We study a two-stage flowshop, where each job is processed on the first (critical) machine, and then continues to one of two second-stage (dedicated) machines. We assume identical (but machine-dependent) job processing times. Jobs are processed on the critical machine in batches, and a setup time is required when starting a new batch. The setting assumes batch-availability, i.e., jobs become available for the second stage only when their entire batch is completed on the critical machine. We consider three objective functions: minimum makespan, minimum total load, and minimum weighted flow-time. Polynomial time dynamic programming algorithms are introduced, which are numerically shown to be able to solve problems of medium size in reasonable time. A heuristic for makespan minimization is presented and shown numerically to be both accurate and efficient.
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Acknowledgement: This paper was supported in part by The Recanati Fund and The Charles Rosen Chair of Management, The School of Business Administration, The Hebrew University, Jerusalem, Israel. We would like to thank Professor Michail Kovalyov for providing us a very relevant reference to this paper.
- Batch scheduling
- Critical machine
- Dynamic programming
- Total load