Model framework to construct a single aggregate sustainability indicator: an application to the biodiesel supply chain

In the present work, we propose a model framework to select a set of sustainability indicators that provides reliable information on the system and use the results to analyze the suitability of four different metrics to describe the sustainability in a given context. We consider an approach that may be applied to study sustainability of a variety of systems and to aggregate 3D indicators into a single metric. Firstly, we identify an initial set of indicators that provides an adequate description of the sustainability conditions of a particular system and satisfy some criteria well established in the literature. Then, we use statistical tools to group the indicators into a valid set, according to their similarity using the inherent statistical information on their structure. This procedure simplifies the analyses of the complex system resulting in an optimum subset of indicators, reducing the dimension and improving the quality of the indicators. Once selected the indicators, established rules are used to aggregate commensurable indicators in a methodological manner into a single aggregate indicator. There is no generally accepted standard methodology to aggregate indicators into a single sustainability indicator. In general, the choice of a metric depends on the problem and on the units expressing the indicators. In the present work, this is analyzed studying four different metrics: Euclidean, Mahalanobis, Canberra, and z -score-normalized Canberra distances. This model framework is then applied to analyze a specific sustainability dimension of a biofuel supply chain in six countries, and compare and discuss the results obtained with the four metrics. It was found that among the four metrics, Canberra distance and Mahalanobis distance are the most adequate single aggregate metrics to describe the sustainability biodiesel chain in countries.