Approximation Algorithms for Multitasking Scheduling Problems

In this work, we incorporate human factors and real-life operations into newly proposed multitasking scheduling problems with periodic shift activities. It is motivated by personnel resource scheduling with periodic work shifts under the requirement of providing continuous service to customers. We model the problem as two identical parallel machine scheduling with complementary non-available time periods, and consider two models with the objectives of the makespan, i.e. the maximum completion time and respectively the total completion time. We then prove that the Greedy algorithm and SPT rule are of asymptotic and parametric approximation ratios for the two models, respectively.