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

• Published in: Computers & operations research Vol. 32; no. 4; pp. 849 - 859
• Main Authors: Cheng, T.C.E., Yuan, J.J., Yang, A.F.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.04.2005; Elsevier Science; Pergamon Press Inc
• Subjects: Algorithms; Applied sciences; Batch processing; Dynamic programming; Exact sciences and technology; Identical processing times; Job shops; Operational research and scientific management; Operational research. Management science; Precedence constraints; Release dates; Scheduling; Scheduling algorithms; Scheduling, sequencing; Studies; Identical processing times; Precedence constraints; Scheduling; Algorithms; Release dates; Batch processing; Optimal algorithm; Makespan; Approximation algorithm; Batch scheduling; Precedence constraint; Objective function; Dynamic programming; Single machine
• ISSN: 0305-0548; 1873-765X; 0305-0548
• DOI: 10.1016/j.cor.2003.09.001

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.