Single-Machine Scheduling with Discretely Controllable Job Processing Times Subject to a Deteriorating Rate-Modifying Activity

Abstract

SYNOPTIC ABSTRACTIn this article, we investigate the problem of scheduling jobs with discretely controllable processing times subject to a deteriorating rate-modifying activity on a single machine. In our problem, each job has multiple processing times to be selected. But for different processing times, different processing costs are required. In addition, we can choose a deteriorating rate-modifying activity to reduce the processing times of jobs that are scheduled subsequently. We aim to minimize the following objectives: the makespan plus the total processing cost; the total completion time plus the total processing cost; and the sum of earliness, tardiness, and common due date penalties plus the total processing cost. We show that all these goals are polynomial-time solvable followed by the numerical examples.