Minimizing makespan in an ordered flow shop with machine-dependent processing times

Authors:
Byung-Cheon Choi;Joseph Y.-T. Leung;Michael L. Pinedo
Affiliations:
Department of Business, Chungnam National University, Yuseong-gu Daejeon, Korea 305-764;Department of Computer Science, New Jersey Institute of Technology, Newark, USA 07102;Department of Information, Operations & Management Sciences, Stern School of Business, New York University, New York, USA 10012-1126
Venue:
Journal of Combinatorial Optimization
Year:
2011

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Abstract

We consider a generalization of the proportionate flow shop problem with the makespan objective. Each job has a processing requirement and each machine has a characteristic value. In our case, we assume that the time a job occupies a machine is equal to the processing requirement of the job plus a setup time that is equal to the characteristic value of that machine. In this paper, we consider permutation schedules and show that the problem is solvable in polynomial time when the number of machines is fixed.