Data envelopment analysis of cities – Investigation of the ecological and economic efficiency of cities using a benchmarking concept from production management

• DEA, originally from production economics, can be successful transferred to the analysis of cities.
• DEA is a promising heuristic tool to help draw the basic outlines of a resource efficient city.
• The suitability of models with constant or variable returns to scale is compared and discussed.
• The scale efficiency was calculated in order to show the influence of economies of scale for cities.
• Cities could have a healthy economic base and the highest possible ecological quality at the same time.

To better understand the economic performance of cities and the accompanying social and environmental implications, one focus of research has been on ways to quantify performance advantages of growth and size while considering the impact of economies of scale. An important aspect of the current discussion is the introduction of the merely environmental driven concept of resource efficiency, defined as minimizing resource consumption while enhancing the quality of life. However, as yet there is no commonly agreed method on how best to measure efficiency. In order to contribute to this debate, an approach is described here of applying Data Envelopment Analysis (DEA) to study the resource efficiency of cities. Originating in the field of economics, DEA is a non-parametric, deterministic method to measure the efficiency of economic production, specifically the relative efficiency of Decision Making Units (DMUs).Here we test the usefulness of DEA to analyze urban efficiency by applying it to an investigation of 116 cities throughout Germany. This entailed the development of two separate economic and ecological models in order to allow more precise identification of the relevance of individual parameters during the evaluation process. The results allow a ranking of cities as well as an estimation of the ratios of economic and ecological efficiencies of the investigated cities, realized with the aid of a nine-field matrix (portfolio).DEA is at the same time a promising heuristic tool to help draw the basic outlines of a resource efficient city and to shed light on the underlying factors that boost or reduce efficiency. We recommend a three-step approach. First, two separate models should be defined (ecological, economic) and used to feed the DEA computation. Second, the results are spread in a portfolio to give an overview of the ecological and economic efficiency scores. This provides a basic overview of the DEA results for the selected cities following a basic and abstract model without determination of causal relationships between these values. Third, the field-dependent commonalities between the cities are considered. Additional indicators that also characterize the selected cities (but which were not selected as inputs to the algorithm) can now be examined. In this way, it is possible to understand the common factors that determine the level of efficiency as well as to learn about the qualitative difference and specific features of cities in the particular matrix quadrants.