Single machine SLK/DIF due window assignment problem with general job-dependent positional effect and outsourcing operations

This paper considers the SLK/DIF due window assignment problems on a single machine with general job-dependent positional effect, where actual processing time of job is subject to and effect. Production schedulers may decide outsource/reject some jobs by paying corresponding costs. Based whether accept tardiness jobs, we consider two different objectives under slack assignment, respectively. The first objective function minimize weighted sum earliness, tardiness, starting time, size, outsourcing costs, while second cost that includes size We study structural properties methods develop polynomial-time solution algorithms for considered problems. A numerical example proves advantage decision distinction between objectives.