Characterization of DEA ranking models

Choi, Sung-Kyun
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Other than measuring relative efficiency, DEA (Data Envelopment Analysis) has been used in a number of other ways to elaborate further on the performance of individual units. Also researchers have developed methods for using DEA as a ranking model. We classified DEA ranking models into two categories based on whether preferences (weights) are given or not.;Since the ranking result from each model is determined by the characteristics each model has, it is important to understand these characteristics. This hopefully can help decision makers to make a better decision. In this dissertation, we analyze the characteristics of A-P (Andersen-Peterson) model and cross-efficiency evaluation in category 1, and cone-ratio and Wong and Beasley weight restrictions in category 2. Alternative models for measuring overall efficiency are proposed.;To better characterize ranking models, we define a new metric, the specialization index (SI), and propose using the Ak score in cross-efficiency evaluation to identify specialized DMUs. Also we examine the popular characterization on the 1st ranker of cross-efficiency evaluation and show that it is not always true. The fixed weighting nature of cross-efficiency evaluation is analyzed in the multiple-input, multiple-output situation analytically and empirically. Biplots are proposed as a method for comparing the characteristics of model with multiple inputs and/or outputs visually.;On the characteristics of cone-ratio weight restrictions, we suggest two properties (P1) and (P2). Property (P1) shows a way to measure the efficiency score when cone-ratio weight restrictions are applied under constant returns to scale with single-input, multiple-outputs. Based on this property, we propose some graphical explanations of other DEA issues.;We investigate the characteristics of Wong and Beasley weight restrictions and compare both their theoretical implications and empirical behavior with those of cone-ratio weight restrictions. We show that under Wong and Beasley weight restrictions, each DMU takes all different weight vectors and some DMUs may have limiting efficiency score.;Finally, we present alternative models for measuring each of overall efficiency (OE) with cone-ratio weight restrictions and compare with previous models using examples.

Industrial and manufacturing systems engineering, Industrial engineering