Intractability of Operations Scheduling in the Presence of Multitasking

Hall, Leung & Li have recently proposed a new model for human multitasking behavior. In their model, a primary job gets interruptions from all waiting jobs whenever it is being processed. Every time an interruption has been received, the worker switches from the primary job to the interrupting job. After part of the interrupting job has complete, the worker switches back to the primary job. Here, we extend from this model by adding that switching costs (SC) are job-dependent and late jobs are not allowed to interrupt. The scheduling problems of six different criteria are then investigated, including makespan, total weighted completion time (TWCT), maximum weighted tardiness (MWT), maximum weighted lateness (MWL), number of late jobs (NLJ) and weighted number of late jobs (WNLJ). For symmetric SC, we show that the makespan, TWCT, MWT and MWL problems are polynomial-time solvable. The NLJ problem is NP-hard. The WNLJ is strongly NP-hard. For asymmetric SC, we show that the makespan problem is NP-hard. The TCT and NLJ problems are strongly NP-hard. Accordingly, the complexity hierarchies of the scheduling problems in the presence of multitasking are sketched. The problems, in which the effect of multitasking on operations scheduling could be analyzed mathematically, can then be solicited.