Reconsidering generalized similarity coefficient via a sequence ratio

Generalized Similarity Coefficient (GSC) is an extension of Jaccard similarity coefficient to deal with cell formation problems that incorporate alternative process routings. A drawback of GSC is that it ignores the impact of material flows. Due to this drawback, flexibilities brought by alternative process routings have been wiped out. The contribution of this paper is to overcome this drawback by introducing a sequence ratio. We extend GSC to take into account operation sequences of parts. We also propose a heuristic algorithm that improves solutions obtained by Average Linkage Clustering (ALC) algorithm. Comparative experimentations are executed to test the new similarity coefficient and the extended-ALC algorithm, and the results of comparison show that the new approach not only performs superior than previous GSC and ALC, but also reflects the real-life production situations accurately. Significance: The new similarity coefficient can model three different scenarios: a traditional cell formation problem; a cell formation problem which incorporates alternative process routings, and a cell formation problem which incorporates both alternative process routings and operation sequences that exist in the real-life production.