Branch and bound algorithm for the flow shop with multiple processors

The sequencing of a flow shop with multiple processors at each stage is a general case of the flow shop problem. It involves sequencing n jobs in a flow shop where, for at least one stage, the facility has one or more identical machines. The purpose of this paper is to present a branch and bound algorithm to solve scheduling problems of such facilities for optimizing the maximum completion time. The lower bounds and elimination rules developed in this research are based upon the generalization of the flow shop problem. Furthermore, a computational algorithm, along with results, is also presented. The branch and bound algorithm can also be used to optimize other measures of performance in a flow shop with multiple processors.