Open-shop batch scheduling with identical jobs

This paper addresses batch scheduling problems on an m-machine open-shop. The objectives are minimum makespan and minimum flowtime. We assume identical processing time jobs, machine- and sequence-independent setup times and batch availability. The minimum makespan problem is shown to be solved in constant time. Specifically, we show that the optimal number of batches is either m   or n⌊n/m⌋ (where m and n are the number of machines and the number of jobs, respectively). The complexity of the minimum flowtime problem is unknown. We propose an O(n) time algorithm which extends the solution of the single-machine case, and produces close-to-optimal solutions.