduling with release dates and job rejection

In this paper we study a parallel machine scheduling model with different job release dates, where each job is either accepted and processed by a machine at or after its release date, or it is rejected and a certain penalty cost is paid. The objective is to minimize the makespan of the accepted job plus the total penalty of all rejected jobs. The scheduling problem is NP-hard in the strong sense. Zhang and Lu (4OR A Q J Oper Res 14:165-172, 2016) have proposed a 2-approximation for the problem, and a fully polynomial time approximation scheme (FPTAS) for the special case when the number of machines m is fixed. In this paper we present an improved 2-approximation and a polynomial time approximation scheme for the problem. We also propose an improved FPTAS for the case when m is fixed.