Abstract
Data envelopment analysis (DEA) as a nonparametric programming approach has been widely extended and applied in many areas. Conventional DEA models can well measure the efficiency of inefficient decision-making units (DMUs) but cannot further discriminate the efficient DMUs. A lot of methods are proposed to address this problem. One of the most important methods is the slacks-based measure of super-efficiency model (S-SBM model) developed by Tone in 2002. However, the projection for a DMU on the efficient frontier identified by S-SBM model may not be strongly Pareto-efficient that makes the super-efficiency score misestimated. This paper revises the usual slacks-based measure of super-efficiency by incorporating input saving and output surplus scaling factors into the objection function for measuring DMUs. We integrate SBM model and S-SBM model effectively and yield input saving and output surplus scaling factors as well as input and output slacks under only one integrated model. According to the study, the projection reference point identified by our method is strongly Pareto-efficient. Meanwhile, how each decision variable influences the efficiency score for a specific DMU is revealed and illustrated through two numerical examples and an empirical study in paper chemical mills.
Highlights
Over the past several decades, the data envelopment analysis (DEA) initially proposed by Charnes et al has proved to be an effective data-oriented programming method for measuring the efficiencies of a group of homogenous decision making units (DMUs) [1]. e technique of DEA depicts a best-practice production efficient frontier formed by observed DMUs and provides a benchmark or reference point on this frontier for each DMU to compute its efficiency score
In the recent years, DEA has been widely extended and applied in many fields [2]. e efficiency value obtained by the classic CCR model indicates how efficiently a DMU has performed when compared with other DMUs so as to determine its efficient level within the group of all DMUs. e CCR model works as a radial model and has both input- and output-orientation styles which permits the DMU under assessment to proportionally reduce all its inputs for producing its given outputs, or to proportionally expand all its outputs by using its given inputs
Conclusions and Remarks e classic slacksbased measure (SBM) model proposed by Tone projects the DMU under evaluation at a Pareto-efficient reference point on the production frontier, while the S-SBM model proposed by Tone may not apply and the reference point on the superefficiency frontier by S-SBM model may not be Pareto-efficient
Summary
Over the past several decades, the data envelopment analysis (DEA) initially proposed by Charnes et al has proved to be an effective data-oriented programming method for measuring the efficiencies of a group of homogenous decision making units (DMUs) [1]. e technique of DEA depicts a best-practice production efficient frontier formed by observed DMUs and provides a benchmark or reference point on this frontier for each DMU to compute its efficiency score. It fails to represent all input saving and output surplus scaling factors explicitly for each DMU. E current paper further investigates this topic and presents a modified slacks-based measure of super-efficiency with input saving and output surplus scaling factors to reevaluate these DMUs. Our approach is devoted to detecting the specific scaling factors for each input and output as well as input and output slacks explicitly by one integrated model. E results indicate that the projection obtained through our proposed model is strongly Paretoefficient In this approach, we can see clearly how each decision variable influences the final efficiency score for a specific DMU.
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