Treffer: Multiple parallel-batch machines scheduling with additive resource assignment and machine available times.

In this paper we study a scheduling problem on multiple bounded parallel-batch (or p-batch) machines to minimize makespan. Each machine processes jobs in batches and has a machine-dependent available time, i.e., not all machines are available simultaneously. The processing time of a batch is equal to the largest processing time of the jobs in it. Multiple kinds of additive resources are given and each of them is consumed by at most one job. Each job consumes exactly one kind of resource and its actual processing time depends on the consumed resource. Our main result is presenting an approximation algorithm with the worst-case bound being 2 − 1 / b for m = 1 , 2 − 2 / (2 b + 1) for m = 2 and 2 − 1 / (m − 1) b for m ≥ 3 , and showing the tightness of this bound, where m is the number of machines and b is the batch capacity. • We propose a new scheduling model on multiple parallel-batch machines. • We design an approximation algorithm and analyze the worst-case bound. • We execute numerical studies to evaluate the performance of the devised algorithms. [ABSTRACT FROM AUTHOR]