범주형 환경변수를 고려한 공정한 효율성측정: DEA와 제약정준상관분석의 결합사용

Efficiency performance or productivity analyses are vital management tools for assessing the extent to which inputs are utilized in the process of achieving desired outputs. There are two distinct approaches to efficiency valuations. One is the parametric approach based on multiple regression, often used in econometric studies, and the other is the nonparametric approach known as data envelopment analysis (DEA). The parametric approach provides a convenient formula relating output to inputs, upon which a single efficient frontier can be based, but is not based on a clearly identified set of efficient units. In sharp contrast, DEA clearly identifies the efficient units and easily incorporates multiple inputs and outputs, but it does not provide a single formula to model the efficient frontier and it suffers from the problems associated with slacks and ranking units. This paper is concerned with a hybrid approach which not only brings together the positive aspects of the two methods but also avoids their drawbacks. The overall process of hybrid approach can be outlined as, first, applying DEA for selecting the efficient units and, second, utilizing constrained canonical correlation analysis (CCCA) for constructing an efficient frontier with the efficient units only. The CCCA is an extension of CCA, a technique for finding linear (or nonlinear) combinations of two sets of input and output variables such that the correlation between these two combined variables is maximized. As a constrained optimization model, the CCCA can avoid an underlying problem of CCA that negative weights may arise. It is noted that there has been a similar hybrid approach, a joint use of DEA and CCCA, to efficiency valuations. However, the existing approach does not consider any categorical variable that often reflects an environmental effect on efficiency performance. Categorical variables are such that some branches of a bank may have a drive-in capability and some others may not, some branches may have automatic tellers while some may not, or branches are rated in terms of their operating situations as “good” or “bad.” The main purpose of this paper is to study how to treat such categorical variables in the framework of the hybrid approach. As illustrated by a managerial performance evaluation problem for the branches of a fast-food company in Korea, the need arises to consider a categorical variable for an equitable efficiency valuation, since the location of branches, “commercial area” or “noncommercial area,” significantly affects their performances. Specifically, a particular branch can be evaluated much more favorably by virtue of its advantageous location (commercial area) only, which is problematic. Therefore, the issue of rising importance in the treatment of categorical variable in the hybrid approach becomes whether we incorporate the categorical variable in the DEA stage, via employing categorical variable DEA, or in the CCCA stage, via introducing a dummy variable. This study compares two possible ways and, as a result, suggests that the way of incorporating the categorical variable in the CCCA stage yields a reasonable result and becomes efficacious in terms of penalizing the advantageous location effect and compensating the disadvantageous location effect. All the comparative analysis is made with the real data from 72 branches of a fast-food company in Korea.