The optimal number of used machines in a two-stage flexible flowshop scheduling problem

Authors:
Enrique Gerstl;Gur Mosheiov
Affiliations:
School of Business Administration, The Hebrew University, Jerusalem, Israel 91905;School of Business Administration, The Hebrew University, Jerusalem, Israel 91905
Venue:
Journal of Scheduling
Year:
2014

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Abstract

We study practical scheduling problems with a major decision referring to the number of machines to be used. We focus on a two-stage flexible flowshop, where each job is processed on the first (critical) machine, and then continues to one of the second-stage parallel machines. Jobs are assumed to have identical processing times, and are processed in batches. A setup time is required when starting a new batch. We consider two objective functions: minimum makespan and minimum flowtime. In both cases, a closed form expression for the optimal number of machines to be used is introduced, and a unique and unusual sequence of decreasing batch sizes is shown to be optimal.