A Parallel Branch&Bound Algorithm for Makespan Optimal Sequencing in Flow Shops with Parallel Machines

In this paper we address the problem of makespan optimal sequencing in a ow shop with parallel machines (FSPM). This kind of production facility is a generalization of the standard ow shop where at least one stage consists of two or more identical machines. We present a branch & bound algorithm and its parallel implementation which minimizes the makespan, i. e. the maximum completion time required to process all operations for a given set of jobs. Compared to other algorithms our method makes use of a quite simple branching scheme and is to our knowledge the rst exact algorithm which can deal with machine available times. Although the minimum makespan scheduling problem in the FSPM environment is NP-hard, this paper shows that instances of small to moderate scale can be solved in a reasonable amount of time. In particular, this is true if the computing performance of massively parallel systems is used to solve such problems.