Multitasking scheduling problems with a rate-modifying activity

Motivated by the behavioral phenomena that occur while human operators are carrying out tasks, we study multitasking scheduling problems with a rate-modifying activity. In the problems, the processing of a selected task suffers from interruptions by other tasks that are available but unfinished, and the human operators regularly engage rest breaks during work shifts allowing them to recover or mitigate some of the negative effects of fatigue. The objectives are to respectively minimize: makespan, total completion time, maximum lateness, and due-date assignment related cost by determining when to schedule the rate modifying activity and the optimal task sequence in the presence of multitasking. Scheduling models and algorithms are proposed to solve the problems. The numerical examples are presented to illustrate the theorems and algorithms.