Exact algorithms for the feedback length minimisation problem

Planning the sequence of interrelated activities of production and manufacturing systems has become a challenging issue due to the existence of cyclic information flows. This study develops efficient exact algorithms for finding an activity sequence with minimum total feedback length in a design structure matrix. First, we present two new properties of the problem. Second, based on the properties, we develop an efficient Parallel Branch-and-Prune algorithm (PBP). Finally, the proposed PBP is further improved by adopting hash functions representing activity sequences, which is referred as hash function-based PBP. Experimental results indicate that the proposed hash function-based PBP can find optimal solutions for problems up to 25 interrelated activities within 1 h, and outperforms existing methods.