Analysis on the Effect of Multitasking

Recently, the ideas of switching cost and interruption function have been introduced in modeling the scheduling problems with multitasking and the effect of multitasking is investigated by computer simulations. In this paper, we analyze the effect of multitasking on the total completion time (TCT) and total weighted completion time (TWCT) by statistical analysis. If the cost of job switching is a constant and the amount of interruption is proportional to the remaining processing time of the interrupting job, the optimal TCT schedule can be obtained by the shortest processing time first (SPTF) rule. Thus, the optimal TCT in the presence of multitasking is derived and compared with the optimal TCT without multitasking. Assuming that the values of switching cost and the proportional constant are small, the optimal TWCT in the presence of multitasking is expressed and compared with the optimal TWCT without multitasking. With mild statistical assumptions on the processing times and weights, the expected TCT and TWCT are derived and the effect of multitasking on TCT (respectively TWCT) is analyzed by numerical plots against the switching cost and the proportional constant. Results reveal that multitasking could have significant effect on both the TCT and TWCT. Hence, multitasking should be avoided in a work place.

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