Some comments on compositional analysis in management and production engineering

This paper introduces the most basic concepts of the compositional analysis of data with a simple but real example form the Management and Production Engineering (MPE) field. Compositional Data (CoDa) are vectors of positive elements that represent parts of a whole and are widely found in MPE, i.e. production times, resource composition, percentage utilization of work stands, waste components... The need for an analysis based on ratios of components (or better log-ratios of components) is illustrated step by step, and findings are compared to the corresponding standard methods applied to raw compositions. The paper also exposes the principles of CoDa analysis and presents two basic descriptive tools suitable for CoDa: the clr-biplot and the CoDa dendrogram. The example is a time series, from 1994 to 2013, of motor vehicle production in 8 countries and regions.