We consider the parallel approximability of two problems arisingfrom high multiplicity scheduling, namely the unweightedmodel with variable processing requirements and the weighted model with identical processing requirements. These twoproblems are known to be modelled by a class of quadratic programsthat are efficiently solvable in polynomial time. On the parallelsetting, both problems are P-complete and hence cannot beefficiently solved in parallel unless P = NC. To deal with theparallel approximablity of these problems, we show first aparallel additive approximation procedure to a subclass ofmulti-valued quadratic programming, called smooth multi-valuedQP, which is defined by imposing certain restrictions onthe coefficients of the instance. We use this procedure to obtainparallel approximation to dense instances of the two problems by observing that denseinstances of these problems are instances of smooth multi-valuedQP. The dense instances of the problemsconsidered here are defined similarly as for other combinatorialproblems in the literature. For such instances we can find inparallel a near optimal schedule. The definition of smoothmulti-valued QP as well as the procedure forapproximating it in parallel are of interest independently of theapplication to the scheduling problems considered in this paper.