Operations Scheduling in the Presence of Multitasking and Symmetric Switching Cost

Hall, Leung & Li have recently proposed a new model for studying operations scheduling in the presence of multitasking – Once a primary job is being processed, the worker gets interruptions from the waiting jobs and needs to switch from the primary job to process for each of the interrupting jobs part of them. Afterward, the worker switches back to process the rest of the primary job. In this paper, we follow their model by introducing two new conditions: (i) the switching costs are job-dependent and symmetric, and (ii) the late jobs are not allowed to interrupt. Complexities of six scheduling problems are investigated. They include the makespan, the total weighted completion time (TWCT), the maximum weighted tardiness (MWT) and the maximum weighted lateness (MWL), the total number of late jobs (TNLJ) and the total weighted number of late jobs (TWNLJ) problems. We show that the makespan, TWCT, MWT and MWL problems are polynomial-time solvable. Under mild conditions on the switching cost function and the interruption function, the total completion time problem can be solved by the shortest processing time first rule. For our late job problems, we show that the TNLJ problem is NP-hard and the TWNLJ is strongly NP-hard. For certain special cases, these problems are polynomial time solvable. Findings in the areas of psychology and management have indicated that multitasking could hamper the mental health and the productivity of a worker. If multitasking is unavoidable, the algorithms presented in this paper could help the human worker to schedule their jobs so as to minimize the effect.