Classifying Inputs and Outputs in Data Envelopment Analysis Based on TOPSIS Method and a Voting Model

Introduction

Data Envelopment Analysis (DEA) was initiated in 1978 when Charnes, Cooper and Rhodes (CCR) demonstrated how to change a fractional linear measure of efficiency into a linear programming (LP) format (Charnes, 1978). DEA provides a relative efficiency measure for peer decision making units (DMUs) with multiple inputs and outputs. Recent years have seen a great variety of applications of DEA. Applications of DEA in hospitals, banks, and maintenance crews can be seen in Cooper’s studies (Cooper, Seiford & Zhu, 2004).

In the conventional application of DEA, it is assumed that the status of performance measures is specified from the input or output point of view. However, in some situations there are variables or measures that are treated as both inputs and outputs, and finding their appropriate status is very difficult. These measures have been called “flexible measures” by Cook and Zhu (2007).

For example, consider the performance evaluation of bank branch operations, as discussed in Cook and Hababou (2001) and Cook et al. (2000). In this study, the output variables are standard counter transactions such as deposits and withdrawals, and the input variables are resources such as various staff types. In evaluating the performance of each bank branch to attract investments, a measure such as the number of high-value customers is treated as both an input and an output. From one viewpoint, this factor is considered as a proxy for future investment, and hence can be classified as an output. Also, it can be considered an input that aids the branch in generating its existing investment portfolio. Such discussion can be put forward, as well, for measures such as deposits. Examples of flexible measures in evaluating performance of universities, hospitals and highway maintenance crew can be seen in (Cook & Zhu, 2007). Cook and Zhu (2007), proposed a DEA model for classifying the status of flexible measures and evaluating the performance of DMUs. Toloo (2009) showed that using Cook and Zhu’s model may produce incorrect efficiency scores in some cases, due to a computational problem as a result of introducing a large positive number to the model. He also introduced a revised model to tackle the computational problem in Cook and Zhu’s model. Hatefi and Jolai(2009) also established a new model based on the translog output distance function for classifying variable status from the input or output point of view and evaluating the performance of decision making units. Their paper preferred the translog output distance function over the Cobb-Douglas production function to establish the model because it considers microeconomic properties. They showed that the Cobb-Douglas form is not an acceptable model of a firm in a purely competitive industry. They used Monte Carlo simulation produced for two-input two-output production data. Their proposed model is validated from the viewpoint of classifying the status of flexible measures and evaluating performance of DMUs in comparison with Cook and Zhu’s model.

The interesting results obtained in their paper are as follows:

• 1.

  Hatefi and Jolai’s model correctly classified flexible measures in all DMUs while Cook and Zhu’s model correctly classified flexible measures in most DMUs;

• 2.

  Measure efficiencies calculated by Hatefi and Jolai’s model are statistically and significantly closer to true efficiencies;

• 3.

  Measure efficiencies obtained by Hatefi and Jolai’s model have higher correlation with true efficiencies than those by Cook and Zhu’s model;

• 4.

  Also, there is a high rank correlation between efficiencies obtained by Hatefi and Jolai’s model and Cook and Zhu’s model.

In this paper, we assume that a problem has a flexible measure. Next, we specify the input versus output status of this measure using TOPSIS method and also a voting model. The proposed method is then illustrated by an example.