Uniform Machine Scheduling Problem with Deteriorating Jobs and Rejection

Abstract

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.