One important issue in DEA which has been studied by many DEA researchers is the sensitivity of the results of an analysis to perturbations in the data.
This paper develops a procedure for performing a sensitivity analysis of the inefficient decision making units (DMUs). The procedure yields an exact “Necessary Change Region” in which the efficiency score of a specific inefficient DMU changes to a defined efficiency score.
In what follows, we identify a new frontier, and prove the efficiency score of each arbitrary unit on it which is defined as the efficiency score.
Data envelopment analysis (DEA) introduced by Charnes et al. [1] (CCR) and extended by Banker et al. [2] (BCC), is a useful method to evaluate the relative efficiency of multiple-input and multiple-output units based on the data observed. The sensitivity analysis has received great attention from researchers in recent years and so much research has been carried out in this regard. Sensitivity analysis in DEA has been deliberated from various points of view.
One important issue in DEA which has been studied by many DEA researchers, is the sensitivity analysis of a specific decision making unit (DMU) which is under evaluation [3], [4], [5], [6] and [7]. Another type of DEA sensitivity analysis is based on the super-efficiency DEA approach in which the DMU under evaluation is not included in the reference set [8], [9], [10], [11] and [12]. Charnes et al. developed a super-efficiency DEA sensitivity analysis technique for the situation where simultaneous proportional change is assumed in all inputs and outputs for a specific DMU under consideration [13] and [14].
DEA sensitivity analysis methods that we have just reviewed are all developed for the situation where data variations are only applied to the efficient DMU under evaluation and the data for the remaining DMUs are assumed fixed.
While the sensitivity analysis of an efficient unit’s classification has been extensively studied, the issue of an inefficient unit’s estimation and classification seems to be ignored.
This paper focusses on inefficient sensitivity analysis DMUs. So, the aim is to research ways to improve the inefficient units using another strategy, in addition to the evaluation of DMUs and classifying them into efficient and inefficient.
The improvement is usually possible, but sometimes, reaching to the efficiency frontier and achieving the score 1 in efficiency by inefficient units are really impossible. Our objective is to reach to the efficiency score of those inefficient units whose efficiency score is less than a fixed constant αα to αα. (This constant is usually close to 1 and is defined by the manager). It means that if we suppose the efficiency score of inefficient unit to be View the MathML sourceθo∗ and View the MathML sourceθo∗<α<1, then after these variations, it will meet the efficiency score of αα, and an improvement of View the MathML sourceα−θo∗ in efficiency is obtained.
The variations region of every inefficient unit is called “Necessary Change Region ”. In what follows, some new frontiers are defined and with the help of some theorems, we will prove that the efficiency score of each unit of the new frontier is αα. In fact, as the efficiency score of all points on the main frontier is supposed to be 1, the efficiency score on the new frontiers is αα.
This paper proceeds as follows. Section 2 discusses the basic DEA models. Section 3 develops a proposed method for finding the “Necessary Change Region”. Section 4 provides a numerical example and finally, conclusions are given in Section 5.
In recent years, many DEA researchers have studied the sensitivity analysis of efficient and inefficient unit classifications with respect to perturbations of data. This paper is focused on the sensitivity analysis of inefficient DMUs. As said before, after determining the inefficient units in the society under study, it is needed, in some scientific subjects, that all of these units have at least the efficiency score of αα. (αα is a constant number smaller than 1 which is defined by the manager.)
As an example, suppose that people who are working in different places such as schools, universities, hospitals, banks, companies and etc., have a score efficiency.
Sometimes, we need, by paying attention to the occupation sensitivity, that all staffs must have at least a score of αα. Obviously, those people with an efficiency score less than the least, should come up with the level by themselves.
This paper develops a procedure for performing a sensitivity analysis of the inefficient decision making units (DMUs). The procedure yields an exact “Necessary Change Region” which the efficiency score of a specific inefficient DMU changes to a defined efficiency score.
The proposed method has some advantages and disadvantages. The most important problem of this method is that, possibly, for every inefficient unit, according to the nature of the problem, a “Necessary Change Region” would not be achieved explicitly.
Moreover, we suppose the (AP) model for all points of View the MathML sourceDMUj(j=1,…,n) to be feasible. Otherwise, other models that are always feasible can be used, e.g. L1L1 norm [19].
As an advantage, making changes for all strategies to improve the performance of inefficient unit is not usually possible. For instance, sometimes, a change in strategy in input (input decreasing) or a change in output (output increasing) or simultaneous changes in input and output (input decreasing and output increasing [20]) is impossible. But the proposed method is valuable because of reaching new efficient frontiers by examining different strategies (those frontiers which have an αα level of efficiency).
