More on aggregating multiple indicators into a single index for sustainability analyses

Sustainability analyses of systems are successful when one can ascertain unambiguous overall superiority of a state of a system compared to alternative states. These alternative states can be system conditions over time intervals, or alternative products or processes for the same function or market application. In such analyses, indicators or metrics that satisfactorily characterize the system can be used to obtain an aggregate index for easy decision making. Previously, the geometric mean of the ratios of the applied indicators was demonstrated to be useful in showing superior or inferior status of any specific state of the system compared to a chosen reference state. This multidimensional index D, in a pairwise comparison, however, does not work if any indicator can assume the value of zero, infinity, or negative numbers. The present work shows that by shifting the multidimensional reference point, this difficulty can be easily avoided. In addition, this technique of shifting the reference point also has been shown to work when the standard multidimensional Euclidean distance, i.e., the square root of the sum of the squares of the differences of the indicator values, appropriately normalized, is used to differentiate among competing alternatives for determining comparative sustainability. Two sets of data, one on fender designs for automobiles, and the other on alternate means of treating automotive shredder residues, were used to illustrate the application of the indicator integration.