Maximum diversity/similarity models with extension to part grouping

Maximum diversity/similarity models involve selecting a subset of desired size from a given pool of objects such that some measure of diversity or similarity among the selected objects is maximized. Such models have found application, among other places, in the formation of various groups, the location of obnoxious facilities and the identification of dense subgraphs. We present a mild generalization, which yields a stronger and more practical formulation and is seen to be solved effectively. As an extension, we consider the part-grouping problem as encountered in manufacturing cell formation. We show how the enhanced diversity/similarity model can be used to form part families in a way that is both flexible and competitive with existing approaches. We provide an illustrative example and limited computational results.