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SPECIFYING WEIGHT RESTRICTION LIMITS IN DATA ENVELOPMENT ANALYSIS WITH THE WONG AND BEASLEY AND CONE RATIO METHODS

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posted on 06.02.2019 by Leonardo Macrini, Antonio Carlos Gonçalves, Renan M.V.R. Almeida, Carlos Patricio Samanez

ABSTRACT This study presents a new approach for the definition of weight restrictions in Data Envelopment Analysis (DEA) for the one output, multiple inputs case, using the results of a Linear Regression model (LRM) developed with the same DEA variables. Thus, the limits of Wong-Beasley and Cone Ratio methods are chosen without interference from a decision maker, with DEA weight search intervals defined from the estimated standardized coefficients of a linear regression (which represent the statistical importance of the inputs for the definition of the DEA efficiency scores). As an example, weight restrictions for a DEA model (Constant Returns to Scale (CRS)) were obtained through the unrestricted, Wong-Beasley and Cone Ratio methods applied to a dataset consisting of hospital admissions (output), number of beds and number of health professionals (inputs) in the year 2016; and rankings were compared by a Spearman correlation procedure. The regression model had R 2 = 0.89 with coefficients 0.43 (professionals) and 0.54 (beds); and the Spearman correlation among rankings was at least R S 2 = 0.84. In conclusion, rankings were consistent and interpretable, and the approach circumvents the need for a subjective intervention by a decision maker when defining weight restrictions in DEA.

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