  As a hybrid of the Parallel Two-stage Flowshop problem and the Multiple
Knapsack problem, we investigate the scheduling of parallel two-stage flowshops
under makespan constraint, which was motivated by applications in cloud
computing and introduced by Chen et al. [3] recently. A set of two-stage jobs
are selected and scheduled on parallel two-stage flowshops to achieve the
maximum total profit while maintaining the given makespan constraint. We give a
positive answer to an open question about its approximability proposed by Chen
et al. [3]. More specifically, based on guessing strategies and rounding
techniques for linear programs, we present a polynomial-time approximation
scheme (PTAS) for the case when the number of flowshops is a fixed constant.
