An enhanced hybrid interval slacks-based DEA model with super-efficiency and application

Abstract

Data envelopment analysis (DEA) models play a significant role in evaluating the efficiency of decision-making units (DMUs) among multiple input and output variables in many fields, such as industry or economy. This method establishes a production possibility set (PPS) that defines the efficient ones, the efficiency boundary or frontier, and provides the projection into the latter, or targets, for the inefficient ones. This paper introduces an enhanced hybrid interval slacks-based DEA when information on inputs and outputs can be discrete (integer) or continuous (real) and presents uncertainty, which can be modeled using intervals (integer or continuous). To this matter, we propose a novel approach that calculates crisp inefficiency scores, interval slacks, and interval targets using interval arithmetic and LU-partial orders on intervals. Mainly, the novelty is based on a reduction and simplicity of the model with respect to others existing, as well as the inclusion of integer interval-valued information with the corresponding mathematical tools and previous results. A super-efficiency slacks-based model is also provided to distinguish among the efficient DMUs and provide a full rank for the set of DMUs. We finally present the practical application of our method in tourism, an essential economic sector in Spain, focusing on different coastal areas.