A review of exact solution methods for the non-preemptive multiprocessor flowshop problem Tam as Kis, Erwin Pesch * Computer and Automation Research Institute, Hungarian Academy of Sciences, 1111 Budapest, Kende utca 13-17, Hungary Faculty of Economics and Business Administration, University of Siegen, H€ olderlinstrasse 3, 57068 Siegen, Germany Received 1 December 2002; accepted 1 December 2003 Available online 6 May 2004 Abstract The hybrid or flexible flowshop problem is a generalization of the flowshop in such a way that every job can be processed by one among several machines on each machine stage. In recent years a number of effective exact methods have been developed. A major reason for this progress is the development of new job and machine based lower bounds as well as the rapidly increasing importance of constraint programming. In this paper we provide the first comprehensive and uniform overview on exact solution methods for flexible flowshops with branching, bounding and propagation of constraints under two different objective functions: minimizing the makespan of a schedule and the mean flow time. Ó 2004 Elsevier B.V. All rights reserved. Keywords: Multiprocessor flowshop; Lower bounds; Branch and bound; Constraint propagation 1. The multiprocessor flowshop model A multiprocessor or hybrid or flexible flowshop is a generalization of the classical flowshop model. There are L stages and each stage ‘ consists of M ð‘Þ parallel machines. The jobs have to visit the stages in the same order starting from stage 1 through stage L. A machine can process at most one job at a time and a job can be processed by at most one machine at a time. Preemption of processing is not allowed. The scheduling problem consists of assigning jobs to machines at each stage and sequencing the jobs assigned to the same machine so that some optimality criterion C is minimized. Multiprocessor flowshop models differ in the type and number of machines at the stages. Namely, at a general stage ‘ there can be either one machine or several parallel machines. In the latter case the processing times of the jobs on the different machines may be identical, uniform, or unrelated. These three possibilities correspond to the three classical parallel machine models with similar names. * Corresponding author. E-mail addresses: tamas.kis@sztaki.hu (T. Kis), pesch@fb5.uni-siegen.de (E. Pesch). 0377-2217/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2003.12.026 European Journal of Operational Research 164 (2005) 592–608 www.elsevier.com/locate/dsw