DEA Problems under Geometrical or Probability Uncertainties of Sample Data

This paper discusses the theoretical and practical aspects of new methods for solving DEA problems under real-life geometrical uncertainty and probability uncertainty of sample data. The proposed minimax approach to solve problems with geometrical uncertainty of sample data involves an implementation of linear programming or minimax optimization, whereas the problems with probability uncertainty of sample data are solved through implementing of econometric and new stochastic optimization methods, using the stochastic frontier functions estimation.DEA, Sample data uncertainty, Linear programming, Minimax optimization, Stochastic optimization, Stochastic frontier functions

Using a modified DEA model to estimate the importance of objectives. An application to agricultural economics.

This paper shows a connection between Data Envelopment Analysis (DEA) and the methodology proposed by Sumpsi et al. (1997) to estimate the weights of objectives for decision makers in a multiple attribute approach. This connection gives rise to a modified DEA model that allows to estimate not only efficiency measures but also preference weights by radially projecting each unit onto a linear combination of the elements of the payoff matrix (which is obtained by standard multicriteria methods). For users of Multiple Attribute Decision Analysis the basic contribution of this paper is a new interpretation of the methodology by Sumpsi et al. (1997) in terms of efficiency. We also propose a modified procedure to calculate an efficient payoff matrix and a procedure to estimate weights through a radial projection rather than a distance minimization. For DEA users, we provide a modified DEA procedure to calculate preference weights and efficiency measures which does not depend on any observations in the dataset. This methodology has been applied to an agricultural case study in Spain.Multicriteria Decision Making, Goal Programming, Weights, Preferences, Data Envelopment Analysis.

Clustering in a Data Envelopment Analysis Using Bootstrapped Efficiency Scores

This paper explores the insight from the application of cluster analysis to the results of a Data Envelopment Analysis of productive behaviour. Cluster analysis involves the identification of groups among a set of different objects (individuals or characteristics). This is done via the definitions of a distance matrix that defines the relationship between the different objects, which then allows the determination of which objects are most similar into clusters. In the case of DEA, cluster analysis methods can be used to determine the degree of sensitivity of the efficiency score for a particular DMU to the presence of the other DMUs in the sample that make up the reference technology to that DMU. Using the bootstrapped values of the efficiency measures we construct two types of distance matrices. One is defined as a function of the variance covariance matrix of the scores with respect to each other. This implies that the covariance of the score of one DMU is used as a measure of the degree to which the efficiency measure for a single DMU is influenced by the efficiency level of another. An alternative distance measure is defined as a function of the ranks of the bootstrapped efficiency. An example is provided using both measures as the clustering distance for both a one input one output case and a two input two output case.