Single‐machine due window assignment and scheduling with a common flow allowance and controllable job processing time

In this paper, we consider single‐machine due window assignment and scheduling with a common flow allowance and controllable job processing times, subject to unlimited or limited resource availability. Due window assignment with a common flow allowance means that each job has a job‐dependent due window, the starting time and completion time of which are equal to its actual processing time plus the job‐independent parameters q1 and q2, respectively, which are common to all the jobs. The processing time of each job is either a linear or a convex function of the amount of a common continuously divisible resource allocated to the job. We study five versions of the problem that differ in terms of the objective function and processing time function being used. We provide structural properties of the optimal schedules and polynomial‐time solution algorithms for the considered problems.