We study a special two-stage flexible flowshop, which consists of several parallel identical machines in the first stage and a single machine in the second stage. We assume identical jobs, and the option of batching, with a required setup time prior to the processing of a new batch. We also consider the option to use only a subset of the available machines. The objective is minimum makespan. A unique optimal solution is introduced, containing the optimal number of machines to be used, the sequence of batch sizes, and the batch schedule. The running time of our proposed solution algorithm is independent of the number of jobs, and linear in the number of machines.
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A flexible flowshop is a machine setting consisting of several stages in series, where each stage contains a number of parallel machines. Minimizing makespan on a general flexible flowshop is clearly NP-hard, since it is a generalization of both minimum makespan on parallel identical machines and minimum makespan on a classical flowshop (with at least three machines). In fact, minimum makespan on a flexible flowshop was shown to be strongly NP-hard even for the special case of () two stages, () two identical machines in one stage and a single machine in the second stage, and () when preemption is allowed (Hoogeveen et al. ). We refer the reader to the recent survey on flexible flowshops by * Enrique Gerstl, School of Business Administration, The Hebrew University, Jerusalem, Israel; Gur Mosheiov, School of Business Administration, The Hebrew University, Jerusalem, Israel. ** Assaf Sarig, The Center for Academics Studies, Or Yehuda, Israel 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.
- Batch Scheduling
- Deterministic Scheduling
- Flexible Flowshop