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In cloud computing,execution times of tasks or jobs on virtual machines are usually uncertain.To obtain accurate execution times,an integrated learning effects model is developed which makes use of experiences.The single virtual machine scheduling problems with the developed learning effects model are proven to be optimally solvable in polynomial time for optimizing makespan,total completion time and the sum of(square)completion times.Those to minimize the total weighted completion time and the maximum lateness are proved to be optimally solvable in polynomial time only for certain assumptions.The developed learning effects model is adapted to two special m-virtual machine flowshop problems.Polynomial-time optimal solutions are provided to them for the same objectives as in the single virtual machine scheduling problems.Optimal solutions are demonstrated by an example for the considered problems using the constructed optimal rules.