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We consider the problem of scheduling independent jobs on identical parallel machines so as to minimize the waiting time variance of the jobs (Pm//WTV). We show that the optimal value of(Pm//WTV) is identical to the optimal value of the problem for minimizing the completion time variance of jobs on identical parallel machines(Pm//WTV). We prove that, given the same job set, any feasible schedule of (Pm//WTV) can be transformed into the feasible solution for (Pm//WTV) with the same job set by applying the polynomial algorithms proposed in this paper. Several other important properties of (Pm//WTV) are also proved. Heuristic algorithms are proposed to solve (Pm//WTV) problems. We present the testing results of these heuristic algorithms, which are applied to problems with both small and large job sets.