A common weights multiplicative aggregation approach for composite indicators: the case of Global City Competitiveness Index

We propose a mathematical programming approach to assess a set of entities against a composite index. The weights used to construct the composite index are derived via optimization process. Specifically, we adopt the multiplicative method for the aggregation of the components (sub-indicators) of the evaluated index, which reduces the effect of compensation between the components. Also, we model the problem of identifying a common weighting scheme for the evaluated entities as a multiple objective programming (MOP) problem, with the performance of each entity being a distinct objective-criterion. This allows for comparisons and inferences between the assessed entities as a common ground is established. We stick to the concept of multiplicative aggregation by scalarizing the MOP problem using the weighted product method. Utilizing the multiplicative aggregation method in our modelling approach results in a nonlinear model that is scale invariant. However, using logarithms we show that is straightforwardly converted to a linear equivalent model, which is translation invariant. We examine whether the derived weighting scheme is unique, and in case there are alternative optimal solutions, we employ a max-min achievement function to identify a unique solution. We demonstrate our approach using synthetic datasets and compare it to other multiplicative approaches in the literature. We show that the proposed approach has neglective computational requirements and discriminates to a greater extent than those approaches with which we are compared, while at the same time provides a similar ranking. Similarities and dissimilarities in the results are justified. Since our approach is translation invariant, it enables us to apply it to cases where the data needs translation. We further illustrate our approach for such a case using the Global City Competitiveness Index, developed by Citigroup's Economist Intelligence Unit (EIU), which evaluates the competitiveness of 120 major cities worldwide.