An FPTAS for Uniform Machine Scheduling to Minimize the Total Completion Time and the Total Rejection Penalty

In this paper, we study the NP-hard problem of schedulingjobs onuniform machines to minimize the total completion time of the accepted jobs and the total rejection penalty of the rejected jobs. Each job's processing time is a simple linear increasing function of its starting time. A job can be rejected by paying a penalty cost. We propose a fully polynomial-time approximation scheme (FPTAS) to show the problem is NP-hard in the ordinary sense.

Uniform Machine Scheduling Problem with Deteriorating Jobs and Rejection

In this paper, we consider uniform machine scheduling problem with deteriorating jobs and rejection. Each job's processing time is a linear nondecreasing function of its starting time. A job can be rejected by paying a penalty cost. The objective is to minimize the sum of the makespan of the accepted jobs and the total rejection penalty of the rejected jobs. We propose a fully polynomial-time approximation scheme (FPTAS), which shows that the problem is NP-hard in the ordinary sense.