A model for efficiency evaluation based upon the theory of chance constrained programming is developed. The model uses a piecewise linear envelopment of confidence regions for observed stochastic multiple-input multiple-output combinations in the Data Envelopment Analysis (DEA) tradition. The model allows for an exogenous decomposition of the total variation in data for each Decision Making Unit (DMU). By varying certain probability levels the model can provide estimates of the sensitivity of efficiency scores regarding an unknown amount of noise in date. An application of the method in an evaluation of the research activities in economic departments at Danish Universities is presented.efficiency measurement, chance constraints, stochastic frontier estimation

In applications of data envelopment analysis (DEA) data about some inputs and outputs is often available only in the form of ratios such as averages and percentages. In this paper we provide a positive answer to the long-standing debate as to whether such data could be used in DEA. The problem arises from the fact that ratio measures generally do not satisfy the standard production assumptions, e.g., that the technology is a convex set. Our approach is based on the formulation of new production assumptions that explicitly account for ratio measures. This leads to the estimation of production technologies under variable and constant returns-to-scale assumptions in which both volume and ratio measures are native types of data. The resulting DEA models allow the use of ratio measures "as is", without any transformation or use of the underlying volume measures. This provides theoretical foundations for the use of DEA in applications where important data is reported in the form of ratios.

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Date Envelopment Analysis (DEA) employs mathematical programming to measure the relative efficiency of Decision Making Units (DMUs). This paper is concerned with development of indicators to determine whether or not the specification of the input and output space is supported by data in the sense that the variation in data is sufficient for estimation of a frontier of the same dimension as the input output space. Insufficient variation in data implies that some inputs/outputs can be substituted along the efficient frontier but only in fixed proportions. Data thus locally supports variation in a subspace of a lower dimension rather than in the input output space of full dimension. Each segment of the efficient frontier is in this sense subject to local collinearity. Insufficient variation in data provides a bound on admissible disaggregations in cases where substitution in fixed proportions is incompatible with a priori information concerning the production process. A data set incapable of estimating a frontier of full dimension will in this case be denoted ill-conditioned. It is shown that the existence of well-defined marginal rates of substitution along the estimated strongly efficient frontier segments requires the existence of Full Dimensional Efficient Facets (FDEFs). A test for the existence of FDEFs is developed, and an operational two-stage procedure for efficiency evaluation relative to an over-all non-fixed technology is developed; the two-stage procedure provides a lower and an upper bound on the efficiency index for each DMU.efficiency measurement, data envelopment analysis, facets, virtual multipliers, model misspecification, rates of sustitutions, maintained hypotheses, Frontier estimation

In a recent paper to this journal, the authors developed a methodology that allows the incorporation of ratio inputs and outputs in the variable and constant returns-to-scale DEA models. Practical evaluation of efficiency of decision making units (DMUs) in such models generally goes beyond the application of standard linear programming techniques. In this paper we discuss how the DEA models with ratio measures can be solved. We also introduce a new type of potential ratio (PR) inefficiency. It characterizes DMUs that are strongly efficient in the model of technology with ratio measures but become inefficient if the volume data used to calculate ratio measures become available. Potential ratio inefficiency can be tested by the programming approaches developed in this paper.