In this paper, we will propose a Slacks-Based measure (SBM) of efficiency in DEA. This scalar measure deals directly with the input surplus and the output shortage of the decision making unit (DMU) concerned. It is unit invariant and monotone decreasing with respect to input surplus and output shortage. Furthermore, this measure is decided only by consulting with the reference set of the DMU and is not affected by statistics over the whole data set. The new measure has a close connection with other measures proposed so far, e.g., CCR and BCC. The dual side of this model can be interpreted as profit maximization, in contrast to the ratio maximization of the CCR model. Numerical experiments show its validity as an efficiency measurement tool and its compatibility with other measures of efficiency.

No abstract

Traditional DEA models deal with measurements of relative efficiency of DMUs regarding multiple-inputs vs. multiple-outputs. One of the drawbacks of these models is the neglect of intermediate products or linking activities. After pointing out needs for inclusion of them in DEA models, we propose a slacks-based network DEA model that can deal with intermediate products. Using this model we can evaluate divisional efficiencies along with the overall efficiency of decision making units (DMUs).

In data envelopment analysis, there are several methods for measuring efficiency change over time, e.g. the window analysis and the Malmquist index. However, they usually neglect carry-over activities between consecutive two terms. These carry-overs play an important role in measuring the efficiency of decision making units in each term as well as over the whole terms based on the long-term viewpoint. Dynamic DEA model proposed by Färe and Grosskopf is the first innovative contribution for such purpose. In this paper we develop their model in the slacks-based measure (SBM) framework, called Dynamic SBM (DSBM). The SBM model is non-radial and can deal with inputs/outputs individually, contrary to the radial approaches that assume proportional changes in inputs/outputs. Furthermore, according to the characteristics of carry-overs, we classify them into four categories, i.e. desirable, undesirable, free and fixed. Desirable carry-overs correspond, for example, to profit carried forward and net earned surplus carried to the next term, while undesirable carry-overs include, for example, loss carried forward, bad debt and dead stock. Free and fixed carry-overs indicate, respectively, discretionary and non-discretionary ones. We develop Dynamic SBM models that can evaluate the overall efficiency of decision making units for the whole terms as well as the term efficiencies.

No abstract

Abstract:We propose a dynamic DEA model involving network structure in each period within the framework of a slacks-based measure approach. We have previously published the network SBM (NSBM) and the dynamic SBM (DSBM) models separately. Hence, this article is a composite of these two models. Vertically, we deal with multiple divisions connected by links of network structure within each period and, horizontally, we combine the network structure by means of carry-over activities between two succeeding periods. This model can evaluate (1) the overall efficiency over the entire observed period, (2) dynamic change of period efficiency and (3) dynamic change of divisional efficiency. In addition, we also introduce dynamic Malmquist index by which we can compare divisional performances over time. We applied this model to a dataset of US electric utilities and compared the result with that of DSBM.

No abstract

Data Envelopment Analysis (DEA) is a decision making tool based on linear programming for measuring the relative efficiency of a set of comparable units. Besides the identification of relatively efficient and inefficient units, DEA identifies the sources and level of inefficiency for each of the inputs and outputs. This paper is a survey of the basic DEA models. A comparison of DEA models is given. The effect of model orientation (input or output) on the efficiency frontier and the effect of the convexity requirements on returns to scale are examined. The paper also explains how DEA models can be used to assess efficiency.