A note on scheduling deteriorating jobs

In scheduling environments with deterioration, jobs processed later in the sequence require more time. In this note, we study a scheduling problem in which the processing time of a job is an increasing function of its position in the sequence (rather than its starting time, as assumed in previous studies). We study a flow-time minimization problem on a single machine, with exponential deterioration function. We show that an optimal schedule is V-shaped with respect to job processing times.