Batch scheduling with controllable setup and processing times to minimize total completion time

• Published in: The Journal of the Operational Research Society Vol. 54; no. 5; pp. 499 - 506
• Main Authors: Ng, C T Daniel, Cheng, T C E, Kovalyov, M Y
• Format: Journal Article
• Language: English
• Published: London Taylor & Francis 01.05.2003; Palgrave Macmillan Press; Palgrave Macmillan UK; Palgrave; Taylor & Francis Ltd
• Subjects: Algorithms; Applied sciences; Batch processing; batching; Business and Management; Computational complexity; controllable setup and processing times; Costs; Dynamic programming; Employment; Exact sciences and technology; Management; Mathematical models; minimizing total completion time; Objective functions; Operational research and scientific management; Operational research. Management science; Operations research; Operations Research/Decision Theory; Optimal solutions; Process engineering; Scheduling; Scheduling, sequencing; Sequencing; Sequential scheduling; single machine; Steel production; Theoretical Paper; Theoretical Papers; Time dependence; Work in process; scheduling; minimizing total completion time; single machine; controllable setup and processing times; batching
• ISSN: 0160-5682; 1476-9360
• DOI: 10.1057/palgrave.jors.2601537

We study a problem of scheduling n jobs on a single machine in batches. A batch is a set of jobs processed contiguously and completed together when the processing of all jobs in the batch is finished. Processing of a batch requires a machine setup time dependent on the position of this batch in the batch sequence. Setup times and job processing times are continuously controllable, that is, they are real-valued variables within their lower and upper bounds. A deviation of a setup time or job processing time from its upper bound is called a compression. The problem is to find a job sequence, its partition into batches, and the values for setup times and job processing times such that (a) total job completion time is minimized, subject to an upper bound on total weighted setup time and job processing time compression, or (b) a linear combination of total job completion time, total setup time compression, and total job processing time compression is minimized. Properties of optimal solutions are established. If the lower and upper bounds on job processing times can be similarly ordered or the job sequence is fixed, then O(n 3 log n) and O(n 5 ) time algorithms are developed to solve cases (a) and (b), respectively. If all job processing times are fixed or all setup times are fixed, then more efficient algorithms can be devised to solve the problems.