Scheduling a batch-processing machine subject to precedence constraints, release dates and identical processing times

We consider the single machine parallel-batching scheduling problem with precedence relations, release dates and identical processing times to minimize a regular objective function. When the processing times are unit, we give an O(n) time optimal algorithm. When there are no precedence relations, we solve this problem by dynamic programming in O(n) time. When the precedence relations are “layerly complete”, we solve this problem by a dynamic programming algorithm that runs in O(n) time. For the total weighted completion time minimization problem, we give an O(n) time 3 2 -approximation algorithm. For the makespan minimization problem, we give an O(n) time optimal algorithm and an expression of the minimum makespan.