Dealing with Desirable Inputs in Data Envelopment Analysis: A Slacks-based Measure Approach

Abstract

In Data Envelopment Analysis (DEA) the situation of inputs vs. outputs is positioned as cause and effect. Effects include desirable (ordinary) outputs and undesirable outputs, e.g. pollutants. This situation is well studied and many applications have been published. In this paper, we introduce a new type of inputs, called Good (Desirable) Inputs. As explained in Introduction, we find several examples of such inputs, e.g. Electric car, Women in office and Test takers of vaccine. We handle this by means of SBM (Slacks-based Measure). Usually, efficiency values of DEA models are in the range (0, 1], while in this model a negative efficiency value may be assigned to inefficient DMUs (decision making units). This is caused by shortages of Good Input values. As an example, we refer to “Women’s Rights Movements” in a country where women’s right is not fully guaranteed. Suppose local governments where men and women are serving as officers. They are inputs to office, while Women are Desirable input and Men are Ordinary input. As outputs, we assume Service as Ordinary output and Claim as Undesirable output. Several extensions of this model are introduced. (a) Variable returns to scale, (b) Weight restrictions, (c) Super-efficiency issue and (d) SBM_Max model.