Scheduling a batch-processing machine subject to precedence constraints, release dates and identical processing times [An article from: Computers and Operations Research]

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Description:
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 32-approximation algorithm. For the makespan minimization problem, we give an O(n^2) time optimal algorithm and an expression of the minimum makespan.