A note to due‐window assignment and single machine scheduling with deteriorating jobs and a rate‐modifying activity

This note considers a single machine scheduling and due‐window assignment problem, in which the processing time of a job is a linear function of its starting time and the job‐independent deterioration rates are identical for all jobs. We allow an option for performing a rate‐modifying activity for changing the normal processing times of the jobs following this activity. The objective is to schedule the jobs, the due‐window and the rate‐modifying activity so as to minimize the sum of earliness, tardiness and due‐window starting time and due‐window size costs. We introduce a polynomial solution for the problem.