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We study the problem of scheduling n jobs on m parallel bounded batch machines to minimize the sum of squared machine loads. Each batch contains at most B jobs, and the processing time of a batch is equal to the longest processing time of the jobs in this batch. We prove this problem to be NP-hard. Furthermore, we present a polynomial time approximation scheme (PTAS) and a fully polynomial time approximation scheme (FPTAS) for this problem.

Some Discussions on Parallel Bounded Batch Scheduling to Minimize the Sum of Squared Machine Loads