データ包絡分析法による写像法の提案と技術的傾向・類似度の評価

概要

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In this paper, a new mapping method with Data Envelopment Analysis (DEA) is proposed. The objective of the mapping with DEA is to grasp the similarities among the Decision Making Units (DMUs). In order to grasp the similarities among the DMUs, a critical line should be determined. The critical line is automatically generated by the proposed method. In the proposed method, the Extended CCR model is employed at first. Each DMU is mapped onto the efficient frontier generated. As the efficient frontier by the Extended CCR model is different from each DMU, non-smooth critical line can be obtained. To obtain a smooth critical line, an objective function of the Lagrange multipliers is minimized. All DMUs are mapped onto this smooth critical line, and the similarities can be evaluated. DEA can handle multiple inputs/outputs, however it is difficult to grasp the similarities among the DMUs. To grasp the similarities, Principal Component Analysis (PCA) is applied for the visualization. When time series data is used, it is also possible to grasp both the similarities and the technical trends. In order to show the effectiveness of the proposed method, automobile data from 1995, 1999 and 2002 are used. It is easy to grasp both the similarities and the technical trends from the results.