A note on single-machine scheduling with learning effect and an availability constraint

Recent empirical studies in several industries have verified that unit costs decline as firms produce more of a product and gain knowledge or experience. This phenomenon is known as the "learning effect." However, most of the papers assume that the machine is available at all times. In reality, the machine might become unavailable due to machine breakdowns or preventive maintenance during the scheduling period. Motivated by this, single-machine scheduling problems with considerations of the learning effect and machine availability are considered in this paper. It is shown that the shortest processing time rule provides the optimal schedules for the makespan and the total completion time minimization problems when jobs are assumed to be resumable. Moreover, mixed integer programming techniques are used to solve the problems when jobs are non-resumable.