Ranking efficient DMUs using cooperative game theory

The problem of ranking Decision Making Units (DMUs) in Data Envelopment Analysis (DEA) has been widely studied in the literature. Some of the proposed approaches use cooperative game theory as a tool to perform the ranking. In this paper, we use the Shapley value of two different cooperative games in which the players are the efficient DMUs and the characteristic function represents the increase in the discriminant power of DEA contributed by each efficient DMU. The idea is that if the efficient DMUs are not included in the modified reference sample then the efficiency score of some inefficient DMUs would be higher. The characteristic function represents, therefore, the change in the efficiency scores of the inefficient DMUs that occurs when a given coalition of efficient units is dropped from the sample. Alternatively, the characteristic function of the cooperative game can be defined as the change in the efficiency scores of the inefficient DMUs that occurs when a given coalition of efficient DMUs are the only efficient DMUs that are included in the sample. Since the two cooperative games proposed are dual games, their corresponding Shapley value coincide and thus lead to the same ranking. The more an ef- ficient DMU impacts the shape of the efficient frontier, the higher the increase in the efficiency scores of the inefficient DMUs its removal brings about and, hence, the higher its contribution to the overall discriminant power of the method. The proposed approach is illustrated on a number of datasets from the literature and compared with existing methods

Ranking intervals for two-stage production systems

Traditional Data Envelopment Analysis (DEA) models find the most desirable weights for each Decision Making Unit (DMU) in order to estimate the highest efficiency score as possible. Usually, decision-makers are using these efficiency scores for ranking the DMUs. The main drawback in this process is that the ranking based on weights obtained from the standard DEA models ignore other feasible weights, this is due to the fact that DEA may have multiple solutions for each DMU. To overcome this problem, Salo and Punkka (2011) deemed each DMU as a “Black box” and developed a mix-integer model to obtain the ranking intervals for each DMU over sets of all its feasible weights. In many real-world applications, there are DMUs that have a two-stage production system. In this paper, we extend the Salo and Punkka (2011)’s model to more common and practical applications considering the two-stage production structure. The proposed approach calculates each DMU’s ranking interval for the overall system as well as for each subsystem/sub-stage. An application for non-life insurance companies is given to illustrate the applicability of the proposed approach. A real application in Chinese commercial banks shows how this approach can be used by policy makers

Ranking Intervals and Dominance Relations for Ratio-Based Efficiency Analysis

We develop comparative results for ratio-based efficiency analysis, based on the decision making units' (DMUs) relative efficiencies over sets of feasible weight that characterize preferences for input and output variables. Specifically, we determine (i) ranking intervals which indicate the best and worst efficiency rankings that a DMU can attain relative to other DMUs, (ii) dominance structures which convey what other DMUs a given DMU dominates in one-on-one efficiency comparisons, and (iii) efficiency bounds which show how much more efficient a DMU can be relative to a given DMU or a subset of other DMUs. These efficiency results-which reflect the full range of feasible input and output weights-are robust in the sense that they are insensitive to possible outliers and do not necessitate particular returns-to-scale assumptions. We also report a real case study where these results supported the efficiency analysis of the twelve departments at a large technical university. Key words : performance measurement, data efficiency analysis, preference modeling Introduction Inspired by the seminal paper of Because the efficiency scores are computed relative to the efficiency frontier, these scores are potentially sensitive to what DMUs are included in or excluded from the analysis: specifically, the introduction/removal of a single outlier (e.g., an exceptionally efficient DMU that produces more outputs per inputs than the other DMUs) may shift the efficient frontier considerably, which may disrupt the reported efficiency scores for other DMUs and hence perplex the users of efficiency results (see, e.g., Seiford and Zhu, 1998ab; Motivated by the above considerations, we develop efficiency results which allow us to answer questions such as: • What are the best/worst rankings that DMU A can attain in comparison with other DMUs, based on their efficiency ratios

Measuring Technical Efficiency of Dairy Farms with Imprecise Data: A Fuzzy Data Envelopment Analysis Approach

This article integrates fuzzy set theory in Data Envelopment Analysis (DEA) framework to compute technical efficiency scores when input and output data are imprecise. The underlying assumption in convectional DEA is that inputs and outputs data are measured with precision. However, production agriculture takes place in an uncertain environment and, in some situations, input and output data may be imprecise. We present an approach of measuring efficiency when data is known to lie within specified intervals and empirically illustrate this approach using a group of 34 dairy producers in Pennsylvania. Compared to the convectional DEA scores that are point estimates, the computed fuzzy efficiency scores allow the decision maker to trace the performance of a decision-making unit at different possibility levels.fuzzy set theory, Data Envelopment Analysis, membership function, α-cut level, technical efficiency, Farm Management, Production Economics, Productivity Analysis, Research Methods/ Statistical Methods, Risk and Uncertainty, D24, Q12, C02, C44, C61,

The competitiveness of nations and implications for human development

This is the post-print version of the final paper published in Socio-Economic Planning Sciences. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2010 Elsevier B.V.Human development should be the ultimate objective of human activity, its aim being healthier, longer, and fuller lives. Thus, if the competitiveness of a nation is properly managed, enhanced human welfare should be the key expected consequence. The research described here explores the relationship between the competitiveness of a nation and its implications for human development. For this purpose, 45 countries were evaluated initially using data envelopment analysis. In this stage, global competitiveness indicators were taken as input variables with human development index indicators as output variables. Subsequently, an artificial neural network analysis was conducted to identify those factors having the greatest impact on efficiency scores

Multi-Criteria versus Data Envelopment Analysis for Assessing the Performance of Biogas Plants

This paper compares multi-criteria decision aiding (MCDA) and data envelopment analysis (DEA) approaches for assessing renewable energy plants, in order to determine their performance in terms of economic, environmental, and social criteria and indicators. The case is for a dataset of 41 agricultural biogas plants in Austria using anaerobic digestion. The results indicate that MCDA constitutes an insightful approach, to be used alternatively or in a complementary way to DEA, namely in situations requiring a meaningful expression of managerial preferences regarding the relative importance of evaluation aspects to be considered in performance assessment.Multi-criteria decision analysis; DEA; Renewable energy; Biogas

Productivity drivers in European banking: Country effects, legal tradition and market dynamics

This paper analyses efficiency drivers of a representative sample of European banks by means of the two-stage procedure proposed by Simar and Wilson (2007). In the first stage, the technical efficiency of banks is estimated using DEA (data envelopment analysis) in order to establish which of them are most efficient. Their ranking is based on total productivity in the period 1993-2003. In the second stage, the Simar and Wilson (2007) procedure is used to bootstrap the DEA scores with a truncated bootstrapped regression. The policy implications of our findings are considered