Scale Efficiency Measurement in Data Envelopment Analysis with Interval Data: A Two-Level Programming Approach

Abstract

Conventional data envelopment analysis (DEA) for measuring the relative efficiency of a set of decision-making units (DMUs) requires the observations to have precise values. When observations are imprecise and represented by interval values, the efficiencies are also expected to reflect interval values. Several methods exist to calculate the interval overall and technical efficiencies, but such methods are unable to calculate the interval scale efficiency. The focus of this paper is the application of a two-level programming technique to formulate the problem of determining the bounds of the interval scale efficiency. The associated models are essentially nonlinear programs with only bound constraints for variables in a sophisticated form. Hence, one can modify the conventional quasi-Newton method for unconstrained nonlinear programming problems to solve the two-level programs. Two examples with interval data, one hypothetical and one real, aid in explaining the proposed method and the properties of the results.