Abstract
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 2) time optimal algorithm. When there are no precedence relations, we solve this problem by dynamic programming in O( n 3) time. When the precedence relations are “layerly complete”, we solve this problem by a dynamic programming algorithm that runs in O( n 7) time. For the total weighted completion time minimization problem, we give an O( n 2) time 3 2 -approximation algorithm. For the makespan minimization problem, we give an O( n 2) time optimal algorithm and an expression of the minimum makespan.
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