Single Machine Scheduling with Rejection and a Non-Availability Interval to Minimize the Maximum Delivery Completion Time Plus the Total Rejection Cost

Abstract

In this paper, we consider the single machine scheduling with rejection and a nonavailability interval. Two types of non-availability intervals are studied, namely the machine non-availability (MNA) intervals and the operator non-availability (ONA) intervals. The objective is to minimize the sum of the maximum delivery completion time of accepted jobs and the total rejection cost of rejected jobs. For these two problems, a pseudo-polynomial-time dynamic programming algorithm and a fully polynomial-time approximation scheme (FPTAS) are proposed, respectively.